hypothesis testing in business research

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A Beginner’s Guide to Hypothesis Testing in Business

• 30 Mar 2021

Becoming a more data-driven decision-maker can bring several benefits to your organization, enabling you to identify new opportunities to pursue and threats to abate. Rather than allowing subjective thinking to guide your business strategy, backing your decisions with data can empower your company to become more innovative and, ultimately, profitable.

If you’re new to data-driven decision-making, you might be wondering how data translates into business strategy. The answer lies in generating a hypothesis and verifying or rejecting it based on what various forms of data tell you.

Below is a look at hypothesis testing and the role it plays in helping businesses become more data-driven.

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What Is Hypothesis Testing?

To understand what hypothesis testing is, it’s important first to understand what a hypothesis is.

A hypothesis or hypothesis statement seeks to explain why something has happened, or what might happen, under certain conditions. It can also be used to understand how different variables relate to each other. Hypotheses are often written as if-then statements; for example, “If this happens, then this will happen.”

Hypothesis testing , then, is a statistical means of testing an assumption stated in a hypothesis. While the specific methodology leveraged depends on the nature of the hypothesis and data available, hypothesis testing typically uses sample data to extrapolate insights about a larger population.

Hypothesis Testing in Business

When it comes to data-driven decision-making, there’s a certain amount of risk that can mislead a professional. This could be due to flawed thinking or observations, incomplete or inaccurate data , or the presence of unknown variables. The danger in this is that, if major strategic decisions are made based on flawed insights, it can lead to wasted resources, missed opportunities, and catastrophic outcomes.

The real value of hypothesis testing in business is that it allows professionals to test their theories and assumptions before putting them into action. This essentially allows an organization to verify its analysis is correct before committing resources to implement a broader strategy.

As one example, consider a company that wishes to launch a new marketing campaign to revitalize sales during a slow period. Doing so could be an incredibly expensive endeavor, depending on the campaign’s size and complexity. The company, therefore, may wish to test the campaign on a smaller scale to understand how it will perform.

In this example, the hypothesis that’s being tested would fall along the lines of: “If the company launches a new marketing campaign, then it will translate into an increase in sales.” It may even be possible to quantify how much of a lift in sales the company expects to see from the effort. Pending the results of the pilot campaign, the business would then know whether it makes sense to roll it out more broadly.

Related: 9 Fundamental Data Science Skills for Business Professionals

Key Considerations for Hypothesis Testing

1. alternative hypothesis and null hypothesis.

In hypothesis testing, the hypothesis that’s being tested is known as the alternative hypothesis . Often, it’s expressed as a correlation or statistical relationship between variables. The null hypothesis , on the other hand, is a statement that’s meant to show there’s no statistical relationship between the variables being tested. It’s typically the exact opposite of whatever is stated in the alternative hypothesis.

For example, consider a company’s leadership team that historically and reliably sees $12 million in monthly revenue. They want to understand if reducing the price of their services will attract more customers and, in turn, increase revenue.

In this case, the alternative hypothesis may take the form of a statement such as: “If we reduce the price of our flagship service by five percent, then we’ll see an increase in sales and realize revenues greater than $12 million in the next month.”

The null hypothesis, on the other hand, would indicate that revenues wouldn’t increase from the base of $12 million, or might even decrease.

Check out the video below about the difference between an alternative and a null hypothesis, and subscribe to our YouTube channel for more explainer content.

2. Significance Level and P-Value

Statistically speaking, if you were to run the same scenario 100 times, you’d likely receive somewhat different results each time. If you were to plot these results in a distribution plot, you’d see the most likely outcome is at the tallest point in the graph, with less likely outcomes falling to the right and left of that point.

With this in mind, imagine you’ve completed your hypothesis test and have your results, which indicate there may be a correlation between the variables you were testing. To understand your results' significance, you’ll need to identify a p-value for the test, which helps note how confident you are in the test results.

In statistics, the p-value depicts the probability that, assuming the null hypothesis is correct, you might still observe results that are at least as extreme as the results of your hypothesis test. The smaller the p-value, the more likely the alternative hypothesis is correct, and the greater the significance of your results.

3. One-Sided vs. Two-Sided Testing

When it’s time to test your hypothesis, it’s important to leverage the correct testing method. The two most common hypothesis testing methods are one-sided and two-sided tests , or one-tailed and two-tailed tests, respectively.

Typically, you’d leverage a one-sided test when you have a strong conviction about the direction of change you expect to see due to your hypothesis test. You’d leverage a two-sided test when you’re less confident in the direction of change.

4. Sampling

To perform hypothesis testing in the first place, you need to collect a sample of data to be analyzed. Depending on the question you’re seeking to answer or investigate, you might collect samples through surveys, observational studies, or experiments.

A survey involves asking a series of questions to a random population sample and recording self-reported responses.

Observational studies involve a researcher observing a sample population and collecting data as it occurs naturally, without intervention.

Finally, an experiment involves dividing a sample into multiple groups, one of which acts as the control group. For each non-control group, the variable being studied is manipulated to determine how the data collected differs from that of the control group.

Learn How to Perform Hypothesis Testing

Hypothesis testing is a complex process involving different moving pieces that can allow an organization to effectively leverage its data and inform strategic decisions.

If you’re interested in better understanding hypothesis testing and the role it can play within your organization, one option is to complete a course that focuses on the process. Doing so can lay the statistical and analytical foundation you need to succeed.

Do you want to learn more about hypothesis testing? Explore Business Analytics —one of our online business essentials courses —and download our Beginner’s Guide to Data & Analytics .

About the Author

• Hypothesis Testing: Definition, Uses, Limitations + Examples

Hypothesis testing is as old as the scientific method and is at the heart of the research process. 

Research exists to validate or disprove assumptions about various phenomena. The process of validation involves testing and it is in this context that we will explore hypothesis testing. 

What is a Hypothesis? 

A hypothesis is a calculated prediction or assumption about a population parameter based on limited evidence. The whole idea behind hypothesis formulation is testing—this means the researcher subjects his or her calculated assumption to a series of evaluations to know whether they are true or false. 

Typically, every research starts with a hypothesis—the investigator makes a claim and experiments to prove that this claim is true or false . For instance, if you predict that students who drink milk before class perform better than those who don’t, then this becomes a hypothesis that can be confirmed or refuted using an experiment.  

Read: What is Empirical Research Study? [Examples & Method]

What are the Types of Hypotheses? 

1. simple hypothesis.

Also known as a basic hypothesis, a simple hypothesis suggests that an independent variable is responsible for a corresponding dependent variable. In other words, an occurrence of the independent variable inevitably leads to an occurrence of the dependent variable. 

Typically, simple hypotheses are considered as generally true, and they establish a causal relationship between two variables. 

Examples of Simple Hypothesis  

• Drinking soda and other sugary drinks can cause obesity. 
• Smoking cigarettes daily leads to lung cancer.

2. Complex Hypothesis

A complex hypothesis is also known as a modal. It accounts for the causal relationship between two independent variables and the resulting dependent variables. This means that the combination of the independent variables leads to the occurrence of the dependent variables . 

Examples of Complex Hypotheses  

• Adults who do not smoke and drink are less likely to develop liver-related conditions.
• Global warming causes icebergs to melt which in turn causes major changes in weather patterns.

3. Null Hypothesis

As the name suggests, a null hypothesis is formed when a researcher suspects that there’s no relationship between the variables in an observation. In this case, the purpose of the research is to approve or disapprove this assumption. 

Examples of Null Hypothesis

• This is no significant change in a student’s performance if they drink coffee or tea before classes. 
• There’s no significant change in the growth of a plant if one uses distilled water only or vitamin-rich water. 

Read: Research Report: Definition, Types + [Writing Guide]

4. Alternative Hypothesis 

To disapprove a null hypothesis, the researcher has to come up with an opposite assumption—this assumption is known as the alternative hypothesis. This means if the null hypothesis says that A is false, the alternative hypothesis assumes that A is true. 

An alternative hypothesis can be directional or non-directional depending on the direction of the difference. A directional alternative hypothesis specifies the direction of the tested relationship, stating that one variable is predicted to be larger or smaller than the null value while a non-directional hypothesis only validates the existence of a difference without stating its direction. 

Examples of Alternative Hypotheses  

• Starting your day with a cup of tea instead of a cup of coffee can make you more alert in the morning. 
• The growth of a plant improves significantly when it receives distilled water instead of vitamin-rich water. 

5. Logical Hypothesis

Logical hypotheses are some of the most common types of calculated assumptions in systematic investigations. It is an attempt to use your reasoning to connect different pieces in research and build a theory using little evidence. In this case, the researcher uses any data available to him, to form a plausible assumption that can be tested. 

Examples of Logical Hypothesis

• Waking up early helps you to have a more productive day. 
• Beings from Mars would not be able to breathe the air in the atmosphere of the Earth. 

6. Empirical Hypothesis  

After forming a logical hypothesis, the next step is to create an empirical or working hypothesis. At this stage, your logical hypothesis undergoes systematic testing to prove or disprove the assumption. An empirical hypothesis is subject to several variables that can trigger changes and lead to specific outcomes. 

Examples of Empirical Testing 

• People who eat more fish run faster than people who eat meat.
• Women taking vitamin E grow hair faster than those taking vitamin K.

7. Statistical Hypothesis

When forming a statistical hypothesis, the researcher examines the portion of a population of interest and makes a calculated assumption based on the data from this sample. A statistical hypothesis is most common with systematic investigations involving a large target audience. Here, it’s impossible to collect responses from every member of the population so you have to depend on data from your sample and extrapolate the results to the wider population. 

Examples of Statistical Hypothesis  

• 45% of students in Louisiana have middle-income parents. 
• 80% of the UK’s population gets a divorce because of irreconcilable differences.

What is Hypothesis Testing? 

Hypothesis testing is an assessment method that allows researchers to determine the plausibility of a hypothesis. It involves testing an assumption about a specific population parameter to know whether it’s true or false. These population parameters include variance, standard deviation, and median. 

Typically, hypothesis testing starts with developing a null hypothesis and then performing several tests that support or reject the null hypothesis. The researcher uses test statistics to compare the association or relationship between two or more variables. 

Explore: Research Bias: Definition, Types + Examples

Researchers also use hypothesis testing to calculate the coefficient of variation and determine if the regression relationship and the correlation coefficient are statistically significant.

How Hypothesis Testing Works

The basis of hypothesis testing is to examine and analyze the null hypothesis and alternative hypothesis to know which one is the most plausible assumption. Since both assumptions are mutually exclusive, only one can be true. In other words, the occurrence of a null hypothesis destroys the chances of the alternative coming to life, and vice-versa. 

Interesting: 21 Chrome Extensions for Academic Researchers in 2021

What Are The Stages of Hypothesis Testing?  

To successfully confirm or refute an assumption, the researcher goes through five (5) stages of hypothesis testing; 

• Determine the null hypothesis
• Specify the alternative hypothesis
• Set the significance level
• Calculate the test statistics and corresponding P-value
• Draw your conclusion
• Determine the Null Hypothesis

Like we mentioned earlier, hypothesis testing starts with creating a null hypothesis which stands as an assumption that a certain statement is false or implausible. For example, the null hypothesis (H0) could suggest that different subgroups in the research population react to a variable in the same way. 

• Specify the Alternative Hypothesis

Once you know the variables for the null hypothesis, the next step is to determine the alternative hypothesis. The alternative hypothesis counters the null assumption by suggesting the statement or assertion is true. Depending on the purpose of your research, the alternative hypothesis can be one-sided or two-sided. 

Using the example we established earlier, the alternative hypothesis may argue that the different sub-groups react differently to the same variable based on several internal and external factors. 

• Set the Significance Level

Many researchers create a 5% allowance for accepting the value of an alternative hypothesis, even if the value is untrue. This means that there is a 0.05 chance that one would go with the value of the alternative hypothesis, despite the truth of the null hypothesis. 

Something to note here is that the smaller the significance level, the greater the burden of proof needed to reject the null hypothesis and support the alternative hypothesis.

Explore: What is Data Interpretation? + [Types, Method & Tools]

• Calculate the Test Statistics and Corresponding P-Value 

Test statistics in hypothesis testing allow you to compare different groups between variables while the p-value accounts for the probability of obtaining sample statistics if your null hypothesis is true. In this case, your test statistics can be the mean, median and similar parameters. 

If your p-value is 0.65, for example, then it means that the variable in your hypothesis will happen 65 in100 times by pure chance. Use this formula to determine the p-value for your data: 

• Draw Your Conclusions

After conducting a series of tests, you should be able to agree or refute the hypothesis based on feedback and insights from your sample data.  

Applications of Hypothesis Testing in Research

Hypothesis testing isn’t only confined to numbers and calculations; it also has several real-life applications in business, manufacturing, advertising, and medicine. 

In a factory or other manufacturing plants, hypothesis testing is an important part of quality and production control before the final products are approved and sent out to the consumer. 

During ideation and strategy development, C-level executives use hypothesis testing to evaluate their theories and assumptions before any form of implementation. For example, they could leverage hypothesis testing to determine whether or not some new advertising campaign, marketing technique, etc. causes increased sales. 

In addition, hypothesis testing is used during clinical trials to prove the efficacy of a drug or new medical method before its approval for widespread human usage. 

What is an Example of Hypothesis Testing?

An employer claims that her workers are of above-average intelligence. She takes a random sample of 20 of them and gets the following results: 

Mean IQ Scores: 110

Standard Deviation: 15 

Mean Population IQ: 100

Step 1: Using the value of the mean population IQ, we establish the null hypothesis as 100.

Step 2: State that the alternative hypothesis is greater than 100.

Step 3: State the alpha level as 0.05 or 5% 

Step 4: Find the rejection region area (given by your alpha level above) from the z-table. An area of .05 is equal to a z-score of 1.645.

Step 5: Calculate the test statistics using this formula

Z = (110–100) ÷ (15÷√20) 

10 ÷ 3.35 = 2.99 

If the value of the test statistics is higher than the value of the rejection region, then you should reject the null hypothesis. If it is less, then you cannot reject the null. 

In this case, 2.99 > 1.645 so we reject the null. 

Importance/Benefits of Hypothesis Testing 

The most significant benefit of hypothesis testing is it allows you to evaluate the strength of your claim or assumption before implementing it in your data set. Also, hypothesis testing is the only valid method to prove that something “is or is not”. Other benefits include: 

• Hypothesis testing provides a reliable framework for making any data decisions for your population of interest. 
• It helps the researcher to successfully extrapolate data from the sample to the larger population. 
• Hypothesis testing allows the researcher to determine whether the data from the sample is statistically significant. 
• Hypothesis testing is one of the most important processes for measuring the validity and reliability of outcomes in any systematic investigation. 
• It helps to provide links to the underlying theory and specific research questions.

Criticism and Limitations of Hypothesis Testing

Several limitations of hypothesis testing can affect the quality of data you get from this process. Some of these limitations include: 

• The interpretation of a p-value for observation depends on the stopping rule and definition of multiple comparisons. This makes it difficult to calculate since the stopping rule is subject to numerous interpretations, plus “multiple comparisons” are unavoidably ambiguous. 
• Conceptual issues often arise in hypothesis testing, especially if the researcher merges Fisher and Neyman-Pearson’s methods which are conceptually distinct. 
• In an attempt to focus on the statistical significance of the data, the researcher might ignore the estimation and confirmation by repeated experiments.
• Hypothesis testing can trigger publication bias, especially when it requires statistical significance as a criterion for publication.
• When used to detect whether a difference exists between groups, hypothesis testing can trigger absurd assumptions that affect the reliability of your observation.

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• alternative hypothesis
• alternative vs null hypothesis
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Article contents

Hypothesis testing in business administration.

• Rand R. Wilcox Rand R. Wilcox Department of Psychology, University of Southern California
• https://doi.org/10.1093/acrefore/9780190224851.013.279
• Published online: 27 August 2020

Hypothesis testing is an approach to statistical inference that is routinely taught and used. It is based on a simple idea: develop some relevant speculation about the population of individuals or things under study and determine whether data provide reasonably strong empirical evidence that the hypothesis is wrong. Consider, for example, two approaches to advertising a product. A study might be conducted to determine whether it is reasonable to assume that both approaches are equally effective. A Type I error is rejecting this speculation when in fact it is true. A Type II error is failing to reject when the speculation is false. A common practice is to test hypotheses with the type I error probability set to 0.05 and to declare that there is a statistically significant result if the hypothesis is rejected.

There are various concerns about, limitations to, and criticisms of this approach. One criticism is the use of the term significant . Consider the goal of comparing the means of two populations of individuals. Saying that a result is significant suggests that the difference between the means is large and important. But in the context of hypothesis testing it merely means that there is empirical evidence that the means are not equal. Situations can and do arise where a result is declared significant, but the difference between the means is trivial and unimportant. Indeed, the goal of testing the hypothesis that two means are equal has been criticized based on the argument that surely the means differ at some decimal place. A simple way of dealing with this issue is to reformulate the goal. Rather than testing for equality, determine whether it is reasonable to make a decision about which group has the larger mean. The components of hypothesis-testing techniques can be used to address this issue with the understanding that the goal of testing some hypothesis has been replaced by the goal of determining whether a decision can be made about which group has the larger mean.

Another aspect of hypothesis testing that has seen considerable criticism is the notion of a p -value. Suppose some hypothesis is rejected with the Type I error probability set to 0.05. This leaves open the issue of whether the hypothesis would be rejected with Type I error probability set to 0.025 or 0.01. A p -value is the smallest Type I error probability for which the hypothesis is rejected. When comparing means, a p -value reflects the strength of the empirical evidence that a decision can be made about which has the larger mean. A concern about p -values is that they are often misinterpreted. For example, a small p -value does not necessarily mean that a large or important difference exists. Another common mistake is to conclude that if the p -value is close to zero, there is a high probability of rejecting the hypothesis again if the study is replicated. The probability of rejecting again is a function of the extent that the hypothesis is not true, among other things. Because a p -value does not directly reflect the extent the hypothesis is false, it does not provide a good indication of whether a second study will provide evidence to reject it.

Confidence intervals are closely related to hypothesis-testing methods. Basically, they are intervals that contain unknown quantities with some specified probability. For example, a goal might be to compute an interval that contains the difference between two population means with probability 0.95. Confidence intervals can be used to determine whether some hypothesis should be rejected. Clearly, confidence intervals provide useful information not provided by testing hypotheses and computing a p -value. But an argument for a p -value is that it provides a perspective on the strength of the empirical evidence that a decision can be made about the relative magnitude of the parameters of interest. For example, to what extent is it reasonable to decide whether the first of two groups has the larger mean? Even if a compelling argument can be made that p -values should be completely abandoned in favor of confidence intervals, there are situations where p -values provide a convenient way of developing reasonably accurate confidence intervals. Another argument against p -values is that because they are misinterpreted by some, they should not be used. But if this argument is accepted, it follows that confidence intervals should be abandoned because they are often misinterpreted as well.

Classic hypothesis-testing methods for comparing means and studying associations assume sampling is from a normal distribution. A fundamental issue is whether nonnormality can be a source of practical concern. Based on hundreds of papers published during the last 50 years, the answer is an unequivocal Yes. Granted, there are situations where nonnormality is not a practical concern, but nonnormality can have a substantial negative impact on both Type I and Type II errors. Fortunately, there is a vast literature describing how to deal with known concerns. Results based solely on some hypothesis-testing approach have clear implications about methods aimed at computing confidence intervals. Nonnormal distributions that tend to generate outliers are one source for concern. There are effective methods for dealing with outliers, but technically sound techniques are not obvious based on standard training. Skewed distributions are another concern. The combination of what are called bootstrap methods and robust estimators provides techniques that are particularly effective for dealing with nonnormality and outliers.

Classic methods for comparing means and studying associations also assume homoscedasticity. When comparing means, this means that groups are assumed to have the same amount of variance even when the means of the groups differ. Violating this assumption can have serious negative consequences in terms of both Type I and Type II errors, particularly when the normality assumption is violated as well. There is vast literature describing how to deal with this issue in a technically sound manner.

• hypothesis testing
• significance
• confidence intervals
• nonnormality
• bootstrap methods
• robust estimators

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Hypothesis Testing in Business Analytics – A Beginner’s Guide

Introduction  

Organizations must understand how their decisions can impact the business in this data-driven age. Hypothesis testing enables organizations to analyze and examine their decisions’ causes and effects before making important management decisions. Based on research by the Harvard Business School Online, prior to making any decision, organizations like to explore the advantages of hypothesis testing and the investigation of decisions in a proper “laboratory” setting. By performing such tests, organizations can be more confident with their decisions. Read on to learn all about hypothesis testing , o ne of the essential concepts in Business Analytics.  

What Is Hypothesis Testing?  

To learn about hypothesis testing, it is crucial that you first understand what the term hypothesis is.   

A hypothesis statement or hypothesis tries to explain why something happened or what may happen under specific conditions. A hypothesis can also help understand how various variables are connected to each other. These are generally compiled as if-then statements; for example, “If something specific were to happen, then a specific condition will come true and vice versa.” Thus, the hypothesis is an arithmetical method of testing a hypothesis or an assumption that has been stated in the hypothesis.  

Turning into a decision-maker who is driven by data can add several advantages to an organization, such as allowing one to recognize new opportunities to follow and reducing the number of threats. In analytics, a hypothesis is nothing but an assumption or a supposition made about a specific population parameter, such as any measurement or quantity about the population that is set and that can be used as a value to the distribution variable. General examples of parameters used in hypothesis testing are variance and mean. In simpler words, hypothesis testing in business analytics is a method that helps researchers, scientists, or anyone for that matter, test the legitimacy or the authenticity of their hypotheses or claims about real-life or real-world events.  

To understand the example of hypothesis testing in business analytics, consider a restaurant owner interested in learning how adding extra house sauce to their chicken burgers can impact customer satisfaction. Or, you could also consider a social media marketing organization. A hypothesis test can be set up to explain how an increase in labor impacts productivity. Thus, hypothesis testing aims to discover the connection between two or more than two variables in the experimental setting.  

How Does Hypothesis Testing Work?  

Generally, each research begins with a hypothesis; the investigator makes a certain claim and experiments to prove that the claim is false or true. For example, if you claim that students drinking milk before class accomplish tasks better than those who do not, then this is a kind of hypothesis that can be refuted or confirmed using an experiment. There are different kinds of hypotheses. They are:  

• Simple Hypothesis : Simple hypothesis, also known as a basic hypothesis, proposes that an independent variable is accountable for the corresponding dependent variable. In simpler words, the occurrence of independent variable results in the existence of the dependent variable. Generally, simple hypotheses are thought of as true and they create a causal relationship between the two variables. One example of a simple hypothesis is smoking cigarettes daily leads to cancer.  
• Complex Hypothesis : This type of hypothesis is also termed a modal. It holds for the relationship between two variables that are independent and result in a dependent variable. This means that the amalgamation of independent variables results in the dependent variables. An example of this kind of hypothesis can be “adults who don’t drink and smoke are less likely to have liver-related problems.  
• Null Hypothesis : A null hypothesis is created when a researcher thinks that there is no connection between the variables that are being observed. An example of this kind of hypothesis can be “A student’s performance is not impacted if they drink tea or coffee before classes.  
• Alternative Hypothesis : If a researcher wants to disapprove of a null hypothesis, then the researcher has to develop an opposite assumption—known as an alternative hypothesis. For example, beginning your day with tea instead of coffee can keep you more alert.  
• Logical Hypothesis: A proposed explanation supported by scant data is called a logical hypothesis. Generally, you wish to test your hypotheses or postulations by converting a logical hypothesis into an empirical hypothesis. For example, waking early helps one to have a productive day.  
• Empirical Hypothesis : This type of hypothesis is based on real evidence, evidence that is verifiable by observation as opposed to something that is correct in theory or by some kind of reckoning or logic. This kind of hypothesis depends on various variables that can result in specific outcomes. For example, individuals eating more fish can run faster than those eating meat.   
• Statistical Hypothesis : This kind of hypothesis is most common in systematic investigations that involve a huge target audience. For example, in Louisiana, 45% of students have middle-income parents.  

Four Steps of Hypothesis Testing  

There are four main steps in hypothesis testing in business analytics :  

Step 1: State the Null and Alternate Hypothesis  

After the initial research hypothesis, it is essential to restate it as a null (Ho) hypothesis and an alternate (Ha) hypothesis so that it can be tested mathematically.  

