examples of hypothesis testing in business

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Hypothesis Testing in Business: Examples

hypothesis testing for business - examples

Are you a product manager or data scientist looking for ways to identify and use most appropriate hypothesis testing for understanding business problems and creating solutions for data-driven decision making? Hypothesis testing is a powerful statistical technique that can help you understand problems during exploratory data analysis (EDA) and identify most appropriate hypotheses / analytical solution. In this blog, we will discuss hypothesis testing with examples from business. We’ll also give you tips on how to use it effectively in your own problem-solving journey. With this knowledge, you’ll be able to confidently create hypotheses, run experiments, and analyze the results to derive meaningful conclusions. So let’s get started!

Before going any further, you may want to check out my detailed blog on hypothesis testing – Hypothesis testing steps & examples .

The picture below represents the key steps you can take to identify appropriate hypothesis tests related to your business problem you are trying to solve.

Table of Contents

Business Objective / Problem Analysis to Asking Key Questions

Here are the steps which you can use to come up with hypothesis tests related to your business problems. You can then use data to perform hypothesis tests and arrive at different conclusions or inferences.

Setting / Identifying business objective : First & foremost, you need to have a business objective which you want to achieve. For example, achieve an increase of 10% revenue in the year ahead.
Identifying key business divisions / units and products & services : Second step is to identify key departments / divisions and related products & services which can help achieve the business objective. For current example, sales can be increased by increase in sales of products and services. For service based companies, it can be increase in sales of existing services and one or more new services. For products based companies, it could be increase in sales of different products.
Identify key personas / stakeholders : For each business division / department, identify key personas or stakeholders who could be accountable for contributing to achievement of business objective. For current example, it could personas / stakeholders who would own the increase in sales of products and / or services.
Are the sales of product A, B and C different?
Are the sales of product A, B and C similar across all the regions, countries, states, etc.?
Are there differences between products and competitors’ products vis-a-vis sales?
Are there any differences between customer queries / complaints across different products (A, B, C)?
Are there any differences between product usage patterns across different products, and for each product?
Are there differences between marketing initiatives run for different products?
Are there differences between teams working on different products?

Hypothesis formulation

Once the questions have been asked / raised, you can create hypotheses from these questions in order to arrive at the answers based on data analysis and create strategy / action plan. Lets take a look at one of the question and how you can formulate hypothesis and perform hypothesis testing. We will also talk about data and analytics aspects.

In order to create strategy around increasing sales revenue, it is very important to understand how has been the sales of different products in past and whether the sales have been different for us to dig deeper into the reasons and create some action plan?

The status quo becomes null hypothesis ([latex]H_0[/latex]. In our current analysis, the status quo is that there is no difference between the sales revenue of different products and that each product is doing equally good and selling well with the customers.

[latex]H_0[/latex]: There is no difference between sales revenue of different products.

The new knowledge for which the null hypothesis can be thrown away can be called as alternate hypothesis, [latex]H_a[/latex]. In current example, the new knowledge or alternate hypothesis is that there is a significant difference between the sales revenue of different products.

[latex]H_a[/latex]: There is a significant difference between sales revenue of different products.

Identifying Test Statistics for Hypothesis Testing

Once the hypothesis has been formulated, the next step is to identify the test statistics which can be used to perform the hypothesis test.

We can perform one-way Anova test to check whether there is a difference between sales based on the product. One-way ANOVA test requires calculation of F-statistics . The factor is product and levels are product A, B and C. Read my blog post on one-way ANOVA test to learn about different aspect of this test. One-Way ANOVA Test: Concepts, Formula & Examples

Apart from Hypothesis test and statistics, one can also set the level of significance based on which one can reject the null hypothesis or otherwise. Generally, it is chosen as 0.05.

Gather Data

Once the hypothesis test and statistics gets chosen, next step is to gather data. You can identify the system which holds the sales data and then gather the data from that system for last 1 year.

Perform Hypothesis Testing

Once the data is gathered, you can use Excel tool or any other statistical packages in Python / R and perform hypothesis testing by doing the following:

Calculating the value of test statistics
Calculate P-value
Comparing the P-value with level of significance
Reject the null hypothesis or otherwise

In conclusion, hypothesis testing is an essential tool for businesses to make data-driven decisions. It involves identifying a problem or question, formulating a hypothesis, identifying the appropriate test statistics, gathering data, and performing hypothesis testing. By following these steps, businesses can gain valuable insights into their operations, identify areas of improvement, and make informed decisions. It is important to note that hypothesis testing is not a one-time process but rather a continuous effort that businesses must undertake to stay ahead of the competition. Examples of hypothesis testing in business can range from identifying the effectiveness of a new marketing campaign to determining the impact of changes in pricing strategies. By analyzing data and performing hypothesis testing, businesses can determine the significance of these changes and make informed decisions that will improve their bottom line.

Ajitesh Kumar

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What Is Hypothesis Testing?

Step 1: define the hypothesis, step 2: set the criteria, step 3: calculate the statistic, step 4: reach a conclusion, types of errors, the bottom line.

