Understanding hypothesis testing, the a-z of hypothesis testing.
Shubhangi Hora
Towards Data Science
Hypothesis testing is an important mathematical concept that’s used in the field of data science. While it’s really easy to call a random method from a python library that’ll carry out the test for you, it’s both necessary and interesting to know what is actually happening behind the scenes! What is hypothesis testing, why do we need it, what does it do and how does it really work? Let’s find out!
Hypothesis testing is a statistical method to determine whether a hypothesis that you have holds true or not. The hypothesis can be with respect to two variables within a dataset, an association between two groups or a situation.
The method evaluates two mutually exclusive statements (two events that cannot occur simultaneously) to determine which statement is best supported by the sample data and make an informed decision.
The building blocks of hypothesis testing are:
The process of hypothesis testing involves two hypotheses — a null hypothesis and an alternate hypothesis.
The conclusion of hypothesis testing is whether the null hypothesis is not rejected (so you accept that there is no change) or is rejected (so you reject that there is no change).
Let’s understand this with an example.
There’s a dataset that contains information on patients who’ve been admitted to a hospital in the past year. Two features present in this dataset are location and total amount spent. We believe there’s a difference in the total amount spent during admission based on where a person lives — this statement is your alternate hypothesis , since it assumes a relationship between location and the amount spent in the hospital.
Hence, the null hypothesis will be that there is no difference in the amount spent at the hospital based on where a person lives .
Now we need to figure out whether we should or should not reject the null hypothesis. How do we do that?
Statistical tests help us in rejecting or not rejecting our null hypothesis by providing us with a test statistic (a single numeric value) from our sample data. This test statistic measures the extent to which the sample data agrees with the null hypothesis — if it agrees then the null hypothesis is not rejected, else it is rejected.
There are multiple statistical tests that exist for different use cases. The selection of which statistical test to use your hypothesis testing depends on several factors, such as — the distribution of the sample (whether it is normally distributed (follows the normal distribution)), what the sample size is, whether the variance is known, the type of data that you have, amongst some other things. Each test has its own test statistic based on the probability model/distribution that the test follows.
For example —
Statistical tests are of two types — one-tailed and two-tailed .
The concept of tails is related to probability distributions.
A probability distribution is a statistical function whose output is the probabilities of the occurrences of different events (possible outcomes) of an experiment.
For example:
A probability distribution is both in the form of data and a graph, but the graph is a better way to understand what tails are.
The tails of a distribution are the endings of the curve / graph on the sides of the distribution. The right end is known as the right tail or the upper tail, and the left end as the left tail or the lower tail.
It is not necessary for a distribution to have both tails in all situations, it could have just one. The number of tails is dependent on your null and alternate hypotheses.
Thus we have one-tailed distributions and two-tailed distributions.
So, a one-tailed statistical test is one whose distribution has only one tail — either the left (left-tailed test) or the right (right-tailed test). A two-tailed statistical test is one whose distribution has two tails — both left and right.
The purpose of a tail in statistical tests is to see whether the test statistic obtained falls within the tail or outside it. The tail region is known as the region of rejection — which makes sense since the null hypothesis is rejected if the test statistic falls within this area. If it falls outside it then the null hypothesis is accepted.
Determining where the tail begins is done with the help of a parameter known as the level of significance — alpha . It is the probability of rejecting the null hypothesis when the null hypothesis is true. The most common value for alpha is 5%, i.e. 0.05. This means that you face a 5% risk of rejecting the null hypothesis, i.e. believing there is a difference in the current situation when there actually isn’t.
In terms of our distribution, alpha is the area of the distribution that makes up the region of rejection — hence it is the tail(s). Since the tails are at the end of the distribution, we are literally saying, with the level of significance, how far away from the null hypothesis our test statistic needs to be for us to actually reject the null hypothesis.
So, if we were to select a right-tailed test and our level of significance was 5%, then the 5% of the area of distribution on the right end of the curve would be our region of rejection. Using this, we calculate the value on the x-axis which demarcates where the region of rejection begins — this is known as the critical value .
In the case of a two-tailed test, we would divide the level of significance by half — 2.5% — and this would be the area of each region of rejection on either side of the curve. Then we would have two critical values and the regions of rejection would also be known as the critical regions.