Step 2: Collate Data  

For a test to be valid, it is essential to do some sampling and collate data in a manner designed to test the hypothesis. If your data are not representative, then statistical inferences cannot be made about the population you are trying to analyze.  

Step 3: Perform a Statistical Test  

Various statistical tests are present, but all of them depend on the contrast of within-group variance (how to spread out the data in a group) against between-group variance (how dissimilar the groups are from one another).  

Step 4: Decide to Reject or Accept Your Null Hypothesis  

Based on the result of your statistical test, you need to decide whether you want to accept or reject your null hypothesis.  

Hypothesis Testing in Business   

When we talk about data-driven decision-making, a specific amount of risk can deceive a professional. This could result from flawed observations or thinking inaccurate or incomplete information , or unknown variables. The threat over here is that if key strategic decisions are made on incorrect insights, it can lead to catastrophic outcomes for an organization. The actual importance of hypothesis testing is that it enables professionals to analyze their assumptions and theories before putting them into action. This enables an organization to confirm the accuracy of its analysis before making key decisions.  

Key Considerations for Hypothesis Testing  

Let us look at the following key considerations of hypothesis testing:  

• Alternative Hypothesis and Null Hypothesis : If a researcher wants to disapprove of a null hypothesis, then the researcher has to develop an opposite assumption—known as an alternative hypothesis. A null hypothesis is created when a researcher thinks that there is no connection between the variables that are being observed.  
• Significance Level and P-Value : The statistical significance level is generally expressed as a p-value that lies between 0 and 1. The lesser the p-value, the more it suggests that you reject the null hypothesis. A p-value of less than 0.05 (generally ≤ 0.05) is significant statistically.  
• One-Sided vs. Two-Sided Testing : One-sided tests suggest the possibility of an effect in a single direction only. Two-sided tests test for the likelihood of the effect in two directions—negative and positive. One-sided tests comprise more statistical power to identify an effect in a single direction than a two-sided test with the same significance level and design.   
• Sampling: For hypothesis testing , you are required to collate a sample of data that has to be examined. In hypothesis testing, an analyst can test a statistical sample with the aim of providing proof of the credibility of the null hypothesis. Statistical analysts can test a hypothesis by examining and measuring a random sample of the population that is being examined.  

Real-World Example of Hypothesis Testing  

The following two examples give a glimpse of the various situations in which hypothesis testing is used in real-world scenarios.  

Example: BioSciences  

Hypothesis tests are frequently used in biological sciences. For example, consider that a biologist is sure that a certain kind of fertilizer will lead to better growth of plants which is at present 10 inches. To test this, the fertilizer is sprayed on the plants in the laboratory for a month. A hypothesis test is then done using the following:  

• H0: μ = 10 inches (the fertilizer has no effect on the plant growth)  
• HA: μ > 10 inches (the fertilizer leads to an increase in plant growth)  

Suppose the p-value is lesser than the significance level (e.g., α = .04). In that case, the null hypothesis can be rejected, and it can be concluded that the fertilizer results in increased plant growth.  

Example: Clinical Trials  

Consider an example where a doctor feels that a new medicine can decrease blood sugar in patients. To confirm this, he can measure the sugar of 20 diabetic patients prior to and after administering the new drug for a month. A hypothesis test is then done using the following:  

• H0: μafter = μbefore (the blood sugar is the same as before and after administering the new drug)  
• HA: μafter < μbefore (the blood sugar is less after the drug)  

If the p-value is less than the significance level (e.g., α = .04), then the null hypothesis can be rejected, and it can be proven that the new drug leads to reduced blood sugar.  

Conclusion  

Now you are aware of the need for hypotheses in Business Analytics . A hypothesis is not just an assumption— it has to be based on prior knowledge and theories. It also needs to be, which means that you can accept or reject it using scientific research methods (such as observations, experiments, and statistical data analysis). Most genuine Hypothesis testing programs teach you how to use hypothesis testing in real-world scenarios. If you are interested in getting a certificate degree in Integrated Program In Business Analytics , UNext Jigsaw is highly recommended.

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Statistics By Jim

Making statistics intuitive

Hypothesis Testing: Uses, Steps & Example

By Jim Frost 4 Comments

What is Hypothesis Testing?

Hypothesis testing in statistics uses sample data to infer the properties of a whole population . These tests determine whether a random sample provides sufficient evidence to conclude an effect or relationship exists in the population. Researchers use them to help separate genuine population-level effects from false effects that random chance can create in samples. These methods are also known as significance testing.

For example, researchers are testing a new medication to see if it lowers blood pressure. They compare a group taking the drug to a control group taking a placebo. If their hypothesis test results are statistically significant, the medication’s effect of lowering blood pressure likely exists in the broader population, not just the sample studied.

Using Hypothesis Tests

A hypothesis test evaluates two mutually exclusive statements about a population to determine which statement the sample data best supports. These two statements are called the null hypothesis and the alternative hypothesis . The following are typical examples:

• Null Hypothesis : The effect does not exist in the population.
• Alternative Hypothesis : The effect does exist in the population.

Hypothesis testing accounts for the inherent uncertainty of using a sample to draw conclusions about a population, which reduces the chances of false discoveries. These procedures determine whether the sample data are sufficiently inconsistent with the null hypothesis that you can reject it. If you can reject the null, your data favor the alternative statement that an effect exists in the population.

Statistical significance in hypothesis testing indicates that an effect you see in sample data also likely exists in the population after accounting for random sampling error , variability, and sample size. Your results are statistically significant when the p-value is less than your significance level or, equivalently, when your confidence interval excludes the null hypothesis value.

Conversely, non-significant results indicate that despite an apparent sample effect, you can’t be sure it exists in the population. It could be chance variation in the sample and not a genuine effect.

Learn more about Failing to Reject the Null .

5 Steps of Significance Testing

Hypothesis testing involves five key steps, each critical to validating a research hypothesis using statistical methods:

• Formulate the Hypotheses : Write your research hypotheses as a null hypothesis (H 0 ) and an alternative hypothesis (H A ).
• Data Collection : Gather data specifically aimed at testing the hypothesis.
• Conduct A Test : Use a suitable statistical test to analyze your data.
• Make a Decision : Based on the statistical test results, decide whether to reject the null hypothesis or fail to reject it.
• Report the Results : Summarize and present the outcomes in your report’s results and discussion sections.

While the specifics of these steps can vary depending on the research context and the data type, the fundamental process of hypothesis testing remains consistent across different studies.

Let’s work through these steps in an example!

Hypothesis Testing Example

Researchers want to determine if a new educational program improves student performance on standardized tests. They randomly assign 30 students to a control group , which follows the standard curriculum, and another 30 students to a treatment group, which participates in the new educational program. After a semester, they compare the test scores of both groups.

Download the CSV data file to perform the hypothesis testing yourself: Hypothesis_Testing .

The researchers write their hypotheses. These statements apply to the population, so they use the mu (μ) symbol for the population mean parameter .

• Null Hypothesis (H 0 ) : The population means of the test scores for the two groups are equal (μ 1 = μ 2 ).
• Alternative Hypothesis (H A ) : The population means of the test scores for the two groups are unequal (μ 1 ≠ μ 2 ).

Choosing the correct hypothesis test depends on attributes such as data type and number of groups. Because they’re using continuous data and comparing two means, the researchers use a 2-sample t-test .

Here are the results.

The treatment group’s mean is 58.70, compared to the control group’s mean of 48.12. The mean difference is 10.67 points. Use the test’s p-value and significance level to determine whether this difference is likely a product of random fluctuation in the sample or a genuine population effect.

Because the p-value (0.000) is less than the standard significance level of 0.05, the results are statistically significant, and we can reject the null hypothesis. The sample data provides sufficient evidence to conclude that the new program’s effect exists in the population.

Limitations

Hypothesis testing improves your effectiveness in making data-driven decisions. However, it is not 100% accurate because random samples occasionally produce fluky results. Hypothesis tests have two types of errors, both relating to drawing incorrect conclusions.

• Type I error: The test rejects a true null hypothesis—a false positive.
• Type II error: The test fails to reject a false null hypothesis—a false negative.

Learn more about Type I and Type II Errors .

Our exploration of hypothesis testing using a practical example of an educational program reveals its powerful ability to guide decisions based on statistical evidence. Whether you’re a student, researcher, or professional, understanding and applying these procedures can open new doors to discovering insights and making informed decisions. Let this tool empower your analytical endeavors as you navigate through the vast seas of data.

Learn more about the Hypothesis Tests for Various Data Types .

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Reader Interactions

June 10, 2024 at 10:51 am

Thank you, Jim, for another helpful article; timely too since I have started reading your new book on hypothesis testing and, now that we are at the end of the school year, my district is asking me to perform a number of evaluations on instructional programs. This is where my question/concern comes in. You mention that hypothesis testing is all about testing samples. However, I use all the students in my district when I make these comparisons. Since I am using the entire “population” in my evaluations (I don’t select a sample of third grade students, for example, but I use all 700 third graders), am I somehow misusing the tests? Or can I rest assured that my district’s student population is only a sample of the universal population of students?

June 10, 2024 at 1:50 pm

I hope you are finding the book helpful!

Yes, the purpose of hypothesis testing is to infer the properties of a population while accounting for random sampling error.

In your case, it comes down to how you want to use the results. Who do you want the results to apply to?

If you’re summarizing the sample, looking for trends and patterns, or evaluating those students and don’t plan to apply those results to other students, you don’t need hypothesis testing because there is no sampling error. They are the population and you can just use descriptive statistics. In this case, you’d only need to focus on the practical significance of the effect sizes.

On the other hand, if you want to apply the results from this group to other students, you’ll need hypothesis testing. However, there is the complicating issue of what population your sample of students represent. I’m sure your district has its own unique characteristics, demographics, etc. Your district’s students probably don’t adequately represent a universal population. At the very least, you’d need to recognize any special attributes of your district and how they could bias the results when trying to apply them outside the district. Or they might apply to similar districts in your region.

However, I’d imagine your 3rd graders probably adequately represent future classes of 3rd graders in your district. You need to be alert to changing demographics. At least in the short run I’d imagine they’d be representative of future classes.

Think about how these results will be used. Do they just apply to the students you measured? Then you don’t need hypothesis tests. However, if the results are being used to infer things about other students outside of the sample, you’ll need hypothesis testing along with considering how well your students represent the other students and how they differ.

I hope that helps!

June 10, 2024 at 3:21 pm

Thank you so much, Jim, for the suggestions in terms of what I need to think about and consider! You are always so clear in your explanations!!!!

June 10, 2024 at 3:22 pm

You’re very welcome! Best of luck with your evaluations!

Comments and Questions Cancel reply

Hypothesis Testing: Understanding the Basics, Types, and Importance

Hypothesis testing is a statistical method used to determine whether a hypothesis about a population parameter is true or not. This technique helps researchers and decision-makers make informed decisions based on evidence rather than guesses. Hypothesis testing is an essential tool in scientific research, social sciences, and business analysis. In this article, we will delve deeper into the basics of hypothesis testing, types of hypotheses, significance level, p-values, and the importance of hypothesis testing.

• Introduction

What is a hypothesis?

What is hypothesis testing, types of hypotheses, null hypothesis, alternative hypothesis, one-tailed and two-tailed tests, significance level and p-values, avoiding type i and type ii errors, making informed decisions, testing business strategies, a/b testing, formulating the null and alternative hypotheses, selecting the appropriate test, setting the level of significance, calculating the p-value, making a decision, common misconceptions about hypothesis testing, understanding hypothesis testing.

A hypothesis is an assumption or a proposition made about a population parameter. It is a statement that can be tested and either supported or refuted. For example, a hypothesis could be that a new medication reduces the severity of symptoms in patients with a particular disease.

Hypothesis testing is a statistical method that helps to determine whether a hypothesis is true or not. It is a procedure that involves collecting and analyzing data to evaluate the probability of the null hypothesis being true. The null hypothesis is the hypothesis that there is no significant difference between a sample and the population.

In hypothesis testing, there are two types of hypotheses: null and alternative.

The null hypothesis, denoted by H0, is a statement of no effect, no relationship, or no difference between the sample and the population. It is assumed to be true until there is sufficient evidence to reject it. For example, the null hypothesis could be that there is no significant difference in the blood pressure of patients who received the medication and those who received a placebo.

The alternative hypothesis, denoted by H1, is a statement of an effect, relationship, or difference between the sample and the population. It is the opposite of the null hypothesis. For example, the alternative hypothesis could be that the medication reduces the blood pressure of patients compared to those who received a placebo.

There are two types of alternative hypotheses: one-tailed and two-tailed. A one-tailed test is used when there is a directional hypothesis. For example, the hypothesis could be that the medication reduces blood pressure. A two-tailed test is used when there is a non-directional hypothesis. For example, the hypothesis could be that there is a significant difference in blood pressure between patients who received the medication and those who received a placebo.

The significance level, denoted by α, is the probability of rejecting the null hypothesis when it is true. It is set at the beginning of the test, usually at 5% or 1%. The p-value is the probability of obtaining a test statistic as extreme as

or more extreme than the observed one, assuming that the null hypothesis is true. If the p-value is less than the significance level, we reject the null hypothesis.

Importance of Hypothesis Testing

Hypothesis testing helps to avoid Type I and Type II errors. Type I error occurs when we reject the null hypothesis when it is actually true. Type II error occurs when we fail to reject the null hypothesis when it is actually false. By setting a significance level and calculating the p-value, we can control the probability of making these errors.

Hypothesis testing helps researchers and decision-makers make informed decisions based on evidence. For example, a medical researcher can use hypothesis testing to determine the effectiveness of a new drug. A business analyst can use hypothesis testing to evaluate the performance of a marketing campaign. By testing hypotheses, decision-makers can avoid making decisions based on guesses or assumptions.

Hypothesis testing is widely used in business analysis to test strategies and make data-driven decisions. For example, a business owner can use hypothesis testing to determine whether a new product will be profitable. By conducting A/B testing, businesses can compare the performance of two versions of a product and make data-driven decisions.

Examples of Hypothesis Testing

• A/B testing is a popular technique used in online marketing and web design. It involves comparing two versions of a webpage or an advertisement to determine which one performs better. By conducting A/B testing, businesses can optimize their websites and advertisements to increase conversions and sales.

A t-test is used to compare the means of two samples. It is commonly used in medical research, social sciences, and business analysis. For example, a researcher can use a t-test to determine whether there is a significant difference in the cholesterol levels of patients who received a new drug and those who received a placebo.

Analysis of Variance (ANOVA) is a statistical technique used to compare the means of more than two samples. It is commonly used in medical research, social sciences, and business analysis. For example, a business owner can use ANOVA to determine whether there is a significant difference in the sales performance of three different stores.

Steps in Hypothesis Testing

The first step in hypothesis testing is to formulate the null and alternative hypotheses. The null hypothesis is the hypothesis that there is no significant difference between the sample and the population, while the alternative hypothesis is the opposite.

The second step is to select the appropriate test based on the type of data and the research question. There are different types of tests for different types of data, such as t-test for continuous data and chi-square test for categorical data.

The third step is to set the level of significance, which is usually 5% or 1%. The significance level represents the probability of rejecting the null hypothesis when it is actually true.

The fourth step is to calculate the p-value, which represents the probability of obtaining a test statistic as extreme as or more extreme than the observed one, assuming that the null hypothesis is true.

The final step is to make a decision based on the p-value and the significance level. If the p-value is less than the significance level, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

There are several common misconceptions about hypothesis testing. One of the most common misconceptions is that rejecting the null hypothesis means that the alternative hypothesis is true. However

this is not necessarily the case. Rejecting the null hypothesis only means that there is evidence against it, but it does not prove that the alternative hypothesis is true. Another common misconception is that hypothesis testing can prove causality. However, hypothesis testing can only provide evidence for or against a hypothesis, and causality can only be inferred from a well-designed experiment.

Hypothesis testing is an important statistical technique used to test hypotheses and make informed decisions based on evidence. It helps to avoid Type I and Type II errors, and it is widely used in medical research, social sciences, and business analysis. By following the steps in hypothesis testing and avoiding common misconceptions, researchers and decision-makers can make data-driven decisions and avoid making decisions based on guesses or assumptions.

• What is the difference between Type I and Type II errors in hypothesis testing?
• Type I error occurs when we reject the null hypothesis when it is actually true, while Type II error occurs when we fail to reject the null hypothesis when it is actually false.
• How do you select the appropriate test in hypothesis testing?
• The appropriate test is selected based on the type of data and the research question. There are different types of tests for different types of data, such as t-test for continuous data and chi-square test for categorical data.
• Can hypothesis testing prove causality?
• No, hypothesis testing can only provide evidence for or against a hypothesis, and causality can only be inferred from a well-designed experiment.
• Why is hypothesis testing important in business analysis?
• Hypothesis testing is important in business analysis because it helps businesses make data-driven decisions and avoid making decisions based on guesses or assumptions. By testing hypotheses, businesses can evaluate the effectiveness of their strategies and optimize their performance.
• What is A/B testing?

If you want to learn more about statistical analysis, including central tendency measures, check out our  comprehensive statistical course . Our course provides a hands-on learning experience that covers all the essential statistical concepts and tools, empowering you to analyze complex data with confidence. With practical examples and interactive exercises, you’ll gain the skills you need to succeed in your statistical analysis endeavors. Enroll now and take your statistical knowledge to the next level!

If you’re looking to jumpstart your career as a data analyst, consider enrolling in our comprehensive  Data Analyst Bootcamp with Internship program . Our program provides you with the skills and experience necessary to succeed in today’s data-driven world. You’ll learn the fundamentals of statistical analysis, as well as how to use tools such as SQL, Python, Excel, and PowerBI to analyze and visualize data. But that’s not all – our program also includes a 3-month internship with us where you can showcase your Capstone Project.

2 Responses

This is a great and comprehensive article on hypothesis testing, covering everything from the basics to practical examples. I particularly appreciate the section on common misconceptions, as it’s important to understand what hypothesis testing can and cannot do. Overall, a valuable resource for anyone looking to understand this statistical technique.

Thanks, Ana Carol for your Kind words, Yes these topics are very important to know in Artificial intelligence.

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• > Machine Learning
• > Statistics

What is Hypothesis Testing? Types and Methods

• Soumyaa Rawat
• Jul 23, 2021

Hypothesis Testing  

Hypothesis testing is the act of testing a hypothesis or a supposition in relation to a statistical parameter. Analysts implement hypothesis testing in order to test if a hypothesis is plausible or not. 

In data science and statistics , hypothesis testing is an important step as it involves the verification of an assumption that could help develop a statistical parameter. For instance, a researcher establishes a hypothesis assuming that the average of all odd numbers is an even number. 

In order to find the plausibility of this hypothesis, the researcher will have to test the hypothesis using hypothesis testing methods. Unlike a hypothesis that is ‘supposed’ to stand true on the basis of little or no evidence, hypothesis testing is required to have plausible evidence in order to establish that a statistical hypothesis is true. 

Perhaps this is where statistics play an important role. A number of components are involved in this process. But before understanding the process involved in hypothesis testing in research methodology, we shall first understand the types of hypotheses that are involved in the process. Let us get started! 

Types of Hypotheses

In data sampling, different types of hypothesis are involved in finding whether the tested samples test positive for a hypothesis or not. In this segment, we shall discover the different types of hypotheses and understand the role they play in hypothesis testing.

Alternative Hypothesis

Alternative Hypothesis (H1) or the research hypothesis states that there is a relationship between two variables (where one variable affects the other). The alternative hypothesis is the main driving force for hypothesis testing. 

It implies that the two variables are related to each other and the relationship that exists between them is not due to chance or coincidence. 

When the process of hypothesis testing is carried out, the alternative hypothesis is the main subject of the testing process. The analyst intends to test the alternative hypothesis and verifies its plausibility.

Null Hypothesis

The Null Hypothesis (H0) aims to nullify the alternative hypothesis by implying that there exists no relation between two variables in statistics. It states that the effect of one variable on the other is solely due to chance and no empirical cause lies behind it. 

The null hypothesis is established alongside the alternative hypothesis and is recognized as important as the latter. In hypothesis testing, the null hypothesis has a major role to play as it influences the testing against the alternative hypothesis. 

(Must read: What is ANOVA test? )

Non-Directional Hypothesis

The Non-directional hypothesis states that the relation between two variables has no direction. 

Simply put, it asserts that there exists a relation between two variables, but does not recognize the direction of effect, whether variable A affects variable B or vice versa. 

Directional Hypothesis

The Directional hypothesis, on the other hand, asserts the direction of effect of the relationship that exists between two variables. 

Herein, the hypothesis clearly states that variable A affects variable B, or vice versa. 

Statistical Hypothesis

A statistical hypothesis is a hypothesis that can be verified to be plausible on the basis of statistics. 

By using data sampling and statistical knowledge, one can determine the plausibility of a statistical hypothesis and find out if it stands true or not. 

(Related blog: z-test vs t-test )

Performing Hypothesis Testing  

Now that we have understood the types of hypotheses and the role they play in hypothesis testing, let us now move on to understand the process in a better manner. 

In hypothesis testing, a researcher is first required to establish two hypotheses - alternative hypothesis and null hypothesis in order to begin with the procedure. 

To establish these two hypotheses, one is required to study data samples, find a plausible pattern among the samples, and pen down a statistical hypothesis that they wish to test. 

A random population of samples can be drawn, to begin with hypothesis testing. Among the two hypotheses, alternative and null, only one can be verified to be true. Perhaps the presence of both hypotheses is required to make the process successful. 

At the end of the hypothesis testing procedure, either of the hypotheses will be rejected and the other one will be supported. Even though one of the two hypotheses turns out to be true, no hypothesis can ever be verified 100%. 

(Read also: Types of data sampling techniques )

Therefore, a hypothesis can only be supported based on the statistical samples and verified data. Here is a step-by-step guide for hypothesis testing.

Establish the hypotheses

First things first, one is required to establish two hypotheses - alternative and null, that will set the foundation for hypothesis testing. 

These hypotheses initiate the testing process that involves the researcher working on data samples in order to either support the alternative hypothesis or the null hypothesis. 

Generate a testing plan

Once the hypotheses have been formulated, it is now time to generate a testing plan. A testing plan or an analysis plan involves the accumulation of data samples, determining which statistic is to be considered and laying out the sample size. 

All these factors are very important while one is working on hypothesis testing.

Analyze data samples

As soon as a testing plan is ready, it is time to move on to the analysis part. Analysis of data samples involves configuring statistical values of samples, drawing them together, and deriving a pattern out of these samples. 

While analyzing the data samples, a researcher needs to determine a set of things -

Significance Level - The level of significance in hypothesis testing indicates if a statistical result could have significance if the null hypothesis stands to be true.

Testing Method - The testing method involves a type of sampling-distribution and a test statistic that leads to hypothesis testing. There are a number of testing methods that can assist in the analysis of data samples. 

Test statistic - Test statistic is a numerical summary of a data set that can be used to perform hypothesis testing.

P-value - The P-value interpretation is the probability of finding a sample statistic to be as extreme as the test statistic, indicating the plausibility of the null hypothesis. 

Infer the results

The analysis of data samples leads to the inference of results that establishes whether the alternative hypothesis stands true or not. When the P-value is less than the significance level, the null hypothesis is rejected and the alternative hypothesis turns out to be plausible. 

Methods of Hypothesis Testing

As we have already looked into different aspects of hypothesis testing, we shall now look into the different methods of hypothesis testing. All in all, there are 2 most common types of hypothesis testing methods. They are as follows -

Frequentist Hypothesis Testing

The frequentist hypothesis or the traditional approach to hypothesis testing is a hypothesis testing method that aims on making assumptions by considering current data. 

The supposed truths and assumptions are based on the current data and a set of 2 hypotheses are formulated. A very popular subtype of the frequentist approach is the Null Hypothesis Significance Testing (NHST). 

The NHST approach (involving the null and alternative hypothesis) has been one of the most sought-after methods of hypothesis testing in the field of statistics ever since its inception in the mid-1950s. 

Bayesian Hypothesis Testing

A much unconventional and modern method of hypothesis testing, the Bayesian Hypothesis Testing claims to test a particular hypothesis in accordance with the past data samples, known as prior probability, and current data that lead to the plausibility of a hypothesis. 