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Hypothesis Testing in Finance: Concept and Examples

Charlene Rhinehart is a CPA , CFE, chair of an Illinois CPA Society committee, and has a degree in accounting and finance from DePaul University.

examples of hypothesis testing in business

Your investment advisor proposes you a monthly income investment plan that promises a variable return each month. You will invest in it only if you are assured of an average $180 monthly income. Your advisor also tells you that for the past 300 months, the scheme had investment returns with an average value of $190 and a standard deviation of $75. Should you invest in this scheme? Hypothesis testing comes to the aid for such decision-making.

Key Takeaways

Hypothesis testing is a mathematical tool for confirming a financial or business claim or idea.
Hypothesis testing is useful for investors trying to decide what to invest in and whether the instrument is likely to provide a satisfactory return.
Despite the existence of different methodologies of hypothesis testing, the same four steps are used: define the hypothesis, set the criteria, calculate the statistic, and reach a conclusion.
This mathematical model, like most statistical tools and models, has limitations and is prone to certain errors, necessitating investors also considering other models in conjunction with this one

Hypothesis or significance testing is a mathematical model for testing a claim, idea or hypothesis about a parameter of interest in a given population set, using data measured in a sample set. Calculations are performed on selected samples to gather more decisive information about the characteristics of the entire population, which enables a systematic way to test claims or ideas about the entire dataset.

Here is a simple example: A school principal reports that students in their school score an average of 7 out of 10 in exams. To test this “hypothesis,” we record marks of say 30 students (sample) from the entire student population of the school (say 300) and calculate the mean of that sample. We can then compare the (calculated) sample mean to the (reported) population mean and attempt to confirm the hypothesis.

To take another example, the annual return of a particular mutual fund is 8%. Assume that mutual fund has been in existence for 20 years. We take a random sample of annual returns of the mutual fund for, say, five years (sample) and calculate its mean. We then compare the (calculated) sample mean to the (claimed) population mean to verify the hypothesis.

This article assumes readers' familiarity with concepts of a normal distribution table, formula, p-value and related basics of statistics.

Different methodologies exist for hypothesis testing, but the same four basic steps are involved:

Usually, the reported value (or the claim statistics) is stated as the hypothesis and presumed to be true. For the above examples, the hypothesis will be:

Example A: Students in the school score an average of 7 out of 10 in exams.
Example B: The annual return of the mutual fund is 8% per annum.

This stated description constitutes the “ Null Hypothesis (H 0 ) ” and is assumed to be true – the way a defendant in a jury trial is presumed innocent until proven guilty by the evidence presented in court. Similarly, hypothesis testing starts by stating and assuming a “ null hypothesis ,” and then the process determines whether the assumption is likely to be true or false.

The important point to note is that we are testing the null hypothesis because there is an element of doubt about its validity. Whatever information that is against the stated null hypothesis is captured in the Alternative Hypothesis (H 1 ). For the above examples, the alternative hypothesis will be:

Students score an average that is not equal to 7.
The annual return of the mutual fund is not equal to 8% per annum.

In other words, the alternative hypothesis is a direct contradiction of the null hypothesis.

As in a trial, the jury assumes the defendant's innocence (null hypothesis). The prosecutor has to prove otherwise (alternative hypothesis). Similarly, the researcher has to prove that the null hypothesis is either true or false. If the prosecutor fails to prove the alternative hypothesis, the jury has to let the defendant go (basing the decision on the null hypothesis). Similarly, if the researcher fails to prove an alternative hypothesis (or simply does nothing), then the null hypothesis is assumed to be true.

The decision-making criteria have to be based on certain parameters of datasets.

The decision-making criteria have to be based on certain parameters of datasets and this is where the connection to normal distribution comes into the picture.

As per the standard statistics postulate about sampling distribution , for any sample size n, the sampling distribution of X is normal if the X from which the sample is drawn is normally distributed. Hence, the probabilities of all other possible sample mean that one could select are normally distributed.

For e.g., determine if the average daily return, of any stock listed on XYZ stock market , around New Year's Day is greater than 2%.

H 0 : Null Hypothesis: mean = 2%

H 1 : Alternative Hypothesis: mean > 2% (this is what we want to prove)

Take the sample (say of 50 stocks out of total 500) and compute the mean of the sample.

For a normal distribution, 95% of the values lie within two standard deviations of the population mean. Hence, this normal distribution and central limit assumption for the sample dataset allows us to establish 5% as a significance level. It makes sense as, under this assumption, there is less than a 5% probability (100-95) of getting outliers that are beyond two standard deviations from the population mean. Depending upon the nature of datasets, other significance levels can be taken at 1%, 5% or 10%. For financial calculations (including behavioral finance), 5% is the generally accepted limit. If we find any calculations that go beyond the usual two standard deviations, then we have a strong case of outliers to reject the null hypothesis.

Graphically, it is represented as follows:

In the above example, if the mean of the sample is much larger than 2% (say 3.5%), then we reject the null hypothesis. The alternative hypothesis (mean >2%) is accepted, which confirms that the average daily return of the stocks is indeed above 2%.

However, if the mean of the sample is not likely to be significantly greater than 2% (and remains at, say, around 2.2%), then we CANNOT reject the null hypothesis. The challenge comes on how to decide on such close range cases. To make a conclusion from selected samples and results, a level of significance is to be determined, which enables a conclusion to be made about the null hypothesis. The alternative hypothesis enables establishing the level of significance or the "critical value” concept for deciding on such close range cases.