One-tailed tests are directional as there is only one region of rejection . You are looking for a test statistic that falls within that sole region of rejection. Two-tailed tests are nondirectional since there are two regions of rejection and if the test statistic falls in either of them then the null hypothesis is rejected.
For example, the sample mean age of patients at a dentist’s clinic is 18 — this is your null hypothesis (since this is the current scenario and you are assuming there is no change). Another dentist joins the practice and you believe that now the sample mean of patients will be greater than 18 — this is your alternate hypothesis. It is directional due to the ‘greater than’ — only if the sample mean is greater than 18 will you reject the null hypothesis. If it is less than 18, your null hypothesis will not be rejected.
If it were a two-tailed test, your alternate hypothesis would simply be that the sample mean age of patients is not equal to 18. The sample mean could be greater than or less than 18, either way the null hypothesis would be rejected, hence it is nondirectional.
So far, we have hypotheses, a statistical test based on a probability distribution, a level of significance from which we get the region of rejection from which we get the critical value, and a test statistic that falls somewhere within our distribution.
As mentioned before, the test statistic is compared with the critical value. The p-value is compared with the level of significance.
P-value is the probability that the test statistic you have obtained is by random chance which would mean the null hypothesis is actually true. If the p-value is lower than the level of significance then it is statistically significant and the null hypothesis is rejected, because it means that there is a less than 5% probability that the null hypothesis is true. If it is higher than the level of significance then the null hypothesis is not rejected.
In terms of the graphical representation of our probability distribution, the p-value is the area of the curve on the right of the test statistic.
A big plus point of the p-value is that it doesn’t need to be recalculated for different levels of significance since it is directly comparable. In the case of test statistics, they have to be compared with critical values which do need to be recalculated for different levels of significance (if the area of the regions of rejection change then the x-axis value for where the regions begin will also change). That’s why it’s always better to work with the p-value in hypothesis testing.
Despite the above mentioned advantage though, the p-value is still probabilistic. Hence there is a chance that the null hypothesis will be rejected even though it is true. Alpha (the level of significance) is the likelihood that this will happen. This error is known as a type I error or a false positive .
The opposite to the above error would be not rejecting the null hypothesis even though it is not true. This is known as a type II error or a false negative .
Both of these errors are inversely related, i.e. if you try to reduce one the other will increase. So how do you get the perfect situation? You don’t, you just have to decide which error is less risky in your situation. For example, it’s less risky to tell someone they are covid-19 positive when they’re actually negative — this is a false positive (type I error). A false negative would be saying someone doesn’t exhibit fraudulent behavior when they actually do.
Finally we have all the building blocks of hypothesis testing sorted so the process is also pretty clear. The steps for hypothesis testing are:
Let’s go through these steps with an example that we used above about the mean age of patients that visit a dentist. We know that the mean age is 18 and the standard deviation is 8. Let’s assume the data follows a normal distribution. We think that the mean age isn’t 18, but is in fact larger than 18.
Since we have directionality in our alternate hypothesis, we need a right-tailed statistical test.
We are comparing the sample mean age, so we can use the z-test to determine whether our alternate hypothesis is probable or not.
Our level of significance is 5% and we are performing a right-tailed test so the right tail of our curve is the region of rejection.
Our sample data is 30 patients at random and we calculate the sample mean age.
So we have:
Now we need to calculate our test statistic, which in the case of the z-test is the z-score. The formula for z-score is
So our z-score is
The critical value of the normal distribution with alpha as 0.05 is 1.645. So we can already see that our test statistic is greater than our critical value, hence we can reject the null hypothesis. But as mentioned before, the p-value is the best way to determine whether or not we should reject the null hypothesis, so let’s calculate that too.
The probability of getting a value of 2.05 on the normal distribution is 0.9798. Since the p-value is the area to the right of the test statistic, it is calculated by subtracting 0.9798 from 1.
A p-value of 0.0202 is less than the 0.05 and hence we can reject our null hypothesis and conclude that it is more probable for the sample mean to be greater than 18.
Let’s actually implement all of this in python now!