The result obtained indicates the posterior probability of the hypothesis. In this method, the researcher relies on ‘prior probability and posterior probability’ to conduct hypothesis testing on hand. 

On the basis of this prior probability, the Bayesian approach tests a hypothesis to be true or false. The Bayes factor, a major component of this method, indicates the likelihood ratio among the null hypothesis and the alternative hypothesis. 

The Bayes factor is the indicator of the plausibility of either of the two hypotheses that are established for hypothesis testing.  

(Also read - Introduction to Bayesian Statistics ) 

To conclude, hypothesis testing, a way to verify the plausibility of a supposed assumption can be done through different methods - the Bayesian approach or the Frequentist approach. 

Although the Bayesian approach relies on the prior probability of data samples, the frequentist approach assumes without a probability. A number of elements involved in hypothesis testing are - significance level, p-level, test statistic, and method of hypothesis testing. 

(Also read: Introduction to probability distributions )

A significant way to determine whether a hypothesis stands true or not is to verify the data samples and identify the plausible hypothesis among the null hypothesis and alternative hypothesis. 

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5.5 Introduction to Hypothesis Tests

One job of a statistician is to make statistical inferences about populations based on samples taken from the population. Confidence intervals are one way to estimate a population parameter.

Another way to make a statistical inference is to make a decision about a parameter. For instance, a car dealership advertises that its new small truck gets 35 miles per gallon on average. A tutoring service claims that its method of tutoring helps 90% of its students get an A or a B. A company says that female managers in their company earn an average of $60,000 per year. A statistician may want to make a decision about or evaluate these claims. A hypothesis test can be used to do this.

A hypothesis test involves collecting data from a sample and evaluating the data. Then the statistician makes a decision as to whether or not there is sufficient evidence to reject the null hypothesis based upon analyses of the data.

In this section, you will conduct hypothesis tests on single means when the population standard deviation is known.

Hypothesis testing consists of two contradictory hypotheses or statements, a decision based on the data, and a conclusion. To perform a hypothesis test, a statistician will perform some variation of these steps:

• Define hypotheses.
• Collect and/or use the sample data to determine the correct distribution to use.
• Calculate test statistic.
• Make a decision.
• Write a conclusion.

Defining your hypotheses

The actual test begins by considering two hypotheses: the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints.

The null hypothesis ( H 0 ) is often a statement of the accepted historical value or norm. This is your starting point that you must assume from the beginning in order to show an effect exists.

The alternative hypothesis ( H a ) is a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 .

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.

After you have determined which hypothesis the sample supports, you make a decision . There are two options for a decision. They are “reject H 0 ” if the sample information favors the alternative hypothesis or “do not reject H 0 ” or “decline to reject H 0 ” if the sample information is insufficient to reject the null hypothesis.

The following table shows mathematical symbols used in H 0 and H a :

NOTE: H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol in the alternative hypothesis depends on the wording of the hypothesis test. Despite this, many researchers may use =, ≤, or ≥ in the null hypothesis. This practice is acceptable because our only decision is to reject or not reject the null hypothesis.

We want to test whether the mean GPA of students in American colleges is 2.0 (out of 4.0). The null hypothesis is: H 0 : μ = 2.0. What is the alternative hypothesis?

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.

Using the Sample to Test the Null Hypothesis

Once you have defined your hypotheses, the next step in the process is to collect sample data. In a classroom context, the data or summary statistics will usually be given to you.

Then you will have to determine the correct distribution to perform the hypothesis test, given the assumptions you are able to make about the situation. Right now, we are demonstrating these ideas in a test for a mean when the population standard deviation is known using the z distribution. We will see other scenarios in the future.

Calculating a Test Statistic

Next you will start evaluating the data. This begins with calculating your test statistic , which is a measure of the distance between what you observed and what you are assuming to be true. In this context, your test statistic, z ο , quantifies the number of standard deviations between the sample mean, x, and the population mean, µ . Calculating the test statistic is analogous to the previously discussed process of standardizing observations with z -scores:

where µ o   is the value assumed to be true in the null hypothesis.

Making a Decision

Once you have your test statistic, there are two methods to use it to make your decision:

• Critical value method (discussed further in later chapters)
• p -value method (our current focus)

p -Value Method

To find a p -value , we use the test statistic to calculate the actual probability of getting the test result. Formally, the p -value is the probability that, if the null hypothesis is true, the results from another randomly selected sample will be as extreme or more extreme as the results obtained from the given sample.

A large p -value calculated from the data indicates that we should not reject the null hypothesis. The smaller the p -value, the more unlikely the outcome and the stronger the evidence is against the null hypothesis. We would reject the null hypothesis if the evidence is strongly against it.

Draw a graph that shows the p -value. The hypothesis test is easier to perform if you use a graph because you see the problem more clearly.

Suppose a baker claims that his bread height is more than 15 cm on average. Several of his customers do not believe him. To persuade his customers that he is right, the baker decides to do a hypothesis test. He bakes ten loaves of bread. The mean height of the sample loaves is 17 cm. The baker knows from baking hundreds of loaves of bread that the standard deviation for the height is 0.5 cm and the distribution of heights is normal.

The null hypothesis could be H 0 : μ ≤ 15.

The alternate hypothesis is H a : μ > 15.

The words “is more than” calls for the use of the > symbol, so “ μ > 15″ goes into the alternate hypothesis. The null hypothesis must contradict the alternate hypothesis.

Suppose the null hypothesis is true (the mean height of the loaves is no more than 15 cm). Then, is the mean height (17 cm) calculated from the sample unexpectedly large? The hypothesis test works by asking how unlikely the sample mean would be if the null hypothesis were true. The graph shows how far out the sample mean is on the normal curve. The p -value is the probability that, if we were to take other samples, any other sample mean would fall at least as far out as 17 cm.

This means that the p -value is the probability that a sample mean is the same or greater than 17 cm when the population mean is, in fact, 15 cm. We can calculate this probability using the normal distribution for means.

A p -value of approximately zero tells us that it is highly unlikely that a loaf of bread rises no more than 15 cm on average. That is, almost 0% of all loaves of bread would be at least as high as 17 cm purely by CHANCE had the population mean height really been 15 cm. Because the outcome of 17 cm is so unlikely (meaning it is happening NOT by chance alone), we conclude that the evidence is strongly against the null hypothesis that the mean height would be at most 15 cm. There is sufficient evidence that the true mean height for the population of the baker’s loaves of bread is greater than 15 cm.

A normal distribution has a standard deviation of one. We want to verify a claim that the mean is greater than 12. A sample of 36 is taken with a sample mean of 12.5.

Find the p -value.

Decision and Conclusion

A systematic way to decide whether to reject or not reject the null hypothesis is to compare the p -value and a preset or preconceived α (also called a significance level ). A preset α is the probability of a type I error (rejecting the null hypothesis when the null hypothesis is true). It may or may not be given to you at the beginning of the problem. If there is no given preconceived α , then use α = 0.05.

When you make a decision to reject or not reject H 0 , do as follows:

• If α > p -value, reject H 0 . The results of the sample data are statistically significant . You can say there is sufficient evidence to conclude that H 0 is an incorrect belief and that the alternative hypothesis, H a , may be correct.
• If α ≤ p -value, fail to reject H 0 . The results of the sample data are not significant. There is not sufficient evidence to conclude that the alternative hypothesis, H a , may be correct.

After you make your decision, write a thoughtful conclusion in the context of the scenario incorporating the hypotheses.

NOTE: When you “do not reject H 0 ,” it does not mean that you should believe that H 0 is true. It simply means that the sample data have failed to provide sufficient evidence to cast serious doubt about the truthfulness of H o .

When using the p -value to evaluate a hypothesis test, the following rhymes can come in handy:

If the p -value is low, the null must go.

If the p -value is high, the null must fly.

This memory aid relates a p -value less than the established alpha (“the p -value is low”) as rejecting the null hypothesis and, likewise, relates a p -value higher than the established alpha (“the p -value is high”) as not rejecting the null hypothesis.

Fill in the blanks:

• Reject the null hypothesis when              .
• The results of the sample data             .
• Do not reject the null when hypothesis when             .

It’s a Boy Genetics Labs claim their procedures improve the chances of a boy being born. The results for a test of a single population proportion are as follows:

• H 0 : p = 0.50, H a : p > 0.50
• p -value = 0.025

Interpret the results and state a conclusion in simple, non-technical terms.

Click here for more multimedia resources, including podcasts, videos, lecture notes, and worked examples.

Figure References

Figure 5.11: Alora Griffiths (2019). dalmatian puppy near man in blue shorts kneeling. Unsplash license. https://unsplash.com/photos/7aRQZtLsvqw

Figure 5.13: Kindred Grey (2020). Bread height probability. CC BY-SA 4.0.

A decision-making procedure for determining whether sample evidence supports a hypothesis

The claim that is assumed to be true and is tested in a hypothesis test

A working hypothesis that is contradictory to the null hypothesis

A measure of the difference between observations and the hypothesized (or claimed) value

The probability that an event will occur, assuming the null hypothesis is true

Probability that a true null hypothesis will be rejected, also known as type I error and denoted by α

Finding sufficient evidence that the observed effect is not just due to variability, often from rejecting the null hypothesis

Significant Statistics Copyright © 2024 by John Morgan Russell, OpenStaxCollege, OpenIntro is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License , except where otherwise noted.

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• How to Write a Strong Hypothesis | Steps & Examples

How to Write a Strong Hypothesis | Steps & Examples

Published on May 6, 2022 by Shona McCombes . Revised on November 20, 2023.

A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection .

Example: Hypothesis

Daily apple consumption leads to fewer doctor’s visits.

Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, other interesting articles, frequently asked questions about writing hypotheses.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Variables in hypotheses

Hypotheses propose a relationship between two or more types of variables .

• An independent variable is something the researcher changes or controls.
• A dependent variable is something the researcher observes and measures.

If there are any control variables , extraneous variables , or confounding variables , be sure to jot those down as you go to minimize the chances that research bias  will affect your results.

In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .

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Step 1. ask a question.

Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.

Step 2. Do some preliminary research

Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.

At this stage, you might construct a conceptual framework to ensure that you’re embarking on a relevant topic . This can also help you identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalize more complex constructs.

Step 3. Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

4. Refine your hypothesis

You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:

• The relevant variables
• The specific group being studied
• The predicted outcome of the experiment or analysis

5. Phrase your hypothesis in three ways

To identify the variables, you can write a simple prediction in  if…then form. The first part of the sentence states the independent variable and the second part states the dependent variable.

In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.

If you are comparing two groups, the hypothesis can state what difference you expect to find between them.

6. Write a null hypothesis

If your research involves statistical hypothesis testing , you will also have to write a null hypothesis . The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .

• H 0 : The number of lectures attended by first-year students has no effect on their final exam scores.
• H 1 : The number of lectures attended by first-year students has a positive effect on their final exam scores.

If you want to know more about the research process , methodology , research bias , or statistics , make sure to check out some of our other articles with explanations and examples.

• Sampling methods
• Simple random sampling
• Stratified sampling
• Cluster sampling
• Likert scales
• Reproducibility

 Statistics

• Null hypothesis
• Statistical power
• Probability distribution
• Effect size
• Poisson distribution

Research bias

• Optimism bias
• Cognitive bias
• Implicit bias
• Hawthorne effect
• Anchoring bias
• Explicit bias

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A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

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Step-by-step guide to hypothesis testing in statistics

Hypothesis testing in statistics helps us use data to make informed decisions. It starts with an assumption or guess about a group or population—something we believe might be true. We then collect sample data to check if there is enough evidence to support or reject that guess. This method is useful in many fields, like science, business, and healthcare, where decisions need to be based on facts.

Learning how to do hypothesis testing in statistics step-by-step can help you better understand data and make smarter choices, even when things are uncertain. This guide will take you through each step, from creating your hypothesis to making sense of the results, so you can see how it works in practical situations.

What is Hypothesis Testing?

Table of Contents

Hypothesis testing is a method for determining whether data supports a certain idea or assumption about a larger group. It starts by making a guess, like an average or a proportion, and then uses a small sample of data to see if that guess seems true or not.

For example, if a company wants to know if its new product is more popular than its old one, it can use hypothesis testing. They start with a statement like “The new product is not more popular than the old one” (this is the null hypothesis) and compare it with “The new product is more popular” (this is the alternative hypothesis). Then, they look at customer feedback to see if there’s enough evidence to reject the first statement and support the second one.

Simply put, hypothesis testing is a way to use data to help make decisions and understand what the data is really telling us, even when we don’t have all the answers.

Importance Of Hypothesis Testing In Decision-Making And Data Analysis

Hypothesis testing is important because it helps us make smart choices and understand data better. Here’s why it’s useful:

• Reduces Guesswork : It helps us see if our guesses or ideas are likely correct, even when we don’t have all the details.
• Uses Real Data : Instead of just guessing, it checks if our ideas match up with real data, which makes our decisions more reliable.
• Avoids Errors : It helps us avoid mistakes by carefully checking if our ideas are right so we don’t make costly errors.
• Shows What to Do Next : It tells us if our ideas work or not, helping us decide whether to keep, change, or drop something. For example, a company might test a new ad and decide what to do based on the results.
• Confirms Research Findings : It makes sure that research results are accurate and not just random chance so that we can trust the findings.

Here’s a simple guide to understanding hypothesis testing, with an example:

1. Set Up Your Hypotheses

Explanation: Start by defining two statements:

• Null Hypothesis (H0): This is the idea that there is no change or effect. It’s what you assume is true.
• Alternative Hypothesis (H1): This is what you want to test. It suggests there is a change or effect.

Example: Suppose a company says their new batteries last an average of 500 hours. To check this:

• Null Hypothesis (H0): The average battery life is 500 hours.
• Alternative Hypothesis (H1): The average battery life is not 500 hours.

2. Choose the Test

Explanation: Pick a statistical test that fits your data and your hypotheses. Different tests are used for various kinds of data.

Example: Since you’re comparing the average battery life, you use a one-sample t-test .

3. Set the Significance Level

Explanation: Decide how much risk you’re willing to take if you make a wrong decision. This is called the significance level, often set at 0.05 or 5%.

Example: You choose a significance level of 0.05, meaning you’re okay with a 5% chance of being wrong.

4. Gather and Analyze Data

Explanation: Collect your data and perform the test. Calculate the test statistic to see how far your sample result is from what you assumed.

Example: You test 30 batteries and find they last an average of 485 hours. You then calculate how this average compares to the claimed 500 hours using the t-test.

5. Find the p-Value

Explanation: The p-value tells you the probability of getting a result as extreme as yours if the null hypothesis is true.

Example: You find a p-value of 0.0001. This means there’s a very small chance (0.01%) of getting an average battery life of 485 hours or less if the true average is 500 hours.

6. Make Your Decision

Explanation: Compare the p-value to your significance level. If the p-value is smaller, you reject the null hypothesis. If it’s larger, you do not reject it.

Example: Since 0.0001 is much less than 0.05, you reject the null hypothesis. This means the data suggests the average battery life is different from 500 hours.

7. Report Your Findings

Explanation: Summarize what the results mean. State whether you rejected the null hypothesis and what that implies.

Example: You conclude that the average battery life is likely different from 500 hours. This suggests the company’s claim might not be accurate.

Hypothesis testing is a way to use data to check if your guesses or assumptions are likely true. By following these steps—setting up your hypotheses, choosing the right test, deciding on a significance level, analyzing your data, finding the p-value, making a decision, and reporting results—you can determine if your data supports or challenges your initial idea.

Understanding Hypothesis Testing: A Simple Explanation

Hypothesis testing is a way to use data to make decisions. Here’s a straightforward guide:

1. What is the Null and Alternative Hypotheses?

• Null Hypothesis (H0): This is your starting assumption. It says that nothing has changed or that there is no effect. It’s what you assume to be true until your data shows otherwise. Example: If a company says their batteries last 500 hours, the null hypothesis is: “The average battery life is 500 hours.” This means you think the claim is correct unless you find evidence to prove otherwise.
• Alternative Hypothesis (H1): This is what you want to find out. It suggests that there is an effect or a difference. It’s what you are testing to see if it might be true. Example: To test the company’s claim, you might say: “The average battery life is not 500 hours.” This means you think the average battery life might be different from what the company says.

2. One-Tailed vs. Two-Tailed Tests

• One-Tailed Test: This test checks for an effect in only one direction. You use it when you’re only interested in finding out if something is either more or less than a specific value. Example: If you think the battery lasts longer than 500 hours, you would use a one-tailed test to see if the battery life is significantly more than 500 hours.
• Two-Tailed Test: This test checks for an effect in both directions. Use this when you want to see if something is different from a specific value, whether it’s more or less. Example: If you want to see if the battery life is different from 500 hours, whether it’s more or less, you would use a two-tailed test. This checks for any significant difference, regardless of the direction.

3. Common Misunderstandings

• Clarification: Hypothesis testing doesn’t prove that the null hypothesis is true. It just helps you decide if you should reject it. If there isn’t enough evidence against it, you don’t reject it, but that doesn’t mean it’s definitely true.
• Clarification: A small p-value shows that your data is unlikely if the null hypothesis is true. It suggests that the alternative hypothesis might be right, but it doesn’t prove the null hypothesis is false.
• Clarification: The significance level (alpha) is a set threshold, like 0.05, that helps you decide how much risk you’re willing to take for making a wrong decision. It should be chosen carefully, not randomly.
• Clarification: Hypothesis testing helps you make decisions based on data, but it doesn’t guarantee your results are correct. The quality of your data and the right choice of test affect how reliable your results are.

Benefits and Limitations of Hypothesis Testing

• Clear Decisions: Hypothesis testing helps you make clear decisions based on data. It shows whether the evidence supports or goes against your initial idea.
• Objective Analysis: It relies on data rather than personal opinions, so your decisions are based on facts rather than feelings.
• Concrete Numbers: You get specific numbers, like p-values, to understand how strong the evidence is against your idea.
• Control Risk: You can set a risk level (alpha level) to manage the chance of making an error, which helps avoid incorrect conclusions.
• Widely Used: It can be used in many areas, from science and business to social studies and engineering, making it a versatile tool.

Limitations

• Sample Size Matters: The results can be affected by the size of the sample. Small samples might give unreliable results, while large samples might find differences that aren’t meaningful in real life.
• Risk of Misinterpretation: A small p-value means the results are unlikely if the null hypothesis is true, but it doesn’t show how important the effect is.
• Needs Assumptions: Hypothesis testing requires certain conditions, like data being normally distributed . If these aren’t met, the results might not be accurate.
• Simple Decisions: It often results in a basic yes or no decision without giving detailed information about the size or impact of the effect.
• Can Be Misused: Sometimes, people misuse hypothesis testing, tweaking data to get a desired result or focusing only on whether the result is statistically significant.
• No Absolute Proof: Hypothesis testing doesn’t prove that your hypothesis is true. It only helps you decide if there’s enough evidence to reject the null hypothesis, so the conclusions are based on likelihood, not certainty.

Final Thoughts 

Hypothesis testing helps you make decisions based on data. It involves setting up your initial idea, picking a significance level, doing the test, and looking at the results. By following these steps, you can make sure your conclusions are based on solid information, not just guesses.

This approach lets you see if the evidence supports or contradicts your initial idea, helping you make better decisions. But remember that hypothesis testing isn’t perfect. Things like sample size and assumptions can affect the results, so it’s important to be aware of these limitations.

In simple terms, using a step-by-step guide for hypothesis testing is a great way to better understand your data. Follow the steps carefully and keep in mind the method’s limits.

What is the difference between one-tailed and two-tailed tests?

 A one-tailed test assesses the probability of the observed data in one direction (either greater than or less than a certain value). In contrast, a two-tailed test looks at both directions (greater than and less than) to detect any significant deviation from the null hypothesis.

How do you choose the appropriate test for hypothesis testing?

The choice of test depends on the type of data you have and the hypotheses you are testing. Common tests include t-tests, chi-square tests, and ANOVA. You get more details about ANOVA, you may read Complete Details on What is ANOVA in Statistics ?  It’s important to match the test to the data characteristics and the research question.

What is the role of sample size in hypothesis testing?  

Sample size affects the reliability of hypothesis testing. Larger samples provide more reliable estimates and can detect smaller effects, while smaller samples may lead to less accurate results and reduced power.

Can hypothesis testing prove that a hypothesis is true?  

Hypothesis testing cannot prove that a hypothesis is true. It can only provide evidence to support or reject the null hypothesis. A result can indicate whether the data is consistent with the null hypothesis or not, but it does not prove the alternative hypothesis with certainty.

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What Is Hypothesis Testing?

• How It Works

4 Step Process

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• Fundamental Analysis

Hypothesis Testing: 4 Steps and Example

Hypothesis testing, sometimes called significance testing, is an act in statistics whereby an analyst tests an assumption regarding a population parameter. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis.

Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data. Such data may come from a larger population or a data-generating process. The word "population" will be used for both of these cases in the following descriptions.

Key Takeaways

• Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data.
• The test provides evidence concerning the plausibility of the hypothesis, given the data.
• Statistical analysts test a hypothesis by measuring and examining a random sample of the population being analyzed.
• The four steps of hypothesis testing include stating the hypotheses, formulating an analysis plan, analyzing the sample data, and analyzing the result.

How Hypothesis Testing Works

In hypothesis testing, an  analyst  tests a statistical sample, intending to provide evidence on the plausibility of the null hypothesis. Statistical analysts measure and examine a random sample of the population being analyzed. All analysts use a random population sample to test two different hypotheses: the null hypothesis and the alternative hypothesis.

The null hypothesis is usually a hypothesis of equality between population parameters; e.g., a null hypothesis may state that the population mean return is equal to zero. The alternative hypothesis is effectively the opposite of a null hypothesis. Thus, they are mutually exclusive , and only one can be true. However, one of the two hypotheses will always be true.

The null hypothesis is a statement about a population parameter, such as the population mean, that is assumed to be true.

• State the hypotheses.
• Formulate an analysis plan, which outlines how the data will be evaluated.
• Carry out the plan and analyze the sample data.
• Analyze the results and either reject the null hypothesis, or state that the null hypothesis is plausible, given the data.

Example of Hypothesis Testing

If an individual wants to test that a penny has exactly a 50% chance of landing on heads, the null hypothesis would be that 50% is correct, and the alternative hypothesis would be that 50% is not correct. Mathematically, the null hypothesis is represented as Ho: P = 0.5. The alternative hypothesis is shown as "Ha" and is identical to the null hypothesis, except with the equal sign struck-through, meaning that it does not equal 50%.

A random sample of 100 coin flips is taken, and the null hypothesis is tested. If it is found that the 100 coin flips were distributed as 40 heads and 60 tails, the analyst would assume that a penny does not have a 50% chance of landing on heads and would reject the null hypothesis and accept the alternative hypothesis.

If there were 48 heads and 52 tails, then it is plausible that the coin could be fair and still produce such a result. In cases such as this where the null hypothesis is "accepted," the analyst states that the difference between the expected results (50 heads and 50 tails) and the observed results (48 heads and 52 tails) is "explainable by chance alone."

When Did Hypothesis Testing Begin?

Some statisticians attribute the first hypothesis tests to satirical writer John Arbuthnot in 1710, who studied male and female births in England after observing that in nearly every year, male births exceeded female births by a slight proportion. Arbuthnot calculated that the probability of this happening by chance was small, and therefore it was due to “divine providence.”

What are the Benefits of Hypothesis Testing?

Hypothesis testing helps assess the accuracy of new ideas or theories by testing them against data. This allows researchers to determine whether the evidence supports their hypothesis, helping to avoid false claims and conclusions. Hypothesis testing also provides a framework for decision-making based on data rather than personal opinions or biases. By relying on statistical analysis, hypothesis testing helps to reduce the effects of chance and confounding variables, providing a robust framework for making informed conclusions.

What are the Limitations of Hypothesis Testing?

Hypothesis testing relies exclusively on data and doesn’t provide a comprehensive understanding of the subject being studied. Additionally, the accuracy of the results depends on the quality of the available data and the statistical methods used. Inaccurate data or inappropriate hypothesis formulation may lead to incorrect conclusions or failed tests. Hypothesis testing can also lead to errors, such as analysts either accepting or rejecting a null hypothesis when they shouldn’t have. These errors may result in false conclusions or missed opportunities to identify significant patterns or relationships in the data.