According to the textbook standard definition, “A critical value is a cutoff value that defines the boundaries beyond which less than 5% of sample means can be obtained if the null hypothesis is true. Sample means obtained beyond a critical value will result in a decision to reject the null hypothesis." In the above example, if we have defined the critical value as 2.1%, and the calculated mean comes to 2.2%, then we reject the null hypothesis. A critical value establishes a clear demarcation about acceptance or rejection.

This step involves calculating the required figure(s), known as test statistics (like mean, z-score , p-value , etc.), for the selected sample. (We'll get to these in a later section.)

With the computed value(s), decide on the null hypothesis. If the probability of getting a sample mean is less than 5%, then the conclusion is to reject the null hypothesis. Otherwise, accept and retain the null hypothesis.

There can be four possible outcomes in sample-based decision-making, with regard to the correct applicability to the entire population:

The “Correct” cases are the ones where the decisions taken on the samples are truly applicable to the entire population. The cases of errors arise when one decides to retain (or reject) the null hypothesis based on the sample calculations, but that decision does not really apply for the entire population. These cases constitute Type 1 ( alpha ) and Type 2 ( beta ) errors, as indicated in the table above.

Selecting the correct critical value allows eliminating the type-1 alpha errors or limiting them to an acceptable range.

Alpha denotes the error on the level of significance and is determined by the researcher. To maintain the standard 5% significance or confidence level for probability calculations, this is retained at 5%.

According to the applicable decision-making benchmarks and definitions:

“This (alpha) criterion is usually set at 0.05 (a = 0.05), and we compare the alpha level to the p-value. When the probability of a Type I error is less than 5% (p < 0.05), we decide to reject the null hypothesis; otherwise, we retain the null hypothesis.”
The technical term used for this probability is the p-value . It is defined as “the probability of obtaining a sample outcome, given that the value stated in the null hypothesis is true. The p-value for obtaining a sample outcome is compared to the level of significance."
A Type II error, or beta error, is defined as the probability of incorrectly retaining the null hypothesis, when in fact it is not applicable to the entire population.

A few more examples will demonstrate this and other calculations.

A monthly income investment scheme exists that promises variable monthly returns. An investor will invest in it only if they are assured of an average $180 monthly income. The investor has a sample of 300 months’ returns which has a mean of $190 and a standard deviation of $75. Should they invest in this scheme?

Let’s set up the problem. The investor will invest in the scheme if they are assured of the investor's desired $180 average return.

H 0 : Null Hypothesis: mean = 180

H 1 : Alternative Hypothesis: mean > 180

Method 1: Critical Value Approach

Identify a critical value X L for the sample mean, which is large enough to reject the null hypothesis – i.e. reject the null hypothesis if the sample mean >= critical value X L

P (identify a Type I alpha error) = P (reject H 0 given that H 0 is true),

This would be achieved when the sample mean exceeds the critical limits.

= P (given that H 0 is true) = alpha

Graphically, it appears as follows:

Taking alpha = 0.05 (i.e. 5% significance level), Z 0.05 = 1.645 (from the Z-table or normal distribution table)

= > X L = 180 +1.645*(75/sqrt(300)) = 187.12

Since the sample mean (190) is greater than the critical value (187.12), the null hypothesis is rejected, and the conclusion is that the average monthly return is indeed greater than $180, so the investor can consider investing in this scheme.

Method 2: Using Standardized Test Statistics

One can also use standardized value z.

Test Statistic, Z = (sample mean – population mean) / (std-dev / sqrt (no. of samples).

Then, the rejection region becomes the following:

Z= (190 – 180) / (75 / sqrt (300)) = 2.309

Our rejection region at 5% significance level is Z> Z 0.05 = 1.645.

Since Z= 2.309 is greater than 1.645, the null hypothesis can be rejected with a similar conclusion mentioned above.

Method 3: P-value Calculation

We aim to identify P (sample mean >= 190, when mean = 180).

= P (Z >= (190- 180) / (75 / sqrt (300))

= P (Z >= 2.309) = 0.0084 = 0.84%

The following table to infer p-value calculations concludes that there is confirmed evidence of average monthly returns being higher than 180:

A new stockbroker (XYZ) claims that their brokerage fees are lower than that of your current stock broker's (ABC). Data available from an independent research firm indicates that the mean and std-dev of all ABC broker clients are $18 and $6, respectively.

A sample of 100 clients of ABC is taken and brokerage charges are calculated with the new rates of XYZ broker. If the mean of the sample is $18.75 and std-dev is the same ($6), can any inference be made about the difference in the average brokerage bill between ABC and XYZ broker?

H 0 : Null Hypothesis: mean = 18

H 1 : Alternative Hypothesis: mean <> 18 (This is what we want to prove.)

Rejection region: Z <= - Z 2.5 and Z>=Z 2.5 (assuming 5% significance level, split 2.5 each on either side).

Z = (sample mean – mean) / (std-dev / sqrt (no. of samples))

= (18.75 – 18) / (6/(sqrt(100)) = 1.25

This calculated Z value falls between the two limits defined by:

- Z 2.5 = -1.96 and Z 2.5 = 1.96.

This concludes that there is insufficient evidence to infer that there is any difference between the rates of your existing broker and the new broker.

Alternatively, The p-value = P(Z< -1.25)+P(Z >1.25)

= 2 * 0.1056 = 0.2112 = 21.12% which is greater than 0.05 or 5%, leading to the same conclusion.

Graphically, it is represented by the following:

Criticism Points for the Hypothetical Testing Method:

A statistical method based on assumptions
Error-prone as detailed in terms of alpha and beta errors
Interpretation of p-value can be ambiguous, leading to confusing results

Hypothesis testing allows a mathematical model to validate a claim or idea with a certain confidence level. However, like the majority of statistical tools and models, it is bound by a few limitations. The use of this model for making financial decisions should be considered with a critical eye, keeping all dependencies in mind. Alternate methods like Bayesian Inference are also worth exploring for similar analysis.

Gregory J. Privitera. " Chapter 8: Introduction to Hypothesis Testing ." Statistics for Behavioral Sciences, Part III: Probability and the Foundations of Inferential Statistics. Sage Publications , pp. 4-5.

Rice University, OpenStax. " Introductory Statistics 2e: 7.1 The Central Limit Theorem for Sample Means (Averages) ."

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Who’s Joe?

“A fact is a simple statement that everyone believes. It is innocent, unless found guilty. A hypothesis is a novel suggestion that no one wants to believe. It is guilty until found effective.”

– Edward Teller, Nuclear Physicist

During my first brainstorming meeting on my first project at McKinsey, this very serious partner, who had a PhD in Physics, looked at me and said, “So, Joe, what are your main hypotheses.” I looked back at him, perplexed, and said, “Ummm, my what?” I was used to people simply asking, “what are your best ideas, opinions, thoughts, etc.” Over time, I began to understand the importance of hypotheses and how it plays an important role in McKinsey’s problem solving of separating ideas and opinions from facts.

What is a Hypothesis?

“Hypothesis” is probably one of the top 5 words used by McKinsey consultants. And, being hypothesis-driven was required to have any success at McKinsey. A hypothesis is an idea or theory, often based on limited data, which is typically the beginning of a thread of further investigation to prove, disprove or improve the hypothesis through facts and empirical data.

The first step in being hypothesis-driven is to focus on the highest potential ideas and theories of how to solve a problem or realize an opportunity.

Let’s go over an example of being hypothesis-driven.

Let’s say you own a website, and you brainstorm ten ideas to improve web traffic, but you don’t have the budget to execute all ten ideas. The first step in being hypothesis-driven is to prioritize the ten ideas based on how much impact you hypothesize they will create.

The second step in being hypothesis-driven is to apply the scientific method to your hypotheses by creating the fact base to prove or disprove your hypothesis, which then allows you to turn your hypothesis into fact and knowledge. Running with our example, you could prove or disprove your hypothesis on the ideas you think will drive the most impact by executing:

1. An analysis of previous research and the performance of the different ideas 2. A survey where customers rank order the ideas 3. An actual test of the ten ideas to create a fact base on click-through rates and cost

While there are many other ways to validate the hypothesis on your prioritization , I find most people do not take this critical step in validating a hypothesis. Instead, they apply bad logic to many important decisions . An idea pops into their head, and then somehow it just becomes a fact.

One of my favorite lousy logic moments was a CEO who stated,

“I’ve never heard our customers talk about price, so the price doesn’t matter with our products , and I’ve decided we’re going to raise prices.”

Luckily, his management team was able to do a survey to dig deeper into the hypothesis that customers weren’t price-sensitive. Well, of course, they were and through the survey, they built a fantastic fact base that proved and disproved many other important hypotheses.

Why is being hypothesis-driven so important?

Imagine if medicine never actually used the scientific method. We would probably still be living in a world of lobotomies and bleeding people. Many organizations are still stuck in the dark ages, having built a house of cards on opinions disguised as facts, because they don’t prove or disprove their hypotheses. Decisions made on top of decisions, made on top of opinions, steer organizations clear of reality and the facts necessary to objectively evolve their strategic understanding and knowledge. I’ve seen too many leadership teams led solely by gut and opinion. The problem with intuition and gut is if you don’t ever prove or disprove if your gut is right or wrong, you’re never going to improve your intuition. There is a reason why being hypothesis-driven is the cornerstone of problem solving at McKinsey and every other top strategy consulting firm.

How do you become hypothesis-driven?

Most people are idea-driven, and constantly have hypotheses on how the world works and what they or their organization should do to improve. Though, there is often a fatal flaw in that many people turn their hypotheses into false facts, without actually finding or creating the facts to prove or disprove their hypotheses. These people aren’t hypothesis-driven; they are gut-driven.

The conversation typically goes something like “doing this discount promotion will increase our profits” or “our customers need to have this feature” or “morale is in the toilet because we don’t pay well, so we need to increase pay.” These should all be hypotheses that need the appropriate fact base, but instead, they become false facts, often leading to unintended results and consequences. In each of these cases, to become hypothesis-driven necessitates a different framing.