Hypothesis testing refers to a statistical process that helps researchers determine the reliability of a study. By using a well-formulated hypothesis and set of statistical tests, individuals or businesses can make inferences about the population that they are studying and draw conclusions based on the data presented. All hypothesis testing methods have the same four-step process, which includes stating the hypotheses, formulating an analysis plan, analyzing the sample data, and analyzing the result.

Sage. " Introduction to Hypothesis Testing ," Page 4.

Elder Research. " Who Invented the Null Hypothesis? "

Formplus. " Hypothesis Testing: Definition, Uses, Limitations and Examples ."

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What Is Level of Significance in Hypothesis Testing and How Can Businesses Use It?

There are so many strategies and methods for collecting data from a target market or group of users. Some methods are passive, interpreting data collected by website cookies and tracking pixels to build an understanding of user behavior. Other methods are more proactive, taking the form of thoughtful marketing surveys to get behavior and attitude insights directly from consumers.

Whatever the data collection method, it is then up to researchers and insights teams to study that data, which leads us to hypothesis testing. Hypothesis testing is a way of life for many researchers when it comes to quantitative and qualitative research studies. Although learning about the level of significance is important, the overall question of what is the purpose of survey research and why researchers, especially in business situations, perform it, are a point to focus on as well.

What Are Some of the Benefits of Survey Research?

While it’s important to understand hypothesis testing in the context of business research, it’s also important to understand this statistical research method in the context of survey data and the important role surveys play in making transformative marketing decisions that impact a target market.

In most cases, the purpose of survey research is to gather information from a large collection of individuals to glean information about prospective customers, current users, and competitors or the competitive landscape. And while surveys are an extremely useful tool for conducting research, they come with a lot of benefits outside of simply gathering data.

For one, because surveys have morphed from in-person settings with pens and paper into digital venues with online forums and discussions, the cost of survey research has drastically diminished. If a business is looking for a cost-effective way to gain data about future client prospects, possible consumers, or brand loyal customers, survey research is a great way to find that information and to then make data-driven business strategy decisions.

Another perk is that survey research is extremely accessible and dependable. Because surveys are often used to directly collect information from a large number of individuals, they must be a highly versatile medium, able to be conducted on desktop and laptop computers, as well as smartphone and tablets when respondents are on the go. The dependability and accessibility of this research medium, in turn, makes survey data a dependable source for researchers to pull their insight.

Not only do some benefits of survey research include cost, accessibility, and dependability, survey research is also valuable in terms of unearthing business solutions through decisive customer data points . With KnowledgeHound’s survey data analysis experience , researchers can get to these important data cuts while eliminating information silos. Find and access key data points with a simple search through KnowledgeHound’s easy-to-use interface and share valuable insight with other members of your team.  

An Intro to Hypothesis Testing: What Is P-Value in Research?

There are a lot of letters thrown about in research and hypothesis testing including something called the P-Value. If you’re someone with a curious mind or have upcoming research to take part in and need to know things, like what the p-value in research is, we’re here to break it down for you. Understanding the purpose and benefits of survey research are one thing, taking part in the analysis of the data from the research is another. 

Prior to and when survey research is being conducted are when you’ll be paying attention to the P-Value. Simply put, the P-Value is the value of calculated probability. When looking to find out that a survey research’s data is statistically significant or if the data is not statistically significant, a researcher will go straight to the P-Value to gauge whether the value found is less than 0.05 or greater than 0.05.

The P-Value is calculated when a researcher is taking part in hypothesis testing that includes a null hypothesis, or rather, if the hypothesis test understands there to be no difference between two groups that are partaking in the testing.

So what is level of significance in hypothesis testing, then? It’s simply the singular value that researchers discover through data analysis to be either statistically significant (where p is <0.05) or insignificant (where p is >0.05). Most researchers will look to have a significance level of 95% (also known as statistically significant) in hypothesis testing and research. 

With a significance level of 95% or greater, a researcher or non researcher will understand that the insights gathered from the data are not readily interpreted by happenstance. Put another way: the insights found and taken through the data are not mere coincidences. In addition, if the data is statistically significant, a researcher can dismiss the null hypothesis.

Hypothesis Testing in Business Research

Data-driven analytics and insights are increasingly important in business decisions for an organizational framework and future strategy development. You don’t have to work in science or in a scientific field of inquiry to use hypothesis testing. Not only is hypothesis testing in business research an important part of building out a strategy, it is also vital to use the data from the testing to verify that the strategy is working and then make adjustments, where needed, to improve results. 

Even with that information, you might be thinking, “How should I practically use hypothesis testing in business research?” Well unfortunately, there’s no simple answer because hypothesis testing can be used in any variety of situations from managing sensitive financial information of a client to determining the effectiveness of a company’s social media strategy.

Even though both scenarios are distinctly different, hypothesis testing can help determine what an end-product would be with regard to an unproven question. What’s more, hypothesis testing in business research, especially when it comes to finances and a company’s internal and external (think clients) fiscal responsibility, is a proven method to guide next steps and decision-making within whole corporations, specific offices of an organization, or even one team of 10 at a large company.

Whether a researcher or non-researcher partakes in hypothesis testing in business through survey research, what’s critical to remember is that the data is what’s most important. However, because the raw numbers hold no meaning until they’re put into context, having a platform where data visualization takes place alongside data discovery including categorization and organization in an easily-digestible and user-friendly platform is essential. Learn how KnowledgeHound helps brands and businesses capitalize on data to further not just business objectives but also relationships with consumers.

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The Craft of Writing a Strong Hypothesis

Table of Contents

Writing a hypothesis is one of the essential elements of a scientific research paper. It needs to be to the point, clearly communicating what your research is trying to accomplish. A blurry, drawn-out, or complexly-structured hypothesis can confuse your readers. Or worse, the editor and peer reviewers.

A captivating hypothesis is not too intricate. This blog will take you through the process so that, by the end of it, you have a better idea of how to convey your research paper's intent in just one sentence.

What is a Hypothesis?

The first step in your scientific endeavor, a hypothesis, is a strong, concise statement that forms the basis of your research. It is not the same as a thesis statement , which is a brief summary of your research paper .

The sole purpose of a hypothesis is to predict your paper's findings, data, and conclusion. It comes from a place of curiosity and intuition . When you write a hypothesis, you're essentially making an educated guess based on scientific prejudices and evidence, which is further proven or disproven through the scientific method.

The reason for undertaking research is to observe a specific phenomenon. A hypothesis, therefore, lays out what the said phenomenon is. And it does so through two variables, an independent and dependent variable.

The independent variable is the cause behind the observation, while the dependent variable is the effect of the cause. A good example of this is “mixing red and blue forms purple.” In this hypothesis, mixing red and blue is the independent variable as you're combining the two colors at your own will. The formation of purple is the dependent variable as, in this case, it is conditional to the independent variable.

Different Types of Hypotheses‌

Types of hypotheses

Some would stand by the notion that there are only two types of hypotheses: a Null hypothesis and an Alternative hypothesis. While that may have some truth to it, it would be better to fully distinguish the most common forms as these terms come up so often, which might leave you out of context.

Apart from Null and Alternative, there are Complex, Simple, Directional, Non-Directional, Statistical, and Associative and casual hypotheses. They don't necessarily have to be exclusive, as one hypothesis can tick many boxes, but knowing the distinctions between them will make it easier for you to construct your own.

1. Null hypothesis

A null hypothesis proposes no relationship between two variables. Denoted by H 0 , it is a negative statement like “Attending physiotherapy sessions does not affect athletes' on-field performance.” Here, the author claims physiotherapy sessions have no effect on on-field performances. Even if there is, it's only a coincidence.

2. Alternative hypothesis

Considered to be the opposite of a null hypothesis, an alternative hypothesis is donated as H1 or Ha. It explicitly states that the dependent variable affects the independent variable. A good  alternative hypothesis example is “Attending physiotherapy sessions improves athletes' on-field performance.” or “Water evaporates at 100 °C. ” The alternative hypothesis further branches into directional and non-directional.

• Directional hypothesis: A hypothesis that states the result would be either positive or negative is called directional hypothesis. It accompanies H1 with either the ‘<' or ‘>' sign.
• Non-directional hypothesis: A non-directional hypothesis only claims an effect on the dependent variable. It does not clarify whether the result would be positive or negative. The sign for a non-directional hypothesis is ‘≠.'

3. Simple hypothesis

A simple hypothesis is a statement made to reflect the relation between exactly two variables. One independent and one dependent. Consider the example, “Smoking is a prominent cause of lung cancer." The dependent variable, lung cancer, is dependent on the independent variable, smoking.

4. Complex hypothesis

In contrast to a simple hypothesis, a complex hypothesis implies the relationship between multiple independent and dependent variables. For instance, “Individuals who eat more fruits tend to have higher immunity, lesser cholesterol, and high metabolism.” The independent variable is eating more fruits, while the dependent variables are higher immunity, lesser cholesterol, and high metabolism.

5. Associative and casual hypothesis

Associative and casual hypotheses don't exhibit how many variables there will be. They define the relationship between the variables. In an associative hypothesis, changing any one variable, dependent or independent, affects others. In a casual hypothesis, the independent variable directly affects the dependent.

6. Empirical hypothesis

Also referred to as the working hypothesis, an empirical hypothesis claims a theory's validation via experiments and observation. This way, the statement appears justifiable and different from a wild guess.

Say, the hypothesis is “Women who take iron tablets face a lesser risk of anemia than those who take vitamin B12.” This is an example of an empirical hypothesis where the researcher  the statement after assessing a group of women who take iron tablets and charting the findings.

7. Statistical hypothesis

The point of a statistical hypothesis is to test an already existing hypothesis by studying a population sample. Hypothesis like “44% of the Indian population belong in the age group of 22-27.” leverage evidence to prove or disprove a particular statement.

Characteristics of a Good Hypothesis

Writing a hypothesis is essential as it can make or break your research for you. That includes your chances of getting published in a journal. So when you're designing one, keep an eye out for these pointers:

• A research hypothesis has to be simple yet clear to look justifiable enough.
• It has to be testable — your research would be rendered pointless if too far-fetched into reality or limited by technology.
• It has to be precise about the results —what you are trying to do and achieve through it should come out in your hypothesis.
• A research hypothesis should be self-explanatory, leaving no doubt in the reader's mind.
• If you are developing a relational hypothesis, you need to include the variables and establish an appropriate relationship among them.
• A hypothesis must keep and reflect the scope for further investigations and experiments.

Separating a Hypothesis from a Prediction

Outside of academia, hypothesis and prediction are often used interchangeably. In research writing, this is not only confusing but also incorrect. And although a hypothesis and prediction are guesses at their core, there are many differences between them.

A hypothesis is an educated guess or even a testable prediction validated through research. It aims to analyze the gathered evidence and facts to define a relationship between variables and put forth a logical explanation behind the nature of events.

Predictions are assumptions or expected outcomes made without any backing evidence. They are more fictionally inclined regardless of where they originate from.

For this reason, a hypothesis holds much more weight than a prediction. It sticks to the scientific method rather than pure guesswork. "Planets revolve around the Sun." is an example of a hypothesis as it is previous knowledge and observed trends. Additionally, we can test it through the scientific method.

Whereas "COVID-19 will be eradicated by 2030." is a prediction. Even though it results from past trends, we can't prove or disprove it. So, the only way this gets validated is to wait and watch if COVID-19 cases end by 2030.

Finally, How to Write a Hypothesis

Quick tips on writing a hypothesis

1.  Be clear about your research question

A hypothesis should instantly address the research question or the problem statement. To do so, you need to ask a question. Understand the constraints of your undertaken research topic and then formulate a simple and topic-centric problem. Only after that can you develop a hypothesis and further test for evidence.

2. Carry out a recce

Once you have your research's foundation laid out, it would be best to conduct preliminary research. Go through previous theories, academic papers, data, and experiments before you start curating your research hypothesis. It will give you an idea of your hypothesis's viability or originality.

Making use of references from relevant research papers helps draft a good research hypothesis. SciSpace Discover offers a repository of over 270 million research papers to browse through and gain a deeper understanding of related studies on a particular topic. Additionally, you can use SciSpace Copilot , your AI research assistant, for reading any lengthy research paper and getting a more summarized context of it. A hypothesis can be formed after evaluating many such summarized research papers. Copilot also offers explanations for theories and equations, explains paper in simplified version, allows you to highlight any text in the paper or clip math equations and tables and provides a deeper, clear understanding of what is being said. This can improve the hypothesis by helping you identify potential research gaps.

3. Create a 3-dimensional hypothesis

Variables are an essential part of any reasonable hypothesis. So, identify your independent and dependent variable(s) and form a correlation between them. The ideal way to do this is to write the hypothetical assumption in the ‘if-then' form. If you use this form, make sure that you state the predefined relationship between the variables.

In another way, you can choose to present your hypothesis as a comparison between two variables. Here, you must specify the difference you expect to observe in the results.

4. Write the first draft

Now that everything is in place, it's time to write your hypothesis. For starters, create the first draft. In this version, write what you expect to find from your research.

Clearly separate your independent and dependent variables and the link between them. Don't fixate on syntax at this stage. The goal is to ensure your hypothesis addresses the issue.

5. Proof your hypothesis

After preparing the first draft of your hypothesis, you need to inspect it thoroughly. It should tick all the boxes, like being concise, straightforward, relevant, and accurate. Your final hypothesis has to be well-structured as well.

Research projects are an exciting and crucial part of being a scholar. And once you have your research question, you need a great hypothesis to begin conducting research. Thus, knowing how to write a hypothesis is very important.

Now that you have a firmer grasp on what a good hypothesis constitutes, the different kinds there are, and what process to follow, you will find it much easier to write your hypothesis, which ultimately helps your research.

Now it's easier than ever to streamline your research workflow with SciSpace Discover . Its integrated, comprehensive end-to-end platform for research allows scholars to easily discover, write and publish their research and fosters collaboration.

It includes everything you need, including a repository of over 270 million research papers across disciplines, SEO-optimized summaries and public profiles to show your expertise and experience.

If you found these tips on writing a research hypothesis useful, head over to our blog on Statistical Hypothesis Testing to learn about the top researchers, papers, and institutions in this domain.

Frequently Asked Questions (FAQs)

1. what is the definition of hypothesis.

According to the Oxford dictionary, a hypothesis is defined as “An idea or explanation of something that is based on a few known facts, but that has not yet been proved to be true or correct”.

2. What is an example of hypothesis?

The hypothesis is a statement that proposes a relationship between two or more variables. An example: "If we increase the number of new users who join our platform by 25%, then we will see an increase in revenue."

3. What is an example of null hypothesis?

A null hypothesis is a statement that there is no relationship between two variables. The null hypothesis is written as H0. The null hypothesis states that there is no effect. For example, if you're studying whether or not a particular type of exercise increases strength, your null hypothesis will be "there is no difference in strength between people who exercise and people who don't."

4. What are the types of research?

• Fundamental research

• Applied research

• Qualitative research

• Quantitative research

• Mixed research

• Exploratory research

• Longitudinal research

• Cross-sectional research

• Field research

• Laboratory research

• Fixed research

• Flexible research

• Action research

• Policy research

• Classification research

• Comparative research

• Causal research

• Inductive research

• Deductive research

5. How to write a hypothesis?

• Your hypothesis should be able to predict the relationship and outcome.

• Avoid wordiness by keeping it simple and brief.

• Your hypothesis should contain observable and testable outcomes.

• Your hypothesis should be relevant to the research question.

6. What are the 2 types of hypothesis?

• Null hypotheses are used to test the claim that "there is no difference between two groups of data".

• Alternative hypotheses test the claim that "there is a difference between two data groups".

7. Difference between research question and research hypothesis?

A research question is a broad, open-ended question you will try to answer through your research. A hypothesis is a statement based on prior research or theory that you expect to be true due to your study. Example - Research question: What are the factors that influence the adoption of the new technology? Research hypothesis: There is a positive relationship between age, education and income level with the adoption of the new technology.

8. What is plural for hypothesis?

The plural of hypothesis is hypotheses. Here's an example of how it would be used in a statement, "Numerous well-considered hypotheses are presented in this part, and they are supported by tables and figures that are well-illustrated."

9. What is the red queen hypothesis?

The red queen hypothesis in evolutionary biology states that species must constantly evolve to avoid extinction because if they don't, they will be outcompeted by other species that are evolving. Leigh Van Valen first proposed it in 1973; since then, it has been tested and substantiated many times.

10. Who is known as the father of null hypothesis?

The father of the null hypothesis is Sir Ronald Fisher. He published a paper in 1925 that introduced the concept of null hypothesis testing, and he was also the first to use the term itself.

11. When to reject null hypothesis?

You need to find a significant difference between your two populations to reject the null hypothesis. You can determine that by running statistical tests such as an independent sample t-test or a dependent sample t-test. You should reject the null hypothesis if the p-value is less than 0.05.

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Hypothesis Testing Used in Business

Business owners like to know how their decisions will impact their businesses. According to Harvard Business School Online, before making decisions, managers may explore the benefits of hypothesis testing, the experimentation of decisions in a "laboratory" setting. By making such tests, managers can have more confidence in their decisions.

Hypothesis Testing Explained

Hypothesis testing involves discerning the effect of one factor on another by exploring the relationship's statistical significance. Hypothesis testing in business examples might include a restaurant owner interested in how adding additional house sauce to their chicken sandwich impacts customer satisfaction. Or, in a social media marketing company, a hypothesis test could be set up in order to explain how much an increase in labor affects productivity. Thus, hypothesis testing serves to explore the relationship between two or more variables in an experimental setting. Business managers may then use the results of a hypothesis test when making management decisions. Hypothesis testing allows managers to examine causes and effects before making a crucial management decision.

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As hypothesis testing is purely a statistical exercise, data is almost always needed before performing a test. Data may be obtained from economic research agencies or management consultancy firms, who may even carry out the hypothesis testing on behalf of the business. Data are compiled for a given hypothesis. So if a business wishes to explore how economic growth affects a firm's profits, the management consultancy will likely collect data concerning gross domestic product growth and the profit margins of the company over the past 10 or 20 years.

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Nitty Gritty of the Hypothesis

When the management consultancy has collected an adequate amount of data, an equation is set up, which would look something like y=ax+b. Using the same example of economic growth and profits, "x" would denote economic growth while "y" would denote company profits. This is because the company wishes to test the effect of "x" on "y."

The parts of the equation the represent real interest is that of "a" and "b." The y-intercept is represented by "b" and the slope of the equation is represented by "a." The hypothesis test focuses on how big "a" is. If "a" were large, then a small change in economic growth would greatly affect company profits. If it were equal to zero, then there would be no effect. The testable hypothesis, or the "null," would be if "a" equals zero. Rejecting the null would imply that economic growth does in fact affect profits.

Hypothesis Testing Processes

Hypothesis testing is performed with specialized statistical software that examines the relationship between variables of very large samples. Data is fed into the system and the program does the rest. It is up to the statistician to interpret the results.

According to Reference for Business, there are two main variables the statistician is looking for. The first is that of "a" itself. The larger the value of "a," the greater the impact of "x" on "y." The other is that of the critical values. Critical values differ depending on the type of statistical test carried out, but often values represent significance levels of 1, 5 or 10 percent. Rejecting the null at 1 percent implies absolute confidence that "x" has no effect on "y." On the flip side, if the statistician is unable to reject the null even at the 10 percent level, then he could say with a reasonable level that "x" does have an impact on "y," and at a magnitude of "a."

• Harvard Business School Online: A Beginner's Guide to Hypothesis Testing in Business
• Reference for Business: Hypothesis Testing

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Lesson 10 of 24 By Avijeet Biswal

Table of Contents

In today’s data-driven world, decisions are based on data all the time. Hypothesis plays a crucial role in that process, whether it may be making business decisions, in the health sector, academia, or in quality improvement. Without hypothesis and hypothesis tests, you risk drawing the wrong conclusions and making bad decisions. In this tutorial, you will look at Hypothesis Testing in Statistics.

What Is Hypothesis Testing in Statistics?

Hypothesis Testing is a type of statistical analysis in which you put your assumptions about a population parameter to the test. It is used to estimate the relationship between 2 statistical variables.

Let's discuss few examples of statistical hypothesis from real-life - 

• A teacher assumes that 60% of his college's students come from lower-middle-class families.
• A doctor believes that 3D (Diet, Dose, and Discipline) is 90% effective for diabetic patients.

Now that you know about hypothesis testing, look at the two types of hypothesis testing in statistics.

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Importance of Hypothesis Testing in Data Analysis

Here is what makes hypothesis testing so important in data analysis and why it is key to making better decisions:

Avoiding Misleading Conclusions (Type I and Type II Errors)

One of the biggest benefits of hypothesis testing is that it helps you avoid jumping to the wrong conclusions. For instance, a Type I error could occur if a company launches a new product thinking it will be a hit, only to find out later that the data misled them. A Type II error might happen when a company overlooks a potentially successful product because their testing wasn’t thorough enough. By setting up the right significance level and carefully calculating the p-value, hypothesis testing minimizes the chances of these errors, leading to more accurate results.

Making Smarter Choices

Hypothesis testing is key to making smarter, evidence-based decisions. Let’s say a city planner wants to determine if building a new park will increase community engagement. By testing the hypothesis using data from similar projects, they can make an informed choice. Similarly, a teacher might use hypothesis testing to see if a new teaching method actually improves student performance. It’s about taking the guesswork out of decisions and relying on solid evidence instead.

Optimizing Business Tactics

In business, hypothesis testing is invaluable for testing new ideas and strategies before fully committing to them. For example, an e-commerce company might want to test whether offering free shipping increases sales. By using hypothesis testing, they can compare sales data from customers who received free shipping offers and those who didn’t. This allows them to base their business decisions on data, not hunches, reducing the risk of costly mistakes.

Hypothesis Testing Formula

Z = ( x̅ – μ0 ) / (σ /√n)

• Here, x̅ is the sample mean,
• μ0 is the population mean,
• σ is the standard deviation,
• n is the sample size.

How Hypothesis Testing Works?

An analyst performs hypothesis testing on a statistical sample to present evidence of the plausibility of the null hypothesis. Measurements and analyses are conducted on a random sample of the population to test a theory. Analysts use a random population sample to test two hypotheses: the null and alternative hypotheses.

The null hypothesis is typically an equality hypothesis between population parameters; for example, a null hypothesis may claim that the population means return equals zero. The alternate hypothesis is essentially the inverse of the null hypothesis (e.g., the population means the return is not equal to zero). As a result, they are mutually exclusive, and only one can be correct. One of the two possibilities, however, will always be correct.

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Null Hypothesis and Alternative Hypothesis

The Null Hypothesis is the assumption that the event will not occur. A null hypothesis has no bearing on the study's outcome unless it is rejected.

H0 is the symbol for it, and it is pronounced H-naught.

The Alternate Hypothesis is the logical opposite of the null hypothesis. The acceptance of the alternative hypothesis follows the rejection of the null hypothesis. H1 is the symbol for it.

Let's understand this with an example.

A sanitizer manufacturer claims that its product kills 95 percent of germs on average. 

To put this company's claim to the test, create a null and alternate hypothesis.

H0 (Null Hypothesis): Average = 95%.

Alternative Hypothesis (H1): The average is less than 95%.

Another straightforward example to understand this concept is determining whether or not a coin is fair and balanced. The null hypothesis states that the probability of a show of heads is equal to the likelihood of a show of tails. In contrast, the alternate theory states that the probability of a show of heads and tails would be very different.

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Hypothesis Testing Calculation With Examples

Let's consider a hypothesis test for the average height of women in the United States. Suppose our null hypothesis is that the average height is 5'4". We gather a sample of 100 women and determine their average height is 5'5". The standard deviation of population is 2.

To calculate the z-score, we would use the following formula:

z = ( x̅ – μ0 ) / (σ /√n)

z = (5'5" - 5'4") / (2" / √100)

z = 0.5 / (0.045)

We will reject the null hypothesis as the z-score of 11.11 is very large and conclude that there is evidence to suggest that the average height of women in the US is greater than 5'4".