• Instead of “doing this discount promotion will increase our profits,” a hypothesis-driven approach is to ask “what are the best marketing ideas to increase our profits?” and then conduct a marketing experiment to see which ideas increase profits the most.

• Instead of “our customers need to have this feature,” ask the question, “what features would our customers value most?” And, then conduct a simple survey having customers rank order the features based on value to them.

• Instead of “morale is in the toilet because we don’t pay well, so we need to increase pay,” conduct a survey asking, “what is the level of morale?” what are potential issues affecting morale?” and what are the best ideas to improve morale?”

Beyond, watching out for just following your gut, here are some of the other best practices in being hypothesis-driven:

Listen to Your Intuition

Your mind has taken the collision of your experiences and everything you’ve learned over the years to create your intuition, which are those ideas that pop into your head and those hunches that come from your gut. Your intuition is your wellspring of hypotheses. So listen to your intuition, build hypotheses from it, and then prove or disprove those hypotheses, which will, in turn, improve your intuition. Intuition without feedback will over time typically evolve into poor intuition, which leads to poor judgment, thinking, and decisions.

Constantly Be Curious

I’m always curious about cause and effect. At Sports Authority, I had a hypothesis that customers that received service and assistance as they shopped, were worth more than customers who didn’t receive assistance from an associate. We figured out how to prove or disprove this hypothesis by tying surveys to transactional data of customers, and we found the hypothesis was true, which led us to a broad initiative around improving service. The key is you have to be always curious about what you think does or will drive value, create hypotheses and then prove or disprove those hypotheses.

Validate Hypotheses

You need to validate and prove or disprove hypotheses. Don’t just chalk up an idea as fact. In most cases, you’re going to have to create a fact base utilizing logic, observation, testing (see the section on Experimentation ), surveys, and analysis.

Be a Learning Organization

The foundation of learning organizations is the testing of and learning from hypotheses. I remember my first strategy internship at Mercer Management Consulting when I spent a good part of the summer combing through the results, findings, and insights of thousands of experiments that a banking client had conducted. It was fascinating to see the vastness and depth of their collective knowledge base. And, in today’s world of knowledge portals, it is so easy to disseminate, learn from, and build upon the knowledge created by companies.

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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: A Step-by-Step Guide With Easy Examples

Introduction

When we hear the word ‘hypothesis,’ the first thing that comes to our mind is a kind of theory. Assuming and explaining theories is a fundamental part of Business Analytics. In the past few years, the field of Business Analytics has proliferated and made several advancements. As the number of people interested in its statistical applications in business has increased, the concept of hypothesis testing has grabbed everyone’s attention.

Let us find out more about testing of hypothesis and the different steps through which you can write a hypothesis.

What is Hypothesis?

A hypothesis’s general definition says, “Hypothesis is an assumption made based on some evidence.” It is a theory you propose about what will happen in the future based on current circumstances. Proposing a hypothesis is the first and most important step of any research or investigation as it decides the future path of the research/investigation and can lead it to a faithful and acceptable answer.

Key Points of a Hypothesis

The assumptions made while proposing the theory should be precise and based on proper evidence.
The hypothesis should target a specific topic only and should have the scope to conduct various experiments for proving the assumptions.
The sources used for developing a hypothesis must be based on scientific theories, common patterns that affect the thought process of the people, and observations made in past research programs on the same topic.

Types of Hypotheses With Examples

There are multiple types of hypotheses which are described below.

1. Simple Hypothesis

As the name suggests, a simple hypothesis is pretty simple to work on. It just deals with a single independent variable and one dependent variable. While proving a simple hypothesis, you just have to confirm that these two variables are linked.

Example: If you eat more vegetables, you will be safe from heart disease. Here eating vegetables is an independent variable and staying safe from heart disease is a dependent variable.

2. Complex Hypothesis

Unlike a simple hypothesis, a complex hypothesis deals with multiple dependent and independent variables in the assumption simultaneously. The involvement of multiple variables makes the hypothesis more accurate and more difficult to prove simultaneously.

Example: Age, diet, and weight affect the chances of diseases like diabetes or blood pressure. Age, diet, and weight are independent variables, and diabetes and blood pressure are dependent variables.

3. Null Hypothesis

The null hypothesis is the opposite of the simple hypothesis. Where a simple hypothesis tries to establish a link between the dependent and the independent variables, the Null hypothesis tries to prove that there’s no link between the given variables. Simply put, it tries to prove a statement opposite to the proposed hypothesis. It is represented as H0.

Example: Age and daily routine affect the chances of heart disease. In a Null hypothesis, you will try to prove that there is no relation between the given factors, i.e., age, weight, and heart disease.

4. Alternative Hypothesis

An alternative hypothesis tries to disapprove the assumptions or statements proposed in a null hypothesis. Generally, alternative and null hypotheses are used together. An alternative hypothesis is represented as HA.

It is to be noted that H0 ≠ H A. The alternate hypothesis further branches into two categories:

Directional Hypothesis: The result obtained through this type of alternative hypothesis is either negative or positive. It is represented by adding ‘>’ or ‘<‘ along with the HA symbol.
Non-Directional Hypothesis: This type of hypothesis only clarifies the dependency of the dependent variables on the independent variable. It does not state anything about the result being positive or negative.

Example:

Age and daily routine affect the chances of heart disease. In an Alternative Hypothesis, you will try to prove that age and daily routine affect heart disease chances.

If you prove the result is positive or negative, i.e., age and daily routine do or do not affect the chances of heart disease, it is a directional hypothesis
If you only prove that the chances of heart disease depend on variables like age and daily routine, it is a non-directional hypothesis.

5. Logical Hypothesis

Logical hypotheses cannot be proved with the help of scientific evidence. The assumptions made in a logical hypothesis are based on some logical explanation that backs up our assumptions. Logical hypotheses are mostly used in philosophy, and as the assumptions made are often too complex or simply unrealistic, they are untestable, and we have to rely on logical explanations.

Dinosaurs are related to the reptile family as both have scales. As the dinosaurs are extinct, we cannot test the given hypothesis and rely on our logical explanation on, not the experimental data.

6. Empirical Hypothesis

It is the complete opposite of the Logical Hypothesis. The assumptions made in an Empirical Hypothesis are based on empirical data and proved through scientific testing and analysis.

It is divided into two parts, namely theoretical and empirical. Both methods of research rely on testing that can be verified through experimental data. So, unlike logical hypotheses, an empirical hypothesis can be and will be tested.

Vegetables grow faster in cold climates as compared to warm and humid climates. The assumption stated here can be thoroughly tested through scientific methods.

7. Statistical Hypothesis

Statistical Hypothesis makes use of large statistical datasets to obtain results that consider larger populations. This type of hypothesis is used when we have to take into consideration all the possible cases present in the assumptions made in the hypothesis. It makes use of datasets or samples so that conclusions can be drawn from the broader dataset. For this, you may conduct tests for sufficient samples and obtain results with high accuracy that would remain stable across all the datasets.

Men in the U.S.A. are taller than men in India. It is simply impossible to measure the height of all the men present in India and the U.S.A., but by conducting the test on sufficient samples, you can obtain results with high accuracy that would remain constant over different samples.

What Makes a Good Hypothesis?

Before developing a good hypothesis, you must consider a few points.

Do the assumptions made in the hypothesis consist of dependent or independent variables?
Can you conduct safety tests for your assumptions in the hypothesis?
Are there any other alternative assumptions present that you can take into consideration?

Characteristics of a Good Hypothesis –

1. Candid Language

Make use of simple language in your hypothesis instead of being vague. Try to focus on the given topic through your assumptions; it should be simple yet justifiable. The use of candid language makes the hypothesis more understandable and reachable to the common people.

2. Cause and Effect

Understand the assumptions made in the hypothesis. For example, the cause of the assumption, the effect of the assumption being accepted or rejected, etc. Try to back up your assumptions with the help of proper scientific data and explanations.

3. The Independent and Dependent Variables

Before starting to write a hypothesis, figure out the number of dependent and independent variables in the hypothesis. This will help you make proper assumptions to establish a link between these variables or to prove that these variables are not interlinked. It will also help you to prepare a mind map for your hypothesis.

4. Accurate Results

One of the most important characteristics of a good hypothesis is the accuracy of the results. Hypotheses are generally used to predict the future based on current scenarios. This can help to figure out the problems that may arise in the future and find solutions accordingly.

5. Adherence to Ethics

Sticking to ethics while working on any research project is very important. You get an idea about the research structure through the generally followed ethics beforehand. It helps to guide the research project or hypothesis in a fruitful direction.

6. Testable Predictions

The conditions used in the hypothesis research project should be easily testable. This helps to make the results of the hypothesis more accurate and reliable. Before starting the research on the assumptions in the hypothesis, you should be aware of all the different ways that can be used to make the hypothesis applicable to modern testing methodologies.

How to Write a Hypothesis?

Well, there are many ways to write a hypothesis; here are the six most efficient and important steps that will help you craft a strong hypothesis:

Step 1: Ask a Question

The first and most important step of writing a hypothesis is deciding upon the questions or assumptions you will implement in your research. A hypothesis can’t be based on random questions or general thoughts. The questions you decide must be approachable and testable as it forms the foundation of your project.

Step 2: Carry out Preliminary Research

Once you have decided on the questions and assumptions to be included in your hypothesis, you should start your preliminary research on the same. For that, you should start reading older research papers on the topic, go through the web, collect the data, prepare the dataset for the experiments, etc.

Step 3: Define Your Variables

After conducting the preliminary research, you need to define the number of variables present in your assumption and classify them into dependent and independent variables. It will help you to conduct further research and establish a link between them or prove that there is no link between them.

Step-4: Collect Data to Support Your Hypothesis

After classifying the variables and conducting the basic preliminary research, you need to start collecting evidence and data that will help you support your hypothesis. This data will help you test your assumptions and infer statistical results about your interesting dataset.

Step-5: Perform Statistical Tests

The data you have collected from the above step can be used to perform different statistical tests. The type of tests you perform depends on the data you collect. All the different tests are based on in-group variance and between-group variance. Depending on the variance, your statistical test will reflect a high or low p-value.

After performing the tests, you should prepare a draft for writing down your hypothesis.