Steps in Hypothesis Testing

Hypothesis testing is a statistical method to determine if there is enough evidence in a sample of data to infer that a certain condition is true for the entire population. Here’s a breakdown of the typical steps involved in hypothesis testing:

Formulate Hypotheses

• Null Hypothesis (H0): This hypothesis states that there is no effect or difference, and it is the hypothesis you attempt to reject with your test.
• Alternative Hypothesis (H1 or Ha): This hypothesis is what you might believe to be true or hope to prove true. It is usually considered the opposite of the null hypothesis.

Choose the Significance Level (α)

The significance level, often denoted by alpha (α), is the probability of rejecting the null hypothesis when it is true. Common choices for α are 0.05 (5%), 0.01 (1%), and 0.10 (10%).

Select the Appropriate Test

Choose a statistical test based on the type of data and the hypothesis. Common tests include t-tests, chi-square tests, ANOVA, and regression analysis. The selection depends on data type, distribution, sample size, and whether the hypothesis is one-tailed or two-tailed.

Collect Data

Gather the data that will be analyzed in the test. To infer conclusions accurately, this data should be representative of the population.

Calculate the Test Statistic

Based on the collected data and the chosen test, calculate a test statistic that reflects how much the observed data deviates from the null hypothesis.

Determine the p-value

The p-value is the probability of observing test results at least as extreme as the results observed, assuming the null hypothesis is correct. It helps determine the strength of the evidence against the null hypothesis.

Make a Decision

Compare the p-value to the chosen significance level:

• If the p-value ≤ α: Reject the null hypothesis, suggesting sufficient evidence in the data supports the alternative hypothesis.
• If the p-value > α: Do not reject the null hypothesis, suggesting insufficient evidence to support the alternative hypothesis.

Report the Results

Present the findings from the hypothesis test, including the test statistic, p-value, and the conclusion about the hypotheses.

Perform Post-hoc Analysis (if necessary)

Depending on the results and the study design, further analysis may be needed to explore the data more deeply or to address multiple comparisons if several hypotheses were tested simultaneously.

Types of Hypothesis Testing

To determine whether a discovery or relationship is statistically significant, hypothesis testing uses a z-test. It usually checks to see if two means are the same (the null hypothesis). Only when the population standard deviation is known and the sample size is 30 data points or more, can a z-test be applied.

A statistical test called a t-test is employed to compare the means of two groups. To determine whether two groups differ or if a procedure or treatment affects the population of interest, it is frequently used in hypothesis testing.

3. Chi-Square 

You utilize a Chi-square test for hypothesis testing concerning whether your data is as predicted. To determine if the expected and observed results are well-fitted, the Chi-square test analyzes the differences between categorical variables from a random sample. The test's fundamental premise is that the observed values in your data should be compared to the predicted values that would be present if the null hypothesis were true.

ANOVA , or Analysis of Variance, is a statistical method used to compare the means of three or more groups. It’s particularly useful when you want to see if there are significant differences between multiple groups. For instance, in business, a company might use ANOVA to analyze whether three different stores are performing differently in terms of sales. It’s also widely used in fields like medical research and social sciences, where comparing group differences can provide valuable insights.

Hypothesis Testing and Confidence Intervals

Both confidence intervals and hypothesis tests are inferential techniques that depend on approximating the sample distribution. Data from a sample is used to estimate a population parameter using confidence intervals. Data from a sample is used in hypothesis testing to examine a given hypothesis. We must have a postulated parameter to conduct hypothesis testing.

Bootstrap distributions and randomization distributions are created using comparable simulation techniques. The observed sample statistic is the focal point of a bootstrap distribution, whereas the null hypothesis value is the focal point of a randomization distribution.

A variety of feasible population parameter estimates are included in confidence ranges. In this lesson, we created just two-tailed confidence intervals. There is a direct connection between these two-tail confidence intervals and these two-tail hypothesis tests. The results of a two-tailed hypothesis test and two-tailed confidence intervals typically provide the same results. In other words, a hypothesis test at the 0.05 level will virtually always fail to reject the null hypothesis if the 95% confidence interval contains the predicted value. A hypothesis test at the 0.05 level will nearly certainly reject the null hypothesis if the 95% confidence interval does not include the hypothesized parameter.

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Simple and Composite Hypothesis Testing

Depending on the population distribution, you can classify the statistical hypothesis into two types.

Simple Hypothesis: A simple hypothesis specifies an exact value for the parameter.

Composite Hypothesis: A composite hypothesis specifies a range of values.

A company is claiming that their average sales for this quarter are 1000 units. This is an example of a simple hypothesis.

Suppose the company claims that the sales are in the range of 900 to 1000 units. Then this is a case of a composite hypothesis.

One-Tailed and Two-Tailed Hypothesis Testing

The One-Tailed test, also called a directional test, considers a critical region of data that would result in the null hypothesis being rejected if the test sample falls into it, inevitably meaning the acceptance of the alternate hypothesis.

In a one-tailed test, the critical distribution area is one-sided, meaning the test sample is either greater or lesser than a specific value.

In two tails, the test sample is checked to be greater or less than a range of values in a Two-Tailed test, implying that the critical distribution area is two-sided.

If the sample falls within this range, the alternate hypothesis will be accepted, and the null hypothesis will be rejected.

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Right Tailed Hypothesis Testing

If the larger than (>) sign appears in your hypothesis statement, you are using a right-tailed test, also known as an upper test. Or, to put it another way, the disparity is to the right. For instance, you can contrast the battery life before and after a change in production. Your hypothesis statements can be the following if you want to know if the battery life is longer than the original (let's say 90 hours):

• The null hypothesis is (H0 <= 90) or less change.
• A possibility is that battery life has risen (H1) > 90.

The crucial point in this situation is that the alternate hypothesis (H1), not the null hypothesis, decides whether you get a right-tailed test.

Left Tailed Hypothesis Testing

Alternative hypotheses that assert the true value of a parameter is lower than the null hypothesis are tested with a left-tailed test; they are indicated by the asterisk "<".

Suppose H0: mean = 50 and H1: mean not equal to 50

According to the H1, the mean can be greater than or less than 50. This is an example of a Two-tailed test.

In a similar manner, if H0: mean >=50, then H1: mean <50

Here the mean is less than 50. It is called a One-tailed test.

Type 1 and Type 2 Error

A hypothesis test can result in two types of errors.

Type 1 Error: A Type-I error occurs when sample results reject the null hypothesis despite being true.

Type 2 Error: A Type-II error occurs when the null hypothesis is not rejected when it is false, unlike a Type-I error.

Suppose a teacher evaluates the examination paper to decide whether a student passes or fails.

H0: Student has passed

H1: Student has failed

Type I error will be the teacher failing the student [rejects H0] although the student scored the passing marks [H0 was true]. 

Type II error will be the case where the teacher passes the student [do not reject H0] although the student did not score the passing marks [H1 is true].

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Practice Problems on Hypothesis Testing

Here are the practice problems on hypothesis testing that will help you understand how to apply these concepts in real-world scenarios:

A telecom service provider claims that customers spend an average of ₹400 per month, with a standard deviation of ₹25. However, a random sample of 50 customer bills shows a mean of ₹250 and a standard deviation of ₹15. Does this sample data support the service provider’s claim?

Solution: Let’s break this down:

• Null Hypothesis (H0): The average amount spent per month is ₹400.
• Alternate Hypothesis (H1): The average amount spent per month is not ₹400.
• Population Standard Deviation (σ): ₹25
• Sample Size (n): 50
• Sample Mean (x̄): ₹250

1. Calculate the z-value:

z=250-40025/50 −42.42

2. Compare with critical z-values: For a 5% significance level, critical z-values are -1.96 and +1.96. Since -42.42 is far outside this range, we reject the null hypothesis. The sample data suggests that the average amount spent is significantly different from ₹400.

Out of 850 customers, 400 made online grocery purchases. Can we conclude that more than 50% of customers are moving towards online grocery shopping?

Solution: Here’s how to approach it:

• Proportion of customers who shopped online (p): 400 / 850 = 0.47
• Null Hypothesis (H0): The proportion of online shoppers is 50% or more.
• Alternate Hypothesis (H1): The proportion of online shoppers is less than 50%.
• Sample Size (n): 850
• Significance Level (α): 5%

z=p-PP(1-P)/n

z=0.47-0.500.50.5/850  −1.74

2. Compare with the critical z-value: For a 5% significance level (one-tailed test), the critical z-value is -1.645. Since -1.74 is less than -1.645, we reject the null hypothesis. This means the data does not support the idea that most customers are moving towards online grocery shopping.

In a study of code quality, Team A has 250 errors in 1000 lines of code, and Team B has 300 errors in 800 lines of code. Can we say Team B performs worse than Team A?

Solution: Let’s analyze it:

• Proportion of errors for Team A (pA): 250 / 1000 = 0.25
• Proportion of errors for Team B (pB): 300 / 800 = 0.375
• Null Hypothesis (H0): Team B’s error rate is less than or equal to Team A’s.
• Alternate Hypothesis (H1): Team B’s error rate is greater than Team A’s.
• Sample Size for Team A (nA): 1000
• Sample Size for Team B (nB): 800

p=nApA+nBpBnA+nB

p=10000.25+8000.3751000+800 ≈ 0.305

z=​pA−pB​p(1-p)(1nA+1nB)

z=​0.25−0.375​0.305(1-0.305) (11000+1800) ≈ −5.72

2. Compare with the critical z-value: For a 5% significance level (one-tailed test), the critical z-value is +1.645. Since -5.72 is far less than +1.645, we reject the null hypothesis. The data indicates that Team B’s performance is significantly worse than Team A’s.

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Applications of Hypothesis Testing

Apart from the practical problems, let's look at the real-world applications of hypothesis testing across various fields:

Medicine and Healthcare

In medicine, hypothesis testing plays a pivotal role in assessing the success of new treatments. For example, researchers may want to find out if a new exercise regimen improves heart health. By comparing data from patients who followed the program to those who didn’t, they can determine if the exercise significantly improves health outcomes. Such rigorous testing allows medical professionals to rely on proven methods rather than assumptions.

Quality Control and Manufacturing

In manufacturing, ensuring product quality is vital, and hypothesis testing helps maintain those standards. Suppose a beverage company introduces a new bottling process and wants to verify if it reduces contamination. By analyzing samples from the new and old processes, hypothesis testing can reveal whether the new method reduces the risk of contamination. This allows manufacturers to implement improvements that enhance product safety and quality confidently.

Education and Learning

In education and learning, hypothesis testing is a tool to evaluate the impact of innovative teaching techniques. Imagine a situation where teachers introduce project-based learning to boost critical thinking skills. By comparing the performance of students who engaged in project-based learning with those in traditional settings, educators can test their hypothesis. The results can help educators make informed choices about adopting new teaching strategies.

Environmental Science

Hypothesis testing is essential in environmental science for evaluating the effectiveness of conservation measures. For example, scientists might explore whether a new water management strategy improves river health. By collecting and comparing data on water quality before and after the implementation of the strategy, they can determine whether the intervention leads to positive changes. Such findings are crucial for guiding environmental decisions that have long-term impacts.

Marketing and Advertising

In marketing, businesses use hypothesis testing to refine their approaches. For instance, a clothing brand might test if offering limited-time discounts increases customer loyalty. By running campaigns with and without the discount and analyzing the outcomes, they can assess if the strategy boosts customer retention. Data-driven insights from hypothesis testing enable companies to design marketing strategies that resonate with their audience and drive growth.

Limitations of Hypothesis Testing

Hypothesis testing has some limitations that researchers should be aware of:

• It cannot prove or establish the truth: Hypothesis testing provides evidence to support or reject a hypothesis, but it cannot confirm the absolute truth of the research question.
• Results are sample-specific: Hypothesis testing is based on analyzing a sample from a population, and the conclusions drawn are specific to that particular sample.
• Possible errors: During hypothesis testing, there is a chance of committing type I error (rejecting a true null hypothesis) or type II error (failing to reject a false null hypothesis).
• Assumptions and requirements: Different tests have specific assumptions and requirements that must be met to accurately interpret results.

Learn All The Tricks Of The BI Trade

After reading this tutorial, you would have a much better understanding of hypothesis testing, one of the most important concepts in the field of Data Science . The majority of hypotheses are based on speculation about observed behavior, natural phenomena, or established theories.

If you are interested in statistics of data science and skills needed for such a career, you ought to explore the Post Graduate Program in Data Science.

1. What is hypothesis testing in statistics with example?

Hypothesis testing is a statistical method used to determine if there is enough evidence in a sample data to draw conclusions about a population. It involves formulating two competing hypotheses, the null hypothesis (H0) and the alternative hypothesis (Ha), and then collecting data to assess the evidence. An example: testing if a new drug improves patient recovery (Ha) compared to the standard treatment (H0) based on collected patient data.

2. What is H0 and H1 in statistics?

In statistics, H0​ and H1​ represent the null and alternative hypotheses. The null hypothesis, H0​, is the default assumption that no effect or difference exists between groups or conditions. The alternative hypothesis, H1​, is the competing claim suggesting an effect or a difference. Statistical tests determine whether to reject the null hypothesis in favor of the alternative hypothesis based on the data.

3. What is a simple hypothesis with an example?

A simple hypothesis is a specific statement predicting a single relationship between two variables. It posits a direct and uncomplicated outcome. For example, a simple hypothesis might state, "Increased sunlight exposure increases the growth rate of sunflowers." Here, the hypothesis suggests a direct relationship between the amount of sunlight (independent variable) and the growth rate of sunflowers (dependent variable), with no additional variables considered.

4. What are the 3 major types of hypothesis?

The three major types of hypotheses are:

• Null Hypothesis (H0): Represents the default assumption, stating that there is no significant effect or relationship in the data.
• Alternative Hypothesis (Ha): Contradicts the null hypothesis and proposes a specific effect or relationship that researchers want to investigate.
• Nondirectional Hypothesis: An alternative hypothesis that doesn't specify the direction of the effect, leaving it open for both positive and negative possibilities.

5. What software tools can assist with hypothesis testing?

Several software tools offering distinct features can help with hypothesis testing. R and RStudio are popular for their advanced statistical capabilities. The Python ecosystem, including libraries like SciPy and Statsmodels, also supports hypothesis testing. SAS and SPSS are well-established tools for comprehensive statistical analysis. For basic testing, Excel offers simple built-in functions.

6. How do I interpret the results of a hypothesis test?

Interpreting hypothesis test results involves comparing the p-value to the significance level (alpha). If the p-value is less than or equal to alpha, you can reject the null hypothesis, indicating statistical significance. This suggests that the observed effect is unlikely to have occurred by chance, validating your analysis findings.

7. Why is sample size important in hypothesis testing?

Sample size is crucial in hypothesis testing as it affects the test’s power. A larger sample size increases the likelihood of detecting a true effect, reducing the risk of Type II errors. Conversely, a small sample may lack the statistical power needed to identify differences, potentially leading to inaccurate conclusions.

8. Can hypothesis testing be used for non-numerical data?

Yes, hypothesis testing can be applied to non-numerical data through non-parametric tests. These tests are ideal when data doesn't meet parametric assumptions or when dealing with categorical data. Non-parametric tests, like the Chi-square or Mann-Whitney U test, provide robust methods for analyzing non-numerical data and drawing meaningful conclusions.

9. How do I choose the proper hypothesis test?

Selecting the right hypothesis test depends on several factors: the objective of your analysis, the type of data (numerical or categorical), and the sample size. Consider whether you're comparing means, proportions, or associations, and whether your data follows a normal distribution. The correct choice ensures accurate results tailored to your research question.

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About the Author

Avijeet is a Senior Research Analyst at Simplilearn. Passionate about Data Analytics, Machine Learning, and Deep Learning, Avijeet is also interested in politics, cricket, and football.

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Strategic Team Building | Benefits Of Hypothesis For Business

By Joe Ferraro | 11 September, 2024

In today’s competitive business environment, teamwork is the key to success. Teams can work together smoothly and effectively by using Hypothesis, a simple yet powerful way to explore ideas and solve problems. By combining Hypothesis with business collaboration tools , teams can communicate better, make smarter decisions, and drive innovation.

In this blog, we’ll explore practical steps and examples that show how applying Hypothesis for  business , supported by the right tools, can lead to successful business strategies and improved team dynamics. Get ready to change the way you think about teamwork and tools in business!

What Is Hypothesis for Business ? 

A hypothesis business is similar to one in science, it’s a guess or prediction made based on existing knowledge that can be tested through further investigation and analysis. In a business context, Hypothesis help teams focus on potential outcomes and test different strategies before fully committing resources. This method helps a culture of evidence-based decision-making and reduces the risk associated with new initiatives.

Hypothesis encourage team members to think critically and test their assumptions, ensuring that every decision is backed by thoughtful consideration and data. Meanwhile, business collaboration tools provide the necessary platform for sharing these ideas and insights, keeping everyone on the same page. Whether you’re working on a small project or a major enterprise, integrating these strategies can transform the way your team operates, making collaboration seamless and more productive.

The Importance Of Hypothesis In Strategic Team Building

• Encourages A Proactive Approach : The hypothesis compels team members to think ahead, anticipate potential outcomes, and prepare for obstacles, promoting a proactive work culture essential in today’s advanced business environment.
• Promote Innovation : By questioning assumptions and validating ideas through systematic testing, hypothesis encourage creative problem-solving and innovation, allowing teams to explore a wide range of possibilities.
• Reduces Waste : Hypothesis helps minimize the wastage of resources, such as time and money, by identifying less viable options early, ensuring that only the most promising ideas are pursued.
• Enhances Learning And Adaptation : Testing hypothesis provides valuable insights, into whether outcomes validate or refute the initial assumptions, which is important for continuous improvement and adaptation to ever-changing business dynamics.
• Promotes Risk Management : The hypothesis allows teams to assess risks in a controlled environment, making it possible to manage potential downsides more effectively before full-scale implementation.
• Improves Decision-Making Quality : The structured approach of hypothesis promotes data-driven decision-making, which tends to be more accurate and effective, leading to better outcomes for the business.
• Strengthens Team Collaboration : As teams come together to formulate, test, and revise hypothesis, the collaborative process is strengthened. This unity helps in building a cohesive team capable of tackling complex projects.
• Clarifies Objectives And Focus : Working with hypothesis requires clear objectives and a focused approach, which helps teams stay aligned with the business’s overall goals and ensures that everyone is working towards the same end.
• Increases Accountability : When teams operate under hypothesis, each member becomes accountable for contributing to the testing and proving of these assumptions, helping a sense of responsibility and ownership.
• Enables Scalability : Hypothesis can be scaled across different teams and departments, allowing successful strategies to be replicated and adapted throughout the organization, leading to overall improvement and efficiency.

Leveraging Business Collaboration Tools

To effectively test and implement hypothesis, businesses must utilize collaboration tools. These tools not only facilitate communication but also ensure that all team members are aligned and informed. Some of the key functionalities of these tools include:

• Document Sharing And Management : Tools like Google Drive and Microsoft OneDrive allow teams to store, share, and edit documents in real-time, ensuring everyone has access to the latest information.
• Communication Platforms : Slack and Microsoft Teams enable real-time messaging, video calls, and team meetings, making it easier to discuss hypothesis and updates without delay.
• Project Management Software : Asana and Trello provide platforms for tracking project progress, assigning tasks, and setting deadlines. These tools help in organizing the testing of hypothesis and monitoring outcomes.
• Data Analysis Tools : Software like Tableau and Microsoft Power BI helps in analyzing data to test hypotheses. These tools can transform raw data into actionable insights, supporting evidence-based decision-making.

Integrating Hypothesis With Collaboration Tools

The integration of Hypothesis and collaboration tools can be transformative, but it requires a structured approach. Here’s how businesses can effectively combine these elements:

• Define Clear Objectives : Start by clearly defining what you want to achieve with your hypothesis. This clarity will guide the testing process and the use of tools.
• Develop A Testable Hypothesis : Ensure the hypothesis is specific, measurable, achievable, relevant, and time-bound (SMART). This specificity will help in the accurate testing and analysis of results.
• Select Appropriate Tools : Choose collaboration tools that best fit your team’s needs and the specifics of the hypothesis being tested. Consider factors like usability, scalability, and integration capabilities.
• Conduct Tests And Collect Data : Use the selected tools to conduct experiments and collect data. Ensure all team members know their roles and how to use the tools effectively to contribute to the process.
• Analyze Results And Make Decisions : Analyze the data to determine whether the hypothesis holds. Use the insights gained to make informed decisions and refine your business strategies.
• Document And Share Learnings : Utilize your collaboration tools to document the outcomes and share learnings with the team. This step ensures that everyone benefits from the experience, regardless of their direct involvement in the testing phase.

Using Hypothesis For Business

The hypothesis for business is a methodical way to approach problem-solving, decision-making, and strategy development. Here’s a step-by-step guide on how to effectively utilize hypothesis in your business processes:

1. Identify The Problem Or Opportunity

Start by clearly defining the problem you want to solve or the opportunity you want to explore. This will form the basis of your hypothesis. It’s essential to be as specific as possible to ensure that your hypothesis is relevant and actionable.

2. Formulate The Hypothesis

A hypothesis is essentially an educated guess about a potential outcome. It should be specific, testable, and based on observations or preliminary data. For example, “Implementing an online ordering system will increase our restaurant’s sales by 20% within the first three months.”

3. Gather Data

Before you can test your hypothesis, gather the necessary data that will inform your experiment. This may involve collecting historical business data, industry benchmarks, or customer feedback relevant to your hypothesis.

4. Design The Experiment

Plan how you will test your hypothesis. This involves setting up the conditions under which you will observe outcomes and decide on the metrics that will indicate success or failure. Ensure that the test is controlled and that variables not related to the hypothesis are minimized.

5. Conduct The Experiment

Implement the changes or introduce the new elements required by your hypothesis. This might involve launching a new marketing campaign, changing a production process, or introducing a new product feature. Monitor the experiment closely to gather real-time data.

6. Analyze The Results

After the experiment, analyze the data to see whether it supports or refutes your hypothesis. Use statistical tools to ensure your findings are valid and reliable. It’s important to remain unbiased and objective during this step.

7. Make Decisions

Based on the results of your hypothesis test, make informed decisions. If the hypothesis is confirmed, consider implementing the change on a larger scale. If it is refuted, use the insights gained to refine your hypothesis or abandon the approach.

8. Refine And Repeat

Whether your hypothesis was confirmed or not, there’s always more to learn. Use the results as a stepping stone to further refine your approach. Adjust your hypothesis based on the insights gained and repeat the process with a new hypothesis to continue optimizing your business operations.

9. Document Everything

Maintain thorough documentation of your hypothesis, the testing process, results, and decisions made. This documentation will help you track progress over time, provide insights into what works and what doesn’t, and inform future hypothesis.

10. Scale And Implement

For a hypothesis that proves successful, consider how to scale the successful initiative. This might involve broader implementation, integrating the change into standard business practices, or investing more resources.

Conclusion 

Incorporating Hypothesis for business practices can lead to more strategic decision-making and innovation. When combined with the right collaboration tools, this approach not only enhances the effectiveness of teamwork but also moves the business toward its objectives. By applying a culture that embraces hypothesis, businesses can ensure that every team action is as informed and impactful as possible.

By adapting to this hypothesis-driven approach, businesses can navigate the complexities of the modern market more effectively, ensuring both short-term success and long-term sustainability.

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Understanding Hypothesis Testing

Hypothesis testing involves formulating assumptions about population parameters based on sample statistics and rigorously evaluating these assumptions against empirical evidence. This article sheds light on the significance of hypothesis testing and the critical steps involved in the process.

What is Hypothesis Testing?

A hypothesis is an assumption or idea, specifically a statistical claim about an unknown population parameter. For example, a judge assumes a person is innocent and verifies this by reviewing evidence and hearing testimony before reaching a verdict.

Hypothesis testing is a statistical method that is used to make a statistical decision using experimental data. Hypothesis testing is basically an assumption that we make about a population parameter. It evaluates two mutually exclusive statements about a population to determine which statement is best supported by the sample data. 

To test the validity of the claim or assumption about the population parameter:

• A sample is drawn from the population and analyzed.
• The results of the analysis are used to decide whether the claim is true or not.

Example: You say an average height in the class is 30 or a boy is taller than a girl. All of these is an assumption that we are assuming, and we need some statistical way to prove these. We need some mathematical conclusion whatever we are assuming is true.