Step-6: Present It in an If-Then Form

Now that everything has been done, it is time to write down your hypothesis. Considering your draft, you should write down the hypothesis accordingly and ensure that it satisfies all the conditions like simple and to-the-point language, accurate results, relevant evidence and data sources, etc. The final hypothesis should be well-framed and address the topic clearly.

Conclusion

Research and hypothesis testing are an important part of the Business Analytics field. To write a good hypothesis or research, you need to conduct a good amount of research. Since you know about the different types of hypotheses and how to write a good hypothesis, writing a good and strong hypothesis by yourself is now much easier! If you want to pursue a career in the field of Business Analytics, you can check out the Integrated Program In Business Analytics by UNext Jigsaw. We hope now you understand “ what is hypothesis testing ?” and hypothesis testing steps in detail.

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3 Statistical Analysis Methods You Can Use to Make Business Decisions

Business professionals using statistical analysis methods

15 Dec 2021

Data is a driving force in business. More information is being collected than ever before, which professionals continually seek to leverage for success. Across all business functions, it’s essential to have analytical skills to interpret data and put it to use.

Statistical analysis is the basis for many business analytics approaches. Gaining a firm understanding of different statistical analysis methods is one of the first steps to unlocking the power of business analytics. With this knowledge, you can make sense of data, project future outcomes, and make more informed decisions.

Related: Examples of Business Analytics in Action

Below are three helpful statistical analysis methods that lead to better business decisions.

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Statistical Analysis Methods for Business

1. hypothesis testing.

Hypothesis testing is a statistical method used to substantiate a claim about a population. This is done by formulating and testing two hypotheses: the null hypothesis and the alternative hypothesis.

Related: A Beginner’s Guide to Hypothesis Testing in Business

The null hypothesis (denoted by H₀) is a statement about the issue at hand, generally based on historical data and conventional wisdom. A hypothesis test always starts by assuming the null hypothesis is true and then testing to see if it can be nullified.

The alternative hypothesis (denoted by H₁) represents the theory or assumption being tested and is the opposite of the null hypothesis. If the data effectively nullifies the null hypothesis, then the alternative hypothesis can be substantiated.

In business, hypothesis testing is an effective means of assessing theories and assumptions before acting on them. For managers, leaders, and those looking to become more data-driven, this method of statistical analysis is a helpful decision-making tool. Putting this practice into action can lead to better foresight and positive outcomes when planning a business’s future.

For example, you might conduct a hypothesis test to substantiate that if your company launches a new product line, sales and revenue will increase as a result. Since this initiative would be expensive, your company might launch the product in a small test market and use the data it collects to justify rolling it out on a larger scale.

Hypothesis testing is a complex yet highly valuable statistical method for business. If you want to learn about hypothesis testing in more detail, taking an online statistics or business analytics course can be worthwhile.

2. Single Variable Linear Regression

Linear regression analysis is used for two main purposes: to identify and evaluate the relationship between two variables and forecast a variable based on its relationship to another one.

In single variable linear regression analysis, the relationship between a dependent variable and an independent variable is evaluated by identifying the line of best fit.

To find the line of best fit, use the following equation:

Single Variable Linear Regression Formula

Here, ŷ represents the expected value of the dependent variable for a given value of X, which represents the independent variable. α is equal to the Y-intercept, or the point at which the regression line crosses the Y-axis, when X is equal to zero. β is the slope that equals the average change of the dependent variable (Y) as the independent variable (X) increases by one. Finally, ε is the error term that equals Y – ŷ, or the difference between the actual value of the dependent variable and its expected value.

Using this method, you can forecast a defined variable based on known data.

Consider the relationship between advertising spend and revenue, for example. A business can use historical data relating the advertising dollars spent to the amount of revenue generated for various campaigns or time periods. Using a single variable linear regression analysis, it can use that information to find the line of best fit and subsequently use the slope to forecast revenue for future campaigns.

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3. Multiple Regression

Whereas single variable linear regression analysis studies the relationship between two variables—a dependent variable and an independent variable— multiple regression analysis investigates the relationship between a dependent variable and multiple independent variables.

Forecasting with multiple regression analysis is similar to using single variable linear regression. However, instead of entering only one value for an independent variable, a value is input for each independent variable. Using the same notation as the single variable linear regression equation, the following equation applies to multiple regression:

In business, multiple regression analysis is helpful for predicting the outcomes of complicated scenarios. For example, think back to the relationship between advertising spend and revenue. Instead of looking at total advertising expenditures, you can use multiple regression analysis to evaluate how different types of campaigns, such as television, radio, and social media ads, impact revenue.

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Developing Your Analytical Skills

An analytical mindset is essential to business success. After all, data is one of the most valuable resources in today’s world, and knowing how to leverage it can lead to better decision-making and outcomes.

Related: How to Improve Your Analytical Skills

Depending on your current knowledge of statistics and business analytics and long-term goals, there are many options you can pursue to develop your skills. Taking an online course dedicated to honing and applying analytical skills in a professional setting is a great way to get started.

Do you want to leverage the power of data within your organization? Explore our eight-week online course Business Analytics —one of three courses comprising our Credential of Readiness (CORe) program —to learn how to use data analysis to solve business problems.

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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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A complete guide on the types of statistical studies, everything you need to know about poisson distribution, your best guide to understand correlation vs. regression, the most comprehensive guide for beginners on what is correlation, hypothesis testing in statistics - types | examples.

Lesson 10 of 24 By Avijeet Biswal

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−pBp(1-p)(1nA+1nB)

z=0.25−0.3750.305(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.

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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.

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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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5 Steps of Hypothesis Testing with Examples
Hypothesis Testing in Business: Examples
Hypothesis Testing in Finance: Concept and Examples
Hypothesis Testing Solved Examples(Questions and Solutions)
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COMMENTS

A Beginner's Guide to Hypothesis Testing in Business
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 ...
Hypothesis Testing in Business: Examples
Examples of hypothesis testing in business can range from identifying the effectiveness of a new marketing campaign to determining the impact of changes in pricing strategies. By analyzing data and performing hypothesis testing, businesses can determine the significance of these changes and make informed decisions that will improve their bottom ...
Hypothesis Testing in Finance: Concept and Examples
Hypothesis testing is a mathematical tool for confirming a financial or business claim or idea. Hypothesis testing is useful for investors trying to decide what to invest in and whether the ...
PDF Hypothesis Testing
23.1 How Hypothesis Tests Are Reported in the News 1. Determine the null hypothesis and the alternative hypothesis. 2. Collect and summarize the data into a test statistic. 3. Use the test statistic to determine the p-value. 4. The result is statistically significant if the p-value is less than or equal to the level of significance.
How McKinsey uses Hypotheses in Business & Strategy by McKinsey Alum
Running with our example, you could prove or disprove your hypothesis on the ideas you think will drive the most impact by executing: 1. An analysis of previous research and the performance of the different ideas 2. A survey where customers rank order the ideas 3. An actual test of the ten ideas to create a fact base on click-through rates and cost
Hypothesis Testing in Business Analytics
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 ...
Hypothesis Testing in Finance
Hypothesis testing is a powerful tool for testing the power of predictions. A Financial Analyst, for example, might want to make a prediction of the mean value a customer would pay for her firm's product. She can then formulate a hypothesis, for example, "The average value that customers will pay for my product is larger than $5.".
A Beginner's Guide to Hypothesis Testing in Business Analytics
Hypothesis testing is a statistical method used to make decisions about a population based on a sample. It helps business analysts draw conclusions about business metrics and make data-driven decisions. This beginner's guide will provide an introduction to hypothesis testing and how it is applied in business analytics.
Hypothesis Testing in Business Administration
"Hypothesis Testing in Business Administration" published on by Oxford University Press. 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 ...
6.4: Hypothesis Testing
Steps in Hypothesis Testing . In order to test a hypothesis, these steps should be followed, in the recommended order: 1. State the hypothesis. This is a necessary first step. Before a study can be designed, a researcher needs to specify exactly what the hypothesis is what they intend to test.
Hypothesis Testing
There are 5 main steps in hypothesis testing: State your research hypothesis as a null hypothesis and alternate hypothesis (H o) and (H a or H 1). Collect data in a way designed to test the hypothesis. Perform an appropriate statistical test. Decide whether to reject or fail to reject your null hypothesis. Present the findings in your results ...
Hypothesis Testing: A Step-by-Step Guide With Easy Examples
Well, there are many ways to write a hypothesis; here are the six most efficient and important steps that will help you craft a strong hypothesis: Step 1: Ask a Question. The first and most important step of writing a hypothesis is deciding upon the questions or assumptions you will implement in your research.
(PDF) Demystifying Hypothesis Testing in Business and ...
Abstract. Hypothesis testing is probably one of the fundamental concepts in academic research especially where one wishes to proof a theory, logic or principle. Business and social research embeds ...
3 Statistical Analysis Methods You Can Use to Make Business Decisions
Statistical Analysis Methods for Business. 1. Hypothesis Testing. Hypothesis testing is a statistical method used to substantiate a claim about a population. This is done by formulating and testing two hypotheses: the null hypothesis and the alternative hypothesis. Related: A Beginner's Guide to Hypothesis Testing in Business.
4 Examples of Hypothesis Testing in Real Life
Hypothesis tests are often used in clinical trials to determine whether some new treatment, drug, procedure, etc. causes improved outcomes in patients. For example, suppose a doctor believes that a new drug is able to reduce blood pressure in obese patients. To test this, he may measure the blood pressure of 40 patients before and after using ...
Hypothesis Testing Used in Business
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 ...
Hypothesis Testing in Statistics
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. ... Hypothesis Testing Calculation With Examples. Let's consider a hypothesis test for the average height of women in the United ...
Applying Hypothesis Testing in Business Statistics
Business Statistics For Dummies. Hypothesis testing isn't just for population means and standard deviations. You can use this procedure to test many different kinds of propositions. For example, a jury trial can be seen as a hypothesis test with a null hypothesis of "innocent" and an alternative hypothesis of "guilty."
Using Hypothesis Testing in Business
Hypothesis testing is a step-by-step process to determine whether a stated hypothesis about a given population is true. It is an important tool in business development. By testing different theories and practices, and the effects they produce on your business, you can make more informed decisions about how to grow your business moving forward.