Defining Hypotheses

• Null hypothesis (H 0 ): In statistics, the null hypothesis is a general statement or default position that there is no relationship between two measured cases or no relationship among groups. In other words, it is a basic assumption or made based on the problem knowledge. Example : A company’s mean production is 50 units/per da H 0 : [Tex]\mu [/Tex] = 50.
• Alternative hypothesis (H 1 ): The alternative hypothesis is the hypothesis used in hypothesis testing that is contrary to the null hypothesis.  Example: A company’s production is not equal to 50 units/per day i.e. H 1 : [Tex]\mu [/Tex] [Tex]\ne [/Tex] 50.

Key Terms of Hypothesis Testing

• Level of significance : It refers to the degree of significance in which we accept or reject the null hypothesis. 100% accuracy is not possible for accepting a hypothesis, so we, therefore, select a level of significance that is usually 5%. This is normally denoted with  [Tex]\alpha[/Tex] and generally, it is 0.05 or 5%, which means your output should be 95% confident to give a similar kind of result in each sample.
• P-value: The P value , or calculated probability, is the probability of finding the observed/extreme results when the null hypothesis(H0) of a study-given problem is true. If your P-value is less than the chosen significance level then you reject the null hypothesis i.e. accept that your sample claims to support the alternative hypothesis.
• Test Statistic: The test statistic is a numerical value calculated from sample data during a hypothesis test, used to determine whether to reject the null hypothesis. It is compared to a critical value or p-value to make decisions about the statistical significance of the observed results.
• Critical value : The critical value in statistics is a threshold or cutoff point used to determine whether to reject the null hypothesis in a hypothesis test.
• Degrees of freedom: Degrees of freedom are associated with the variability or freedom one has in estimating a parameter. The degrees of freedom are related to the sample size and determine the shape.

Why do we use Hypothesis Testing?

Hypothesis testing is an important procedure in statistics. Hypothesis testing evaluates two mutually exclusive population statements to determine which statement is most supported by sample data. When we say that the findings are statistically significant, thanks to hypothesis testing. 

One-Tailed and Two-Tailed Test

One tailed test focuses on one direction, either greater than or less than a specified value. We use a one-tailed test when there is a clear directional expectation based on prior knowledge or theory. The critical region is located on only one side of the distribution curve. If the sample falls into this critical region, the null hypothesis is rejected in favor of the alternative hypothesis.

One-Tailed Test

There are two types of one-tailed test:

• Left-Tailed (Left-Sided) Test: The alternative hypothesis asserts that the true parameter value is less than the null hypothesis. Example: H 0 ​: [Tex]\mu \geq 50 [/Tex] and H 1 : [Tex]\mu < 50 [/Tex]
• Right-Tailed (Right-Sided) Test : The alternative hypothesis asserts that the true parameter value is greater than the null hypothesis. Example: H 0 : [Tex]\mu \leq50 [/Tex] and H 1 : [Tex]\mu > 50 [/Tex]

Two-Tailed Test

A two-tailed test considers both directions, greater than and less than a specified value.We use a two-tailed test when there is no specific directional expectation, and want to detect any significant difference.

Example: H 0 : [Tex]\mu = [/Tex] 50 and H 1 : [Tex]\mu \neq 50 [/Tex]

To delve deeper into differences into both types of test: Refer to link

What are Type 1 and Type 2 errors in Hypothesis Testing?

In hypothesis testing, Type I and Type II errors are two possible errors that researchers can make when drawing conclusions about a population based on a sample of data. These errors are associated with the decisions made regarding the null hypothesis and the alternative hypothesis.

• Type I error: When we reject the null hypothesis, although that hypothesis was true. Type I error is denoted by alpha( [Tex]\alpha [/Tex] ).
• Type II errors : When we accept the null hypothesis, but it is false. Type II errors are denoted by beta( [Tex]\beta [/Tex] ).

How does Hypothesis Testing work?

Step 1: define null and alternative hypothesis.

State the null hypothesis ( [Tex]H_0 [/Tex] ), representing no effect, and the alternative hypothesis ( [Tex]H_1 [/Tex] ​), suggesting an effect or difference.

We first identify the problem about which we want to make an assumption keeping in mind that our assumption should be contradictory to one another, assuming Normally distributed data.

Step 2 – Choose significance level

Select a significance level ( [Tex]\alpha [/Tex] ), typically 0.05, to determine the threshold for rejecting the null hypothesis. It provides validity to our hypothesis test, ensuring that we have sufficient data to back up our claims. Usually, we determine our significance level beforehand of the test. The p-value is the criterion used to calculate our significance value.

Step 3 – Collect and Analyze data.

Gather relevant data through observation or experimentation. Analyze the data using appropriate statistical methods to obtain a test statistic.

Step 4-Calculate Test Statistic

The data for the tests are evaluated in this step we look for various scores based on the characteristics of data. The choice of the test statistic depends on the type of hypothesis test being conducted.

There are various hypothesis tests, each appropriate for various goal to calculate our test. This could be a Z-test , Chi-square , T-test , and so on.

• Z-test : If population means and standard deviations are known. Z-statistic is commonly used.
• t-test : If population standard deviations are unknown. and sample size is small than t-test statistic is more appropriate.
• Chi-square test : Chi-square test is used for categorical data or for testing independence in contingency tables
• F-test : F-test is often used in analysis of variance (ANOVA) to compare variances or test the equality of means across multiple groups.

We have a smaller dataset, So, T-test is more appropriate to test our hypothesis.

T-statistic is a measure of the difference between the means of two groups relative to the variability within each group. It is calculated as the difference between the sample means divided by the standard error of the difference. It is also known as the t-value or t-score.

Step 5 – Comparing Test Statistic:

In this stage, we decide where we should accept the null hypothesis or reject the null hypothesis. There are two ways to decide where we should accept or reject the null hypothesis.

Method A: Using Crtical values

Comparing the test statistic and tabulated critical value we have,

• If Test Statistic>Critical Value: Reject the null hypothesis.
• If Test Statistic≤Critical Value: Fail to reject the null hypothesis.

Note: Critical values are predetermined threshold values that are used to make a decision in hypothesis testing. To determine critical values for hypothesis testing, we typically refer to a statistical distribution table , such as the normal distribution or t-distribution tables based on.

Method B: Using P-values

We can also come to an conclusion using the p-value,

• If the p-value is less than or equal to the significance level i.e. ( [Tex]p\leq\alpha [/Tex] ), you reject the null hypothesis. This indicates that the observed results are unlikely to have occurred by chance alone, providing evidence in favor of the alternative hypothesis.
• If the p-value is greater than the significance level i.e. ( [Tex]p\geq \alpha[/Tex] ), you fail to reject the null hypothesis. This suggests that the observed results are consistent with what would be expected under the null hypothesis.

Note : The p-value is the probability of obtaining a test statistic as extreme as, or more extreme than, the one observed in the sample, assuming the null hypothesis is true. To determine p-value for hypothesis testing, we typically refer to a statistical distribution table , such as the normal distribution or t-distribution tables based on.

Step 7- Interpret the Results

At last, we can conclude our experiment using method A or B.

Calculating test statistic

To validate our hypothesis about a population parameter we use statistical functions . We use the z-score, p-value, and level of significance(alpha) to make evidence for our hypothesis for normally distributed data .

1. Z-statistics:

When population means and standard deviations are known.

[Tex]z = \frac{\bar{x} – \mu}{\frac{\sigma}{\sqrt{n}}}[/Tex]

• [Tex]\bar{x} [/Tex] is the sample mean,
• μ represents the population mean, 
• σ is the standard deviation
• and n is the size of the sample.

2. T-Statistics

T test is used when n<30,

t-statistic calculation is given by:

[Tex]t=\frac{x̄-μ}{s/\sqrt{n}} [/Tex]

• t = t-score,
• x̄ = sample mean
• μ = population mean,
• s = standard deviation of the sample,
• n = sample size

3. Chi-Square Test

Chi-Square Test for Independence categorical Data (Non-normally distributed) using:

[Tex]\chi^2 = \sum \frac{(O_{ij} – E_{ij})^2}{E_{ij}}[/Tex]

• [Tex]O_{ij}[/Tex] is the observed frequency in cell [Tex]{ij} [/Tex]
• i,j are the rows and columns index respectively.
• [Tex]E_{ij}[/Tex] is the expected frequency in cell [Tex]{ij}[/Tex] , calculated as : [Tex]\frac{{\text{{Row total}} \times \text{{Column total}}}}{{\text{{Total observations}}}}[/Tex]

Real life Examples of Hypothesis Testing

Let’s examine hypothesis testing using two real life situations,

Case A: D oes a New Drug Affect Blood Pressure?

Imagine a pharmaceutical company has developed a new drug that they believe can effectively lower blood pressure in patients with hypertension. Before bringing the drug to market, they need to conduct a study to assess its impact on blood pressure.

• Before Treatment: 120, 122, 118, 130, 125, 128, 115, 121, 123, 119
• After Treatment: 115, 120, 112, 128, 122, 125, 110, 117, 119, 114

Step 1 : Define the Hypothesis

• Null Hypothesis : (H 0 )The new drug has no effect on blood pressure.
• Alternate Hypothesis : (H 1 )The new drug has an effect on blood pressure.

Step 2: Define the Significance level

Let’s consider the Significance level at 0.05, indicating rejection of the null hypothesis.

If the evidence suggests less than a 5% chance of observing the results due to random variation.

Step 3 : Compute the test statistic

Using paired T-test analyze the data to obtain a test statistic and a p-value.

The test statistic (e.g., T-statistic) is calculated based on the differences between blood pressure measurements before and after treatment.

t = m/(s/√n)

• m  = mean of the difference i.e X after, X before
• s  = standard deviation of the difference (d) i.e d i ​= X after, i ​− X before,
• n  = sample size,

then, m= -3.9, s= 1.8 and n= 10

we, calculate the , T-statistic = -9 based on the formula for paired t test

Step 4: Find the p-value

The calculated t-statistic is -9 and degrees of freedom df = 9, you can find the p-value using statistical software or a t-distribution table.

thus, p-value = 8.538051223166285e-06

Step 5: Result

• If the p-value is less than or equal to 0.05, the researchers reject the null hypothesis.
• If the p-value is greater than 0.05, they fail to reject the null hypothesis.

Conclusion: Since the p-value (8.538051223166285e-06) is less than the significance level (0.05), the researchers reject the null hypothesis. There is statistically significant evidence that the average blood pressure before and after treatment with the new drug is different.

Python Implementation of Case A

Let’s create hypothesis testing with python, where we are testing whether a new drug affects blood pressure. For this example, we will use a paired T-test. We’ll use the scipy.stats library for the T-test.

Scipy is a mathematical library in Python that is mostly used for mathematical equations and computations.

We will implement our first real life problem via python,

import numpy as np from scipy import stats # Data before_treatment = np . array ([ 120 , 122 , 118 , 130 , 125 , 128 , 115 , 121 , 123 , 119 ]) after_treatment = np . array ([ 115 , 120 , 112 , 128 , 122 , 125 , 110 , 117 , 119 , 114 ]) # Step 1: Null and Alternate Hypotheses # Null Hypothesis: The new drug has no effect on blood pressure. # Alternate Hypothesis: The new drug has an effect on blood pressure. null_hypothesis = "The new drug has no effect on blood pressure." alternate_hypothesis = "The new drug has an effect on blood pressure." # Step 2: Significance Level alpha = 0.05 # Step 3: Paired T-test t_statistic , p_value = stats . ttest_rel ( after_treatment , before_treatment ) # Step 4: Calculate T-statistic manually m = np . mean ( after_treatment - before_treatment ) s = np . std ( after_treatment - before_treatment , ddof = 1 ) # using ddof=1 for sample standard deviation n = len ( before_treatment ) t_statistic_manual = m / ( s / np . sqrt ( n )) # Step 5: Decision if p_value <= alpha : decision = "Reject" else : decision = "Fail to reject" # Conclusion if decision == "Reject" : conclusion = "There is statistically significant evidence that the average blood pressure before and after treatment with the new drug is different." else : conclusion = "There is insufficient evidence to claim a significant difference in average blood pressure before and after treatment with the new drug." # Display results print ( "T-statistic (from scipy):" , t_statistic ) print ( "P-value (from scipy):" , p_value ) print ( "T-statistic (calculated manually):" , t_statistic_manual ) print ( f "Decision: { decision } the null hypothesis at alpha= { alpha } ." ) print ( "Conclusion:" , conclusion )

T-statistic (from scipy): -9.0 P-value (from scipy): 8.538051223166285e-06 T-statistic (calculated manually): -9.0 Decision: Reject the null hypothesis at alpha=0.05. Conclusion: There is statistically significant evidence that the average blood pressure before and after treatment with the new drug is different.

In the above example, given the T-statistic of approximately -9 and an extremely small p-value, the results indicate a strong case to reject the null hypothesis at a significance level of 0.05. 

• The results suggest that the new drug, treatment, or intervention has a significant effect on lowering blood pressure.
• The negative T-statistic indicates that the mean blood pressure after treatment is significantly lower than the assumed population mean before treatment.

Case B : Cholesterol level in a population

Data: A sample of 25 individuals is taken, and their cholesterol levels are measured.

Cholesterol Levels (mg/dL): 205, 198, 210, 190, 215, 205, 200, 192, 198, 205, 198, 202, 208, 200, 205, 198, 205, 210, 192, 205, 198, 205, 210, 192, 205.

Populations Mean = 200

Population Standard Deviation (σ): 5 mg/dL(given for this problem)

Step 1: Define the Hypothesis

• Null Hypothesis (H 0 ): The average cholesterol level in a population is 200 mg/dL.
• Alternate Hypothesis (H 1 ): The average cholesterol level in a population is different from 200 mg/dL.

As the direction of deviation is not given , we assume a two-tailed test, and based on a normal distribution table, the critical values for a significance level of 0.05 (two-tailed) can be calculated through the z-table and are approximately -1.96 and 1.96.

The test statistic is calculated by using the z formula Z = [Tex](203.8 – 200) / (5 \div \sqrt{25}) [/Tex] ​ and we get accordingly , Z =2.039999999999992.

Step 4: Result

Since the absolute value of the test statistic (2.04) is greater than the critical value (1.96), we reject the null hypothesis. And conclude that, there is statistically significant evidence that the average cholesterol level in the population is different from 200 mg/dL

Python Implementation of Case B

import scipy.stats as stats import math import numpy as np # Given data sample_data = np . array ( [ 205 , 198 , 210 , 190 , 215 , 205 , 200 , 192 , 198 , 205 , 198 , 202 , 208 , 200 , 205 , 198 , 205 , 210 , 192 , 205 , 198 , 205 , 210 , 192 , 205 ]) population_std_dev = 5 population_mean = 200 sample_size = len ( sample_data ) # Step 1: Define the Hypotheses # Null Hypothesis (H0): The average cholesterol level in a population is 200 mg/dL. # Alternate Hypothesis (H1): The average cholesterol level in a population is different from 200 mg/dL. # Step 2: Define the Significance Level alpha = 0.05 # Two-tailed test # Critical values for a significance level of 0.05 (two-tailed) critical_value_left = stats . norm . ppf ( alpha / 2 ) critical_value_right = - critical_value_left # Step 3: Compute the test statistic sample_mean = sample_data . mean () z_score = ( sample_mean - population_mean ) / \ ( population_std_dev / math . sqrt ( sample_size )) # Step 4: Result # Check if the absolute value of the test statistic is greater than the critical values if abs ( z_score ) > max ( abs ( critical_value_left ), abs ( critical_value_right )): print ( "Reject the null hypothesis." ) print ( "There is statistically significant evidence that the average cholesterol level in the population is different from 200 mg/dL." ) else : print ( "Fail to reject the null hypothesis." ) print ( "There is not enough evidence to conclude that the average cholesterol level in the population is different from 200 mg/dL." )

Reject the null hypothesis. There is statistically significant evidence that the average cholesterol level in the population is different from 200 mg/dL.

Limitations of Hypothesis Testing

• Although a useful technique, hypothesis testing does not offer a comprehensive grasp of the topic being studied. Without fully reflecting the intricacy or whole context of the phenomena, it concentrates on certain hypotheses and statistical significance.
• The accuracy of hypothesis testing results is contingent on the quality of available data and the appropriateness of statistical methods used. Inaccurate data or poorly formulated hypotheses can lead to incorrect conclusions.
• Relying solely on hypothesis testing may cause analysts to overlook significant patterns or relationships in the data that are not captured by the specific hypotheses being tested. This limitation underscores the importance of complimenting hypothesis testing with other analytical approaches.

Hypothesis testing stands as a cornerstone in statistical analysis, enabling data scientists to navigate uncertainties and draw credible inferences from sample data. By systematically defining null and alternative hypotheses, choosing significance levels, and leveraging statistical tests, researchers can assess the validity of their assumptions. The article also elucidates the critical distinction between Type I and Type II errors, providing a comprehensive understanding of the nuanced decision-making process inherent in hypothesis testing. The real-life example of testing a new drug’s effect on blood pressure using a paired T-test showcases the practical application of these principles, underscoring the importance of statistical rigor in data-driven decision-making.

Frequently Asked Questions (FAQs)

1. what are the 3 types of hypothesis test.

There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed. Right-tailed tests assess if a parameter is greater, left-tailed if lesser. Two-tailed tests check for non-directional differences, greater or lesser.

2.What are the 4 components of hypothesis testing?

Null Hypothesis ( [Tex]H_o [/Tex] ): No effect or difference exists. Alternative Hypothesis ( [Tex]H_1 [/Tex] ): An effect or difference exists. Significance Level ( [Tex]\alpha [/Tex] ): Risk of rejecting null hypothesis when it’s true (Type I error). Test Statistic: Numerical value representing observed evidence against null hypothesis.

3.What is hypothesis testing in ML?

Statistical method to evaluate the performance and validity of machine learning models. Tests specific hypotheses about model behavior, like whether features influence predictions or if a model generalizes well to unseen data.

4.What is the difference between Pytest and hypothesis in Python?

Pytest purposes general testing framework for Python code while Hypothesis is a Property-based testing framework for Python, focusing on generating test cases based on specified properties of the code.

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Entrepreneurship

The Science of Successful Start-Ups

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In the competitive world of business, entrepreneurs have long sought novel formulas such as the Business Model Canvas and the Lean Start-Up Method in their quest for success. The most potent tool, however, might be one that's centuries old: the scientific approach.

From a series of experiments involving 759 start-ups across industries in Milan, Turin and London, my colleagues* and I found that companies that embraced the practice of rigorously formulating and testing hypotheses consistently outperformed their peers.  They were more likely to weed out unviable ideas early on, pivot to more promising directions, and generate more revenue.

This study is built on a   smaller one from 2020 and was recently   published in Strategic Management Journal . Both papers have also been   featured in Harvard Business Review.  Replicating studies is a crucial way of validating and extending initial findings. Our latest study not only reinforces the original findings but also provides deeper insights into the effectiveness of the scientific approach in entrepreneurship.

The scientific entrepreneur

What does it mean for a start-up to "use the scientific approach"? At its core, it's about treating business ideas as hypotheses to be tested, rather than gospel truths to be defended.

Importantly, our study demonstrates that this scientific mindset can be taught. It was the entrepreneurs who received training in the following steps that showed measurable improvements in their decision-making and business outcomes.

• Start with a theory: Begin with your strongest intuition, but be prepared to test alternative theories if necessary.
• State your hypotheses: Clearly articulate your specific individual assumptions about your business idea.
• Validate your hypotheses: Design experiments to test your hypotheses.
• Refine and retest: Continuously refine your theories based on experimental results.

Take MiMoto, an Italian electric-moped sharing service that participated in the study. The start-up's initial hypothesis was that college students rushing from class to class would be their primary market. But when they placed mopeds near an urban campus, they quickly discovered that usage was spread evenly across age groups, with a particular concentration among professionals with unpredictable commute patterns.

Armed with this data, MiMoto's founders went back to the drawing board. They developed a new hypothesis – that young professionals, particularly lawyers constantly shuttling between client meetings, would be their ideal customers. This pivot, grounded in empirical evidence rather than gut feeling, set the company on a more promising path.

Another participant in our study, sustainability-focused venture Osense, likewise avoided wasting time and resources on their envisioned product – a peer-to-peer rental platform – after collecting data that indicated it would tank. 

Instead, by rigorously testing their hypothesis, Osense’s founders pivoted quickly to a more promising idea: a platform for tracking scope 3 (indirect) carbon emissions. After just 10 interviews with sustainability managers, nine of which were overwhelmingly positive, they knew they were onto something big.

The power of pivoting

In fact, one of our key findings is that scientifically minded entrepreneurs are more likely to pull the plug on dubious projects, and hence less likely to go belly-up. By recognising when an idea isn't working, founders can redirect their efforts to more promising ventures, avoiding the sunk cost fallacy that plagues many start-ups.

There is more to this point. Founders using the scientific approach in our experiment were more likely to make one or two major strategic shifts, and less likely to never pivot or pivot endlessly. This suggests that scientific thinking leads to more focused and deliberate changes, rather than erratic flailing or stubborn adherence to a failing model.

Two key mechanisms likely underpin these positive effects. The first is efficient search . This refers to founders’ higher efficiency in searching for possible solutions, thanks to being better able to prioritise ideas that are more likely to be successful. 

The second mechanism is methodic doubt . Scientific founders tend to have healthy scepticism and are more likely to critically examine their assumptions and identify potential pitfalls.

Strikingly, the impact of the scientific approach was particularly obvious among the more successful ventures. Of the top 25 percent of revenue generators in our latest study, those using the scientific method made an average of €28,000 more than counterparts in the control group over the course of the experiment. For the top 5 percent, the difference was €492,000.

While the scientific approach can significantly increase a start-up's chances of success, it doesn't guarantee a smooth path. Failure is still a possibility, but even failed experiments provide valuable lessons. Success in entrepreneurship may be less about unwavering belief in a singular vision, and more about the disciplined, systematic testing of ideas.

Our research could benefit not just entrepreneurs. For investors and policymakers, it offers a potential framework for evaluating and supporting new ventures. The hypotheses may be brilliant, but it's rigorous testing and willingness to adapt that will ultimately lead to success.

* Arnaldo Camuffo and   Alfonso Gambardella , Bocconi University;   Danilo Messinese , IE University;   Elena Novelli , City St. George’s, University of London; and   Emilio Paolucci , Politecnico di Torino.

About the author(s)

Chiara spina.

is an Assistant Professor of Entrepreneurship and Family Enterprise at INSEAD. Her research focuses on understanding how entrepreneurial firms leverage systematic decision-making and experimentation to innovate and grow. 

About the research

“ A scientific approach to entrepreneurial decision-making: Large-scale replication and extension ”  is published in Strategic Management Journal.

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More From Forbes

Research data vs. empirical evidence: what really works in the food & beverage business.

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Teja Chekuri is the Founder of Full Stack Ventures.

Ah, the age-old debate: research data vs. empirical evidence. It’s a bit like the “chicken or the egg” conundrum but with more spreadsheets and fewer feathers. As an entrepreneur in the food and beverage industry, I often find myself torn between the cold, hard numbers and the warm, fuzzy feeling of firsthand experience. So, what really works when setting up a brand? Let’s dig in (pun intended) and find out!

The Case For Data: Because Numbers Don’t Lie

Data is the backbone of any solid business strategy. It’s like the yeast in your bread—without it, things just won’t rise. Market research, consumer trends and sales forecasts provide valuable insights that can guide your decisions.

Market Research: Understanding your target audience is crucial. Data can tell you who your customers are, what they want and how much they’re willing to spend.

Consumer Trends: Data helps you stay ahead of the curve. Whether it’s the latest superfood craze or the rise of plant-based diets, being in the know can set you apart from the competition. Remember when kale was king and then turmeric coffee was on the rise? Exactly.

Sales Forecasts: Predicting future sales can help with budgeting, inventory management and staffing. It’s like having a crystal ball, but without the mystical mumbo jumbo.

Google Chrome Deadline—You Have 72 Hours To Update Your Browser

Canelo alvarez vs. edgar berlanga results: winner and highlights, samsung updates millions of galaxy phones to stop users leaving, the case for empirical evidence: because sometimes your gut never lies.

While data is undoubtedly important, empirical evidence—the insights gained from direct experience—can be equally valuable if not more. After all, who knows your business better than you? A few things can help inform your gut.

Real-World Testing: Data can predict trends, but nothing beats tasting your own product and getting feedback from real customers from your catchment area. It’s like the difference between reading a recipe and actually cooking the dish. You might think adding extra garlic is a good idea until your taste testers start breathing fire.

Intuition: Sometimes, you just have to trust your instincts. If something feels right, it probably is. Ever had a gut feeling that a certain dish would be a hit, even though the data said otherwise? That’s the magic of empirical evidence. I have used it several times to create a winning combination in a menu.

Adaptability: The ability to pivot based on real-time feedback is invaluable. Data might tell you to stay the course, but if your customers are clamoring for avocado toast instead of your signature waffles, it’s time to listen. Flexibility is key in the ever-evolving food and beverage landscape.

The Perfect Recipe: A Blend Of Both

So, what’s the secret sauce? Numbers alone won’t get the customers raving about your food and launching a new menu without any research data is winging it in the extreme. The truth is that the best approach combines both data and empirical evidence. Think of it as a balanced diet—too much of one thing can leave you lacking in other areas. And this is a combination I can vouch for several times over. Here are the key ingredients:

Informed Decision-Making: Use data to guide your big-picture strategy, but use empirical evidence for the day-to-day decisions to make sense of the numbers. It’s like using a map to plan your road trip but still stopping to ask for directions when you’re lost (or, you know, using Google Maps because it’s 2024).

Continuous Learning: Keep gathering data and refining your empirical knowledge with the Excel sheet tabulating numbers at the back of your mind. The more you know, the better equipped you’ll be to make smart, informed choices. And never stop taste-testing—that’s the fun part!

Customer Feedback: Marry data with customer insights. Surveys, reviews and direct feedback are gold mines of empirical evidence that can validate or challenge your data-driven assumptions. Many a time I have removed or added a dish and argued about price points with the culinary team to create a signature dish that I know the audience will like and are willing to pay for and how much.

In the end, building a successful brand in the food and beverage industry is both an art and a science. By blending the precision of data with the intuition of empirical evidence, you can create a recipe for success that’s uniquely your own. So, whether you’re crunching numbers or just crunching on some chips remember: It’s all about balance.

Now, who’s hungry?

Forbes Business Council is the foremost growth and networking organization for business owners and leaders. Do I qualify?

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A Systems View Across Time and Space

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• Published: 12 September 2024

Business strategies, bureaucratic ties, and firms’ innovation novelty: insights from the World Bank enterprise survey

• Samuel Amponsah Odei   ORCID: orcid.org/0000-0001-8340-4155 1 &
• Ivan Soukal 1  

Journal of Innovation and Entrepreneurship volume  13 , Article number:  63 ( 2024 ) Cite this article

Metrics details

We draw intuitions from the systemic perspective of innovation to develop and test a conceptual model aimed at examining the various factors capable of influencing the novelty of innovations within firms in Visegrad countries. The empirical results based on the analyses of about 2,132 firms revealed that organisational strategies, external collaborations, engaging in research and development, and the legal status of firms marginally influence innovation novelties. Contrary to our expectations, we found that intellectual property rights and bureaucratic ties do not significantly influence innovation novelties. Business cities are also positively correlated with firms’ innovation novelties whilst legal status is not. The main practical implication of the research is that firm managers in the Visegrad Group aiming to improve and sustain the novelty of innovations should consider strengthening their external collaborations as well as having business strategies that must include innovations as well as research and development (R&D). We discuss some implications for theory and policy.

Introduction

Firms are constantly looking for methods to be more cost-effective and responsive to enhance their performance, given the demands of ever-changing external surroundings (Al-Twal et al., 2024 ). Innovation has become a formidable component of firms’ strategies and policies in the quest for improved competitiveness; it has long remained a plausible goal of firms and national policies (Anderson & Stejskal, 2019a ; Boateng & Abaye, 2019 ; Kiveu et al., 2019 ; Odei et al., 2021 ). The ability of firms to adopt innovations in their production process, marketing, and organisation is known to help position them better and sustain their competitive advantage. Engaging in research and development (R&D) has been proven to be one of the most imperative approaches for improving and sustaining firms’ productivity, competitiveness, and innovations (Leung & Sharma, 2021 ), which has become a key factor of economic growth and social prosperity. Several studies have used various measures for innovation; some measure innovations from both a technological and non-technological standpoint (Odei & Appiah, 2023 ; Odei & Novak, 2022 ), with varying degrees of novelty (Diaz-Diaz & De Saá-Pérez, 2012 ; Majeed & Breunig, 2022 ). Irrespective of the measures adopted, the consensus is that the invention must be significantly improved and must either be new to the firm or new to the market where the firm operates. The Visegrad Group was created in the early 1990s, right after the collapse of the Soviet Union. It is an agglomeration of neighbouring countries—the Czech Republic, Slovakia, Hungary, and Poland—that began economic transitioning simultaneously. The level of innovativeness of the Visegrad Group is low, usually lagging European Union (EU) averages (Odei & Appiah, 2023 ). Though innovation has remained low in this group of countries, various governments have committed to improving infrastructure and public support for research and development, which is critical for the successful adoption of innovations. However, the group faces key innovation problems such as the slow overhaul of educational systems to make them technically oriented (Koišová et al., 2021 ), low firms’ expenditures on research and development, and weak incentives for institutional interactions, among others. These problems among others make the groups’ transitioning into fully fledged knowledge-based economies slow.

Research on firm-level innovations is increasing in the Visegrad Group of countries (see, for instance, Odei & Appiah, 2023 ). However, the bourgeoning research displays several weaknesses that still limit the complete understanding of the innovation landscape in these countries. First, the measures of innovations adopted in existing studies in these countries have narrowly focused on technological and non-technological perspectives (Cieślik & Michałek, 2018 ; Odei & Novak, 2022 ). This means that other measures, such as degrees of novelty, that could help distinguish between innovations new to firms and to the market have not been given enough scholarly attention. Another aspect where existing research show caveats is their neglect of bureaucratic structures in external environment, which could potentially influence the innovation processes through resource and time allocation (Krammer, 2019 ). Depending on how it is handled, bureaucracy can either promote or impede innovation. Well-organised bureaucratic systems can enhance access to critical information and knowledge within organisations, which is vital for the innovation process (Eckhard, 2021 ). On the contrary, stringent bureaucratic procedures can slow down decision-making processes, making it challenging for firms to respond swiftly to new opportunities or changes in the market (Potter, 2017 ). This could hinder the adoption and implementation of innovation activities. Research elsewhere, for instance, by Tian, Wang, Xie, Jiao, & Jiao (2019), concluded that effective bureaucracy positively influences firms’ innovation performance, hence the call for research in these countries to examine the influence of this external relationship. We argue that the neglect of research on bureaucracy means that our knowledge of the regulatory quality in these countries is missing, but it could potentially affect firms’ operations and their innovation search. Furthermore, existing studies on innovations in the Visegrad Group have not focused on analysing business strategies and how they could potentially influence the innovation process (see, for instance, Odei et al., 2021 ; Odei & Appiah, 2023 ). We argue that firms especially innovative ones often develop and implement business strategies that could play a critical role in influencing the direction, and success of their innovation efforts. These strategies are closely intertwined with firms’ innovation process and can have a profound impact on their innovation outcomes, therefore their role in the innovation process cannot be ignored. In sum, the relationship between bureaucratic structures, business strategy, and external collaboration in fostering or hindering innovation novelty remains underexplored. The current body of research inadequately addresses how these three factors influence the creation of novel innovations especially in the context of transitioned countries like the Visegrad. This gap in understanding limits the ability of firms to effectively design and implement strategies that involve bureaucratic structures and external collaborations to enhance innovation. The omission of these critical aspects of innovation reduces our understanding of the innovation ecosystem in these economies, highlighting the need for new research that incorporates all these overlooked but critical factors to provide a comprehensive understanding of firm-level innovation. This study addresses these research gaps by examining the influence of bureaucracy, external collaboration, business strategies on firms’ ability to introduce innovation that could be novel to the firm and the market. To fulfil this research aim, we draw intuitions from the systemic perspective of innovation (Johannessen, 2013 ; Midgley & Lindhult, 2021 ), which highlights the entire ecosystem in which innovation occurs, emphasising the interconnectedness and interdependence of various elements and actors for sustainable innovation. We develop a conceptual model that aims to assess the influence of business strategies, external collaboration, and bureaucracy on firms’ innovation novelty.

The empirical analysis used data from the World Bank's Enterprise Survey, which involved a sample of small and large firms from the manufacturing and service sectors in Visegrad countries. The study is novel and differs from existing studies as we have shown that bureaucracy in these countries do not significantly influence firms’ abilities to introduce innovative products new to the market and the firm. This result shows that the regulatory quality in these countries is favourable, so firms do not have to spend productive time meeting them. This finding is in line with the systemic perspective of innovation (Johannessen, 2013 ; Midgley & Lindhult, 2021 ). Another aspect that makes our research novel and different from existing studies is the measure of innovation used. Previous studies that measured innovations by their degrees of novelty were undertaken in the Czech Republic but not in the three remaining countries (see Odei & Hamplová, 2022 ). While the measures are the same, the sampled population differs and has greater variability. Our results have also shown that business strategies, especially those on innovations, are likely to contribute to influencing firms’ ability to introduce innovations that could be new to the firm and the market. To the best of our knowledge, there are no existing studies that have explored the relationship between business strategies and degrees of innovation novelty in the Visegrad countries. Our findings, particularly those concerning business strategies and their ability to influence new product introductions and firm innovations, have practical implications for firm managers. Firms in these countries that want to be innovative should consider developing business strategies that can serve as a practical guide for innovation activities and resource allocations. Finally, our results pointed out that external collaboration influences firms’ abilities to introduce inventions that could be new to the firm or the market where the firm operates. This has not received enough scholarly attention in these group of countries, and our result therefore contributes to the growing literature on the importance of external collaboration in spurring novel inventions (Odei & Hamplová, 2022 ; Storz et al., 2022 ; Un & Asakawa, 2015 ). The main practical implication from our findings is that policymakers and firm managers in the Visegrad countries should consider both internal and external factors when developing innovation policies. The main limitation of the paper relates to the pooled cross-sectional data used, which makes it difficult to understand the trend of firm-level innovations in these countries.

The rest of this article is arranged in the following order: section two of the paper is dedicated to reviews and discussion of literature on the concepts of degree of novelty related to new-to-firm and new-to-market innovations and the various determinants influencing them. Section three focuses on the source of data, research methodology, and description of variables used for the empirical specification; section four is devoted to the detailed result discussions pertaining to the previous literature. Section five concludes the research with suggestions for further research, practical and policy implications, and research limitations.

Theoretical background and hypothesis development

Innovation refers to firms and organisations abilities to adopt significantly improved knowledge, ideas, or behaviours, which often result in improved products, processes, or new technologies or organisational management processes (Martínez-Ros, 2019 ). Innovation has become the most powerful strategic resource that can be utilised by firms to improve their performance and productivity. The sustained improvements in firms’ innovation capabilities are conducive to improving and positioning them better in terms of competitive advantage amidst the rapidly changing environment (Dereli, 2015 ; Gupta et al., 2013 ). Firms’ innovation competence lies in their ability to incessantly metamorphose new knowledge and ideas into significantly new products, processes, marketing, and organisational processes to reap more profits (Audretsch & Belitski, 2023 ). New knowledge helps firms to infuse fresh ideas which could be stagnant internally due to same thinking internally. Innovations could be new to the firm that introduced them, but they could also be new to the market where the firm operates. This means that the innovation could be novel to the firms’ competitors, giving them a temporary competitive advantage in the market. The extent of novelty of innovations helps to distinguish between inventions that are significantly new to the firm that implemented or introduced them and those that are new to the market environment where the firm operates (Odei & Appiah, 2023 ). The degree of novelty of an innovation is often used to differentiate between major and minor forms of innovation. Based on the degrees of novelty, innovations could be lumped as minor and major; those inventions new to the introducing firm itself are considered minor, and those new to the market where the innovative firm operates is known as major innovations (Odei & Hamplová, 2022 ).

This research is built on the systemic perspective of innovation and aims to explore the factors capable of influencing firms’ innovation novelties. The systemic perspective of innovation theorises that successful and sustainable innovation depends on firms’ aptitude to organise and incorporate a wide array of internal and external sources of technical and scientific knowledge (Johannessen, 2013 ; Midgley & Lindhult, 2021 ). The systemic perspective of innovation is a holistic approach that considers innovation as a complex, interconnected process that comprises various actors, organisations, and elements within a given ecosystem. Since the 1990s, national innovation systems in many countries have focused on the linear innovation model. The linear innovation model posits that firms exclusively rely on internal knowledge; this was pigeonholed by a moderately weak reliance on the assimilation of knowledge from external sources. The linear model of innovation policy primarily focused on providing financial support for firms and the provision of needed R&D infrastructure to stimulate innovation. In recent times, innovation has been considered an open process with a systemic and social disposition that is mainly boosted by external knowledge (Chesbrough, 2017 ). Firms can acquire external knowledge through collaborating with partners such as higher education institutions, other firms in the market environment, suppliers, and customers. The knowledge acquired from external sources becomes vital for firms’ innovation performance if they develop their absorptive capacities internally through human capital development. We measured innovation using the degrees of novelty, which distinguishes between innovations that are novel to the firm that introduced it and those that are first to hit the market where the firm operates (Odei & Hamplová, 2022 ; Storz et al., 2022 ). Since innovation is considered a complex process, the systemic perspective of innovation is employed in this study to propose a model to determine how firms’ businesses strategies, external collaboration, relationships with governments and firm-level and regional controls impact innovation novelty abilities. The new model hypotheses that business strategies, external collaboration, and firms’ relationships with governments affect their aptitude to introduce innovations that could be new to the firm or the market. The new proposed model built on the systemic perspective of innovation theory provides a comprehensive and interconnected framework for analysing firms’ innovation novelty (Midgley & Lindhult, 2021 ). By considering the broader context, interactions among partners, feedback loops, knowledge flow, regulatory factors, and internal activities, this perspective enhances the ability to assess and understand the novelty of innovations in an integrated approach. This model helps capture the richness and multidimensionality of the innovation processes, hence, makes it a valuable tool for researchers, policymakers, and firm managers seeking to navigate and promote novelty of innovation in the Visegrád Group of countries.

Research on firms’ strategies and how they shape innovations and competitiveness has gained ample scholarly attention because it shapes and guides firm-level activities and performances (Laosirihongthong et al., 2014 ). A firm's strategy is a set of planned actions and decisions taken or intended to be taken by firms to achieve specific goals and objectives. A business strategy outlines what the firm needs to do to achieve its goals, guide the decision-making process for human capital, and make other vital resource allocations. Innovative firms are expected to include innovations as part of their strategies. These strategies, including those on innovation, guide decisions on how scarce resources are to be utilised to meet businesses’ innovation goals, deliver value, and improve competitive advantage. These firms’ strategies should include an assessment of their competitiveness, technological capabilities, and environment, as well as external threats and opportunities (Čirjevskis, 2019 ). Firm strategies also address how firms can work to compensate for any gaps in internal and external knowledge as well as outline strategies for improving their innovation competencies. Besides strategies' influence on innovative performance, it could also influence their abilities to influence how they will deal with institutional weaknesses, especially in transition countries (Rodríguez-Pose & Zhang, 2020 ). It is anticipated that firms’ strategies will broadly involve innovations, and this strategic plan will influence firms’ commitment to improving the innovation process. It will also ensure that firms fully commit resources such as finances and human capital, among others. This could ensure that firms will improve their technological abilities through research and development as well as investments in technology acquisitions, which can increase their competitive advantages. There is, however, limited research that has focused on analysing how different strategies implemented by individual firms impact their innovation capability, and, oftentimes, such studies reach inconsistent results. Akman and Yilmaz ( 2008 ), for instance, found that firm strategy could positively influence innovation outcomes. Goedhuys and Veugelers ( 2012 ) also concluded that firms’ strategies are positively correlated with successful process and product innovations. We, therefore, summarise the belief that business strategies determine how firms allocate their resources, including financial, human, and technological resources. Innovative firms may tend to allocate a significant portion of their resources to innovation and research and development (R&D) activities. The emphasis on resource allocation to innovation activities enshrined in business strategies could help firms utilise their resources effectively and efficiently to produce goods and services that could be new to implementing firm or the market where the firm sells their products. We therefore hypothesise that:

Hypothesis 1: Firms’ business strategies will be positively related to new to firm and market innovations.

The growing open innovation literature has recognised the significant contributions of external knowledge to firms’ innovation performance and activities (Anderson & Stejskal, 2019b ; Odei & Appiah, 2023 ). External knowledge is fundamental to firms’ innovation outcomes, as it usually balances and refreshes dormant internal knowledge that no longer offers improved benefits to firms. In terms of improving innovation performance, external partnerships are imperative because they enable firms to gain access to economically viable knowledge prevailing in other organisations, which can be absorbed to advance organisational learning and innovation abilities in the long run (Majeed & Breunig, 2022 ). The open innovation literature has also emphasised that firms benefit from collaborations, and this positively impacts their innovative outputs through three fundamental benefits: risk reduction, knowledge sharing, and swiftness in development (Lassen & Laugen, 2017 ). Through innovation alliances, each partner can possibly acquire a greater expanse of new knowledge than would have been possible through independent investment. Resource sharing between partners in the synergies becomes one of the potential means of reducing the cost of investments in product development as well as reducing the possible risk of failure (Jimenez-Jimenez et al., 2019 ). Firms require external knowledge because they may not have the financial muscle to generate it internally because of the exorbitant costs involved. When firms cannot generate this external knowledge due to its high cost, they can cooperate with other firms or organisations by pooling their resources. In addition to the above, collaboration also allows firms to quickly respond to market needs via an increased rate of new product development to be able to meet customer needs. Firms can forge synergies with partners in the market environment (Gesing et al., 2015 ) or with knowledge depositories such as universities and other public research organisations (Odei & Anderson, 2021 ; Odei & Hamplová, 2022 ). The influence of external collaboration diverges based on the type of innovation involved. Fındık and Beyhan ( 2015 ) study in Turkey concluded that external collaboration positively influenced product-oriented impacts of innovation, implying that firms that have external partnerships during the innovation process witness improvements in their products ahead of their competitors. Un and Asakawa ( 2015 ) also established that R&D partnerships with universities and suppliers positively influence process innovations, whereas other forms of collaboration do not significantly exert any influence. Lassen and Laugen ( 2017 ) also found that external collaboration significantly provides different effects on the degree of innovation, and this is dependent on the type of external partners they collaborate with. Based on the conclusions of these studies, we summarise the understanding that external collaborations could be beneficial for firms’ innovations because it is a source of new knowledge and expertise that could contribute to firms’ abilities to introduce new inventions that could be new to the firm and to the market. The systemic perspective aligns with the open innovation concept, which emphasises collaboration and knowledge exchange beyond organisational boundaries. Open innovation can lead to more novel and diverse ideas that could help in inventions that could be new to the firm that implemented it or to the market because it leverages external expertise and resources. We therefore propose our second hypothesis as:

Hypothesis 2: External collaboration is positively associated with inventions new to firm and the market.

Research on bureaucratic ties has gained enough scholarly attention in recent times because of its ability to influence firms' general and innovation performance (Krammer, 2019 ). Bureaucracy is an important non-market environment for the survival and development of firms. According to Tian et al. ( 2019 ), political relations refer to the inherent political connection between firms and an individual who is vested with political power. Governments the world over have been untrusted with several responsibilities, such as vital resource allocation and control, administrative oversight, land and property acquisition, loan guarantees, and partisan policies. They also take on critical duties and responsibilities such as law enforcement, public goods involvement, and regional economic and resilience building. Scholars, however, remain divided about the role political connections could play in firms’ performance. Some scholars believe that the presence of political ties is beneficial, as these connections play significant roles by serving as a means of support for firms (Krammer & Jimenez, 2020 ). In the context of developing and transitioning economies, firms need to deepen their connections with governments to constantly receive favour, financial resources, and other development opportunities via informal alternative mechanisms such as bribery and corruption due to the ineffectiveness of formal systems of law and investments. This ineffective formal system could result in a situation that will make senior managers spend more of their total productive time dealing with requirements and regulations imposed by governments (Rodríguez-Pose & Zhang, 2020 ). The more time senior managers spend dealing with draconian requirements and regulations imposed by governments, the less time they devote to concentrating on normal business activities, including innovations. More time spent could also mean that these government regulations are not flexible and straightforward, which could undermine firm performance in general. However, the objective level of these bureaucracies could be perceived differently because firms have different connections with governments or have different levels of experience dealing with governments (Odei & Appiah, 2024 ). Bureaucracy can facilitate the efficient allocation and utilisation of scarce resources, ensuring that innovation activities are well-funded and supported. Suzuki and Demircioglu (2017) study across several countries concluded that bureaucratic impartiality is significantly and positively related to innovation outputs. Bureaucratic structures provide well-defined guidelines and standardised processes, which can ensure consistent and reliable execution of innovation activities and projects (Best, 2016). On the contrary, research in China by Rodríguez-Pose and Zhang ( 2020 ) also revealed that weak regulatory quality ensures that senior management spends much time dealing with government regulations, which strongly hinders firm-level innovations. Based on the findings of these studies, we conclude that strict government requirements and regulations would necessitate significant expenditures by senior management to comply with these regulations. Government regulations could play a significant role in shaping the extent to which firms could generate novelty of innovations. According to the systemic perspective government regulations and policies could either promote or hinder firms’ abilities to introduce products and services (Midgley & Lindhult, 2021 ), that could be novel to the implementing firm or the market. Based on the study by Suzuki and Demircioglu (2017), we summarise the understanding that when there is impartiality in the bureaucratic environment, it could ensure that firms comply with regulatory standards (Carcelli, 2024 ), which is crucial for firms to undertake innovations that could be new to the firm or market. Hence, understanding this contextual factor is vital to navigating the regulatory landscape of innovation novelty. We therefore provide our third hypothesis as:

Hypothesis 3: Bureaucracy ties is positively associated with innovation novelty.

Relationships between control variables and innovation novelty

The relationship between firms’ legal status and innovation performance has been well researched (see Nam & Thanh, 2021 ; Xu et al., 2022 ). We controlled for legal status because it can affect firms’ abilities to access critical innovation resources, manage risks, attract human capital, and navigate regulatory landscapes, all of which are crucial for innovation (Odei & Appiah, 2023 ). Firms’ legal status can also influence vital decisions, such as those involving introducing innovations new to the firm and those new to the market ahead of their competitors. Shareholding companies might have unique characteristics that could make them more inclined to introduce innovations new to the firm and the market. The legal status relates to the existing ownership structure, as firm owners play key roles in firms' decisions, including those regarding innovations (Opoku-Mensah & Yin, 2021 ). In shareholding companies, shareholders essentially own and oversee the affairs of the company, which places certain rights and responsibilities on them. This type of ownership allows shareholders to exercise considerable powers to influence essential operational decisions, including human resources and investing in innovations, among others. Shareholding companies would be more likely to be innovative in comparison to sole proprietors in the sense that numerous individuals or firms come together to own a business. Firms in shareholding partnerships can pool resources and use them to, for instance, influence innovations, so they stand lofty chances of introducing innovations first to the market or to other firms within the same firm. Xu et al. ( 2022 ) study among Chinese firms found that major shareholders are likely to engage in short-term benefits and have the habit of supporting financial asset investment but not R&D investment. A related study by Jibir and Abdu ( 2021 ) concluded that firms’ legal status positively contributes to stimulating new to market and firm innovations. We summarise the idea that firms’ characteristics, such as their ownership structure, could affect their quest for innovations, and this depends on the motive of the owners. This motive could further influence key investment decisions, such as whether to engage in research and development for innovations.

Knowledge and innovation activities are localised and not uniformly distributed across geographic areas (James et al., 2016 ). We controlled for business cities because they are proven to influence innovation performance through a combination of human capital concentration, resource and infrastructure availability, co-operative ecosystems, supportive regulatory environments, and cultural dynamics (Dohse et al., 2019 ; Marchesani et al., 2022 ). These factors create a favourable environment needed for the continuous generation of innovation. In general, cities are viewed as a creative environment that can greatly assist firms in developing and improving their innovation performance. Clusters of firms in cities (agglomeration) create multiple positive spillover effects and encourage and sustain learning processes that stimulate the production, dissemination, and prompt adoption of new ideas in the long run (Amrin & Nurlanova, 2020 ; Dohse et al., 2019 ). Cities, especially business ones, usually abound in knowledge resources and inflows that promote the formation and expansion of knowledge-based firms. Another aspect of the cities that makes them capable of spurring innovations is the cluster of institutions such as higher education and other public research organisations. By their nature, they are knowledge producers as well as human capital developers, so their cluster in cities could promote knowledge accumulation as well as dissemination through their alumni networks. Countries' main business cities are noted to be appropriate locations for firms’ innovations and general performance. Business cities across the world are usually the economic hubs with the highest concentrations or agglomerations, which makes them dense in terms of economic activities (Dohse et al., 2019 ). They also hyphenate and connect with other countries (Odei et al., 2021 ). This special attribute of cities means that they enable vibrant interfaces and knowledge interchange within and across regions. The readily available knowledge and physical infrastructure also allow them to access international technologies and knowledge, which could spill over to firms. They are also known to have a high population concentration, which can facilitate knowledge exchange between individuals or between firms and other institutions. The large pool of population, especially a skilled workforce, could increase the city's absorptive capacity, making it able to absorb new knowledge from both within and from abroad. Firms are generally considered to be dependent on the density of specialised human capital, knowledge institutions, suppliers, and a large customer base embedded in cities (Andersson et al., 2019 ). These special attributes of business cities could make them the preferred locations for innovative firms, which might locate in these cities to take advantage of the positive externalities.

Data and methodology

Data used for the empirical analysis are based on a sample of 2132 enterprises, sourced from the World Bank Enterprise Survey (WBES), conducted between 2018 and 2020. The WBES is jointly conducted by three financial institutions, specifically the European Investment Bank (EIB), the World Bank Group (WBG), and the European Bank for Reconstruction and Development (EBRD). The WBES currently has data on over 200,000 innovative and non-innovative enterprises spanning about 152 countries. The WBES collects data from firms using the sample survey, employing the stratified random sampling technique based on firm size, sectors, and regions. The WBES has a wide array of data spanning innovation novelty, intellectual property rights protection, external collaboration, and firms’ characteristics such as legal status, firm size, etc. This makes the WBES one of the best datasets for analysing firm-level innovations. The final sample consisted of both large and small businesses from both the manufacturing and service sectors, with a breakdown as follows: Czech Republic (502), Slovakia (429), Hungary (805), and Poland (1369). The data were cleaned before the empirical assessment; outliers and missing values were dropped; we also omitted all "don’t know spontaneous" responses, which further shrank the final sample.

To investigate the determinants influencing firms’ innovation novelty in the Visegrad four countries, we employed the quantitative technique that adheres to the positivist epistemology and the objectivity view of reality. The study's cause-and-effect methodology necessitated the employment of an explanatory research design to examine how internal and external antecedents influence firms’ innovation novelties (Fox & Bayat, 2007 ). For the empirical estimation approach, this study used the logistic regression model. The logit model was chosen due to the binary nature of the dependent variable, thus innovation novelty. In the WBES, firms were asked to report on innovations that are significantly new to the firm that introduced them or to the market; this helped us determine the extent of the novelty of inventions. The logistic regression model allowed us to predict firms’ innovations novelties using various determinants. We were able to distinguish between important predictors of innovation novelties and determine the direction of these relationships by using this model. We used the average marginal effects from the initial analysis to compute the effects of variations in the dependent variable that are caused by a unit change in any of the predictors (Lüdecke, 2018 ). The conventional formula for the logistic regression model is provided by Tranmer and Elliot ( 2008 ):

where Logit ( P ) = the logit (log of the odds ratio); P  = the probability of introducing innovation novelties; and 1- P  = the probability of not introducing innovation novelties.

The marginal effect for the logit model is then given as:

\(\text{Pr}\left(y-1\right)\) represents the introducing innovation novelties, \(\varnothing \left(x\beta \right)\) represents the standard normal density computed at \(x\) β, \(\beta x\) is weighted by a factor \(f\) that depends on the values of regressors in \(x\)

However, the logit model could be biased in the presence of endogeneity in the variables. This situation could imply that the correlation amongst the covariates and the error term will not be equal to zero (E (X, u) ≠ 0), leading to inconsistent estimation results (Wooldridge, 2010 ). One possible way to overcome this econometric issue is to use instrumental variables. The instrumental variable probit model was used in the second stage of the analysis to check for potential endogeneity in the data. We anticipate that there is a possibility that one or more of our covariates could be endogenous and could lead to unreliable results. The estimation of the endogenous probit model was done using Newey's two-step option. The independent and control variables used in the models were carefully selected based on existing innovation literature. Table 1 provides the definitions of both the dependent, independent and control variables used in the empirical specification.

Results and discussion

We begin the discussion of the empirical results to determine the various factors driving innovation novelties with the descriptive statistics. Table 2 reports the descriptive statistics and the Kendall's tau-b correlations for the variables employed throughout this study. On average, about 18% of the sampled firms reported introducing innovations that were significantly different, either to the firm or the market. About 37% of the firms confirmed that they have business strategies that guide their operations. The results also show that the extent of each firm’s collaboration in the sample is very low; just about 9% of firms reported having external collaborations with other entities and institutions. This low level of institutional collaboration has been confirmed by other studies (see Vlckova & Thakur-Weigold, 2019 ; Odei & Hamplová, 2022 ). Furthermore, a little over 15% of these firms reported engaging in research and development activities for their innovations. The levels of intellectual property rights protection in the sampled firms were also very low; approximately 6% of firms reported having patents or trademarks. Regarding the time firm managers spend to meet government regulations, we found that it was less; on average, it was confirmed to be about 12% of all top managers’ time. Regarding the legal status of firms, the results show that about 27% of these firms are classified as shareholding companies with non-traded shares or shares sold privately. Finally, about 20% of the sampled firms are in business cities. The correlations between the different independent variables and the dependent variable measured with innovation novelty were also found to be low. The Kendall's tau-b results show that the coefficients are low and were all statistically significant at the 0.1 and 0.05 levels, indicating that potential collinearity problems are reduced. Nevertheless, to accomplish discriminant validity, valid measures of single constructs must not be highly correlated among themselves (Bagozzi et al., 1991 ). We used the F-ratio to test whether the canonical correlations between our constructs are zero. The F value of a variable reveals its statistical significance in group discrimination; that is, it is a measure of how much a variable contributes uniquely to the prediction of group membership. The dimension for the discriminant validity was grouped by countries, leading to three dimensions. The result showed that the canonical correlations for the three dimensions are all statistically significant at the 0.05 level. The canonical correlations for the three dimensions are 0.466, 0.270 and 0.114, respectively. We therefore reject the null hypothesis that there is a small canonical correlation which is equal to zero. Since the correlations are low, and all the F-tests are significant, it implies that all the dimensions are significant and are needed to describe the differences between the three groups of countries.

The results of the regression models in Table  3 show that there is a positive and statistically significant association between business strategies and innovation. This result indicates that there is compelling evidence within the sample supporting hypothesis 1. With regard to Hypothesis 2, which sought to establish whether external collaboration influences firms’ innovation novelties, we found more evidence that there is a statistically significant relationship between external collaboration and innovation novelty. Engaging in research and development was positively correlated with innovation novelty. We also found that intellectual property rights and bureaucracy do not significantly influence innovation novelty. The results on the insignificant association between bureaucracy and innovation mean that hypothesis 3 is rejected. The results of the firm characteristics show that the legal status of firms is negatively correlated with their abilities to offer significantly improved products and services that are either new to the firm or the market. Firms in business cities are also less likely to have greater ability to introduce significantly new products and services, either to the firm that introduced them or to its market rivals.

The positive relationship between external collaboration and innovation novelty is as expected and coherent with the open innovation literature. As shown by the marginal effect results, firms that collaborate with other R&D partners are more likely to increase their innovation novelties marginally by about 12 percentage points. This can be explained as follows: firms are limited in their potential to internalise all necessary knowledge and capabilities (Rauter et al., 2019 ). As shown in the literature review section, innovation collaborations allow firms to access new knowledge, expertise, and resources that they cannot generate by themselves, and this could be vital in the innovation process. External innovation collaborations allow firms to search for and incorporate external knowledge into new or ongoing innovation activities, and this can enable them to significantly introduce products and services that could be new to the firm itself or its competitors. Without these forms of collaboration, the likelihood of novel innovations could be reduced because firms' knowledge bases would be stacked. The choice of collaborating partners influences overall firm innovation performance; for instance, firms’ collaborations with knowledge repositories such as universities will enable them to access scientific knowledge that can be absorbed in the innovation process. This result is consistent with the findings of Majeed and Breunig ( 2022 ) study on Australian firms, which concluded that external collaboration is significantly correlated with increased levels of novelty in innovation. Yan et al. ( 2020 ) also concluded that external collaboration with other industries' customers is a positive signal for innovation novelty. Research in the Czech Republic by Odei and Hamplová ( 2022 ) also concluded that firms’ collaborations with universities and other public research organisations increase the likelihood of major and minor innovations.

The findings also confirmed that R&D has only a minor impact on the likelihood of innovation novelty, as measured by both new-to-firm and new-to-market product innovation. This result is as expected and in line with the conclusion of several studies (see Gómez et al., 2020 ). Research and development activities have been demonstrated to have the highest marginal effect on innovation novelty, implying that it is likely to increase by 22 percentage points. R&D has been proven to be a catalyst for innovations, and firms increasingly invest in R&D to enhance their innovation performance, which allows them to introduce innovative products and services that could be novel to the firm or its market rivals (Leung & Sharma, 2021 ). Internal R&D activities by local firms play a bifold role in creating new knowledge as well as expanding absorptive capacity, which could all favour innovation novelty introduction. This finding is in line with those of Díaz-Díaz and De Saá-Pérez ( 2012 ), Gómez et al. ( 2020 ), and Odei and Hamplová ( 2022 ), emphatically supporting Hypothesis H3.

The results show that there is a positive and statistically significant relationship between business strategies and innovation novelty. The marginal effect result also shows that firms with business strategies are 3 percentage points more likely to increase their innovation novelties. Having business strategies with an emphasis on innovation could serve as a guide and yardstick to determine whether the firm is on track to achieve innovations. Business strategy could also inform the firm's choices, especially those related to internal and external resources such as information and new knowledge. Having a business strategy will allow managers to overcome operational obstacles to remain focused on innovation resources to produce high-innovation novelties. Hajar ( 2015 ) found that business strategies have a positive and statistically significant influence on innovation, which could lead to improved firm performance. Wu ( 2013 ) also concluded that business strategies, especially those focused on R&D, are a vital determinant of overall organisational innovation performance.

The results also revealed that the time top management spent to meet government regulations do not significantly influence innovation novelties within the sampled firms. This result is surprising, however, a look at the descriptive statistics in Table  1 shows that top managers of the sampled firms spend on average 12% of their time meeting government regulations. This result means that firms spend less time on government regulations, this will allow them to allocate their resources (both financial and human) towards activities that directly contribute to their core business objectives, such as market expansion among others. The more time senior managers spend on government regulations, the less time they must devote to innovation activities, which can affect overall innovation performance. However, our results mean that government regulations in these countries are not stringent, which is one possible reason why senior firm managers do not spend much time meeting them. As a result, top management can be expected to encourage management innovation by spending less time on regulatory compliance. The results on senior management time spent on meeting government regulations differ from the finding of Krammer ( 2019 ) study conducted in Central Asia and Eastern Europe, who concluded that bureaucracy has a significantly negative influence on firms' overall innovation performance. The contradictory result indicates that the regional variations could play key roles in how bureaucracy impacts firm-level innovations.

The results of the control variables show that business cities marginally reduce the prospects of innovation novelties in the sampled firms; they are likely to marginally decrease it by 6 percentage points. Main business cities such as Prague, Brno, Budapest, Bratislava, Warsaw, Ostrava, etc., have enhanced constant interactions, transaction costs, and informal knowledge flows that could influence the tendency of firms to benefit from city spillovers to introduce innovation novelties. However, as shown by the descriptive statistics in Table  1 , less of these firms are in these business cities, so they do not benefit from advantages business cities provide. The possible reason for the negative relationship could be that these business cities are able to attract top talent, but they also create severe competition for qualified labour (Glaeser & Resseger, 2010 ). Because skilled people may be attracted away by higher compensation or better prospects elsewhere, this rivalry can make it difficult for firms to retain or attract innovative personnel. Also, the cost of operating in business cities is typically high, resulting in increased operational costs for businesses (Zhai et al., 2022 ). These increased costs may limit the resources available for R&D, innovative projects, or risk-taking. Because of the large stakes involved, firms in business cities may become risk averse. The need to maintain profitability and shareholder value might deter innovation because it often involves uncertainty and the possibility of financial losses in the short term. The results further show that the legal status of firms is negatively related to innovations, implying that firms’ innovations decrease with their legal status. According to the marginal effect results, legal status reduces innovation novelties by 5 percentage points. This result shows that the legal status of a firm does not positively contribute to spurring innovation novelties. This result shows that the ownership structure within the sampled firms is not likely to positively drive their abilities to introduce innovations that are either new to the firms themselves or to their market rivals. Our result on legal status contradicts the findings of Jibir and Abdu ( 2021 ), as they found a positive correlation. The results also revealed that intellectual property rights protection measured with patents or trademarks marginally increase innovation novelty. This result resonates the findings of Verhoeven et al., ( 2016 ) and Guo et al., ( 2019 ), who also found that intellectual property rights protection positively influences firms’ innovation.

Robustness checks

We evaluated the robustness of the models and tested the various hypotheses using two other estimation methods, i.e. instrumental variable models and introducing additional sets of control variables. First, we introduced alternative sets of control variables that have been proven by the innovation literature to influence firm-level innovations. Following the literature, we included years of managerial experience (Odei & Appiah, 2023 ), firm size (Dunyo & Odei, 2023 ; Shefer & Frenkel, 2005 ), and formal training (Odei & Hamplová, 2022 ). The results in Table  4 , model 1, show that R&D and patents marginally increase innovation novelty by 25 and 9 percentage points, respectively, while legal status and business cities marginally reduce it by 5 percentage points. When we introduced business strategies in Model 2, we found that business strategies marginally increased innovation novelty by 3 percentage points. This result confirms hypothesis 1. In model 2, we find support for hypothesis 2, as the results show that external collaboration marginally increases innovation novelty by 12 percentage points. As shown in model 4, we did not find support for hypothesis 3, as the bureaucracy was statistically insignificant. As shown by these results, we validate all the hypothesised relationships described above, as the results do not vary when additional control variables are included. Based on the results of our robustness test, which involved including different additional sets of control variables into the models, we conclude that our key findings remain unchanged.

Next, we used instrumental variable models which are well-known to be suitable for endogeneity tests. The robustness tests involved assessing the existence of possible endogeneity in the variables, which could contaminate our findings, leading to inconsistent conclusions. Although the carefully selected covariates measure innovation novelty, as shown by the first stage results, we believe that the potential presence of endogeneity could contaminate the results. We believe that R&D activities could potentially influence firms’ business strategies, external collaborations, and abilities to acquire patents. We verified whether the research and development considered endogenous could be tested for exogeneity. Following the literature (see Odei & Appiah, 2023 ), we used the instrumental variable (IV) probit model with Newey's two-step estimation approach to test for possible endogeneity in our variables. For the endogenous variable as described above, we used research and development with innovation novelty as a dependent variable while maintaining the remaining covariates. The Wald test of exogeneity measures whether our data support or reject the null hypothesis of exogeneity. The Wu–Hausman F test and Durbin–Wu–Hausman Chi-square test were further used to assess endogeneity to support the Wald test result. We further tested the strength of the selected instrument, as weak instruments could result in econometric issues that can cause biased estimates of covariates (Stock et al., 2002 ). Weak instruments can also cause the estimator's distribution to deviate considerably from a normal distribution. This was tested using the Stock–Yogo F statistics as well as the Cragg–Donald Wald F statistic.

The results of the robustness tests are shown in Table  5 . According to the Wald test result, Chi-squared (2.61), prob > Chi-squared = 0.106. This result is statistically insignificant at the 95% level, suggesting that we can accept the null hypothesis that the R&D is considered exogenous and not endogenous. This result was further confirmed by both the Wu–Hausman F test and the Durbin–Wu–Hausman Chi-squared test with p-values greater than the 0.05 significant level. Based on these results, we deduce that our variables are not impacted by potential endogeneity concerns. The test F statistic is 23.68, exceeding the Stock–Yogo recommended threshold of 10. The Cragg–Donald f-test statistic based on the relevance test of the instrument is 49.10, which is greater than the recommended cut-off value of 10; hence, we reject the null hypothesis that the instrument is weak. The under-identification test using the Anderson canon. corr. LM statistic shows that the chosen instrument is relevant and the overidentifying constraints are valid. Since there are no endogeneity issues in the variables, there is no need for IV models. We do not discuss the IV results since in the absence of endogeneity, the logit model discussed in the first stage above, are considered consistent and robust.

Firms’ abilities to introduce new and significantly improved products that are either new to the firm itself or its market rivals are considered important because they give firms the competitive edge. The existing evidence suggests that the nexus between innovations and firms’ performance is highly complex, although several studies have concluded that innovation drives firms’ success. However, there is no consensus among scholars as to how innovation should be measured, but several studies have focused on the technological and non-technological perspectives. Other measures of innovation, such as degrees of novelty, have received less scholarly attention. This research filled this gap by drawing insight from the systemic perspective to develop a simplified model to assess the effects of business strategies, government–business relations, external collaboration on innovation novelty among firms in Visegrad countries. Using pooled cross-sectional data from firms listed in the Czech Republic, Slovakia, Hungary, and Poland and employing a combination of three estimation approaches, our study revealed that just 18% of firms reported introducing innovations that were entirely new to themselves and their market competitors. The empirical results also showed that patents, R&D activities, business strategies, and external collaboration marginally influence firms’ innovation novelties. The study did not find statistical evidence to support the role of government–business relations in influencing innovation novelties in the sample, contrary to expectations. Finally, we found that the control variables, such as the legal status and business cities, marginally decrease firms’ aptitudes to introduce innovations that could be new to the firm or to market ahead of their competitors. These findings are robust, as they passed two well-known robustness tests.

Theoretical implications

The findings of the study make significant theoretical contributions and extend the growing literature on bureaucracy in the context of transitioned and catching-up countries such as the Visegrad Four. Theoretically, the results revealed that bureaucracy, measured by the time senior managers spend meeting government regulations, do not significantly influence the abilities of firms to introduce innovation novelties. This signifies that these firms spend less time meeting government regulations. In most transition countries, where there are stringent regulations, firms spend time they could devote to the innovation process to meet government regulations (Tian et al., 2019 ). Our result signifies that regulatory compliance in these countries are not stringent, so they are favourable for firms’ operations. This allows firms to devote enough time which could be spent on meeting government regulations on other firm activities. This result differs from existing studies in emerging economies (see, Krammer, 2019 ). This result is in line with the systemic perspective of innovation theory from the context of transitioned economies perspective, as relationships are integral part of the theory. Second, the findings of this research indicate that external collaboration marginally increases firms’ abilities to introduce innovation that could be new to the firm or the market. The result is a significant addition to the conventional explanation on the importance of external collaboration to the innovation process (e.g., Lassen & Laugen, 2017 ; Midgley & Lindhult, 2021 ; Odei & Hamplová, 2022 ). This result indicates that firms in these group of countries can derive new knowledge, expertise and resources from external collaboration which could improve their abilities to introduce innovations that could be novel to both the firm and the market. This finding is in line with the systemic perspective literature. Thirdly, the results have shown that business strategies could significantly influence firms’ investment decisions, especially those on innovations and R&D. This result calls for firms aiming to be innovative to have a business strategy that focuses on investments in R&D and innovation as well as all related activities. Finally, this research used data from the Visegrád Group of countries, thus Poland, Slovakia, Hungary, and the Czech Republic, which have all transitioned into market economies, to show that external collaboration and having business strategies, especially those with a focus on innovation, can serve as enablers for innovation novelties in these transitioned market firms that often lag in innovations. Accordingly, the study contributes to research on firm-level innovation in the Visegrád Group (Odei & Appiah, 2023 ) by examining whether business strategies, external collaboration, and bureaucracy in transitioned country-based firms are likely to spur innovations that are new to the firm or the market. This is an important addition to the growing literature on innovation because very little scholarly attempts have been dedicated to investigating how these factors influence innovation novelties, especially in transitioned economies such as the Visegrád Group. This addition provides a rich transitioned market context for theory building.

Managerial and policy implications

Drawing on the key outcomes of this study, several policy pathways can be proposed for firm managers and policymakers in the Visegrád Group. First, the finding that external collaboration positively influences innovation novelty in transitioned countries suggests several policy implications aimed at fostering innovation. Policymakers in these countries could offer tax incentives, grants, and subsidies to incentivise firms, research institutions, and scientists to engage in open innovation projects with both domestic and foreign partners. These incentives can help offset the costs and risks associated with collaboration, which usually constrain such interactions. Developing robust R&D infrastructure is essential for attracting especially foreign partners who could complement for any shortfalls in the domestic ecosystem. Policymakers should invest in research institutions and infrastructure such as laboratories, and technology parks that provide the necessary resources and support for innovation and its related activities. Firm managers in these countries are encouraged to actively seek out partnerships with both domestic and international organisations that bring diverse perspectives, resources, and expertise to the innovation process. This might include knowledge repositories such as universities, research institutions, start-ups, as well as other established firms in related or complementary industries. Second, leveraging the positive impacts of business strategies on the novelty of innovation is very crucial for firms in catching up economies such the Visegrád Group. Firm managers should ensure that their existing and new business strategies are aligned with their innovation goals. This may involve revisiting and possibly adjusting strategies to prioritise innovation and novelty, especially in transitioned countries where the business environment might be evolving rapidly. Third, the finding that bureaucracy does not significantly influence innovation novelty in transitioned countries could also have several policy implications. Policymakers may need to re-evaluate the efficiency and relevance of bureaucratic structures in fostering innovation. The fact that bureaucracy in these countries does not significantly impact innovation novelty, could mean that there might be opportunities to streamline the bureaucratic processes to ensure that they do not negatively affect firms’ innovation outcomes. Policymakers could therefore shift their attention to other factors that could influence innovation novelty, such as investment in research and development (R&D), human capital development, access to capital, and fostering a culture of intellectual property right protection. Emphasising these aspects of the innovation environment could potentially lead to an improvement in innovation outcomes. While bureaucracy has been proven to not directly affect innovation novelty, it can still hinder efficiency and agility within firms (Luo & Junkunc, 2008 ). Firm managers should strive to streamline bureaucratic processes to reduce unnecessary obstacles and enhance overall organisational performance. Managers could direct their attention towards other direct drivers of innovation, such as organisational culture, leadership style, resource allocation, and collaboration mechanisms. Emphasising these aspects could ensure that they yield greater returns in fostering and sustaining innovation.

Research limitations and future directions

A few limitations have been acknowledged in this paper, which could provide directions for further research. First, the research was based on pooled cross-sectional datasets. We recommend that future studies use longer panel datasets when they become available to fully capture the dynamics and factors influencing innovation novelties. Secondly, our study is limited to these four transitioned and catching-up countries. Future studies need to be done in other transition economies, especially in Europe and other parts of the world, to further study the possibilities of generalising this study's findings. Lastly, we analysed the influence of bureaucracy on all firms; however, firms could have different relationships with governments, and this will require further research to examine which firms could be most affected by government regulations.

Availability of data and materials

The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Abbreviations

Research and development

European Union

World Bank Enterprise Survey

European Investment Bank

World Bank Group

European Bank for Reconstruction and Development

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The research has been partially supported by the Faculty of Informatics and Management UHK specific research project 2107 Addressing modern research topics with increased students’ involvement .

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Odei, S.A., Soukal, I. Business strategies, bureaucratic ties, and firms’ innovation novelty: insights from the World Bank enterprise survey. J Innov Entrep 13 , 63 (2024). https://doi.org/10.1186/s13731-024-00424-1

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• Innovation novelty
• Business strategies
• Bureaucracy
• Collaboration
• Legal status
• Visegrad countries

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