We’re going to use a covid-19 datatset. It contains region wise confirmed cases and deaths from early 2020. It also contains temperature, humidity, latitude and longitude.
The first step is to import all the required packages:
We’ll be using pandas to read our data and stasmodels to actually carry out our hypothesis test.
Read the data into a dataframe:
I believe that there is a relationship between temperature and the number of confirmed covid-19 cases — is the average temperature in regions with confirmed covid-19 cases greater than 12 degrees?
The first step of hypothesis testing is to formulate the hypotheses. Ours would be:
Since our alternate hypothesis is directional, we will be performing a one-tailed statistical test (a right-tailed test) — the z-test.
The level of significance will be 0.05, the test statistic is the z-score and the critical value is 1.645.
It’s really easy to calculate the test statistic and the p-value using the statsmodels ztest method. Let’s wrap this functionality in a function of our own and add the comparison between alpha and the p-value.
Now we call our function — pass the temperature column (since that’s the variable present in our hypothesis), the number 12 as value since that is the metric we are testing for, and “larger” in the alternative parameter since our alternate hypothesis is that the average is larger than the value.
The results are the z-score, the p-value and the conclusion respectively. Since the p-value is greater than 0.05, we do not reject our null hypothesis.
And that’s how you carry out a hypothesis test!
Some key things to remember are:
Please do let me know your thoughts about this article in the comments below or reach out to me on LindkedIn and we can connect!
The raw data has been taken from John Hopkins’ GitHub repository and then modified to get the temperature of the region. The code used to perform the test and to create the graphs can be found here .
A python developer working on AI and ML, with a background in Computer Science and Psychology. Interested in healthcare AI, specifically mental health!
Text to speech
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.
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:
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.
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 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.
There are two types of one-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
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.
Null Hypothesis is True | Null Hypothesis is False | |
---|---|---|
Null Hypothesis is True (Accept) | Correct Decision | Type II Error (False Negative) |
Alternative Hypothesis is True (Reject) | Type I Error (False Positive) | Correct Decision |
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.
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.
Gather relevant data through observation or experimentation. Analyze the data using appropriate statistical methods to obtain a 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.
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.
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.
Comparing the test statistic and tabulated critical value we have,
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.
We can also come to an conclusion using the p-value,
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.
At last, we can conclude our experiment using method A or B.
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 .
When population means and standard deviations are known.
[Tex]z = \frac{\bar{x} – \mu}{\frac{\sigma}{\sqrt{n}}}[/Tex]
T test is used when n<30,
t-statistic calculation is given by:
[Tex]t=\frac{x̄-μ}{s/\sqrt{n}} [/Tex]
Chi-Square Test for Independence categorical Data (Non-normally distributed) using:
[Tex]\chi^2 = \sum \frac{(O_{ij} – E_{ij})^2}{E_{ij}}[/Tex]
Let’s examine hypothesis testing using two real life situations,
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.
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.
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)
then, m= -3.9, s= 1.8 and n= 10
we, calculate the , T-statistic = -9 based on the formula for paired t test
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
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.
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.
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)
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
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.
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.
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.
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.
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.
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.
Similar reads.
About hypothesis testing.
Watch the video for a brief overview of hypothesis testing:
Can’t see the video? Click here to watch it on YouTube.
Contents (Click to skip to the section):
What is hypothesis testing.
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A hypothesis is an educated guess about something in the world around you. It should be testable, either by experiment or observation. For example:
It can really be anything at all as long as you can put it to the test.
If you are going to propose a hypothesis, it’s customary to write a statement. Your statement will look like this: “If I…(do this to an independent variable )….then (this will happen to the dependent variable ).” For example:
A good hypothesis statement should:
Hypothesis testing can be one of the most confusing aspects for students, mostly because before you can even perform a test, you have to know what your null hypothesis is. Often, those tricky word problems that you are faced with can be difficult to decipher. But it’s easier than you think; all you need to do is:
If you trace back the history of science, the null hypothesis is always the accepted fact. Simple examples of null hypotheses that are generally accepted as being true are:
You won’t be required to actually perform a real experiment or survey in elementary statistics (or even disprove a fact like “Pluto is a planet”!), so you’ll be given word problems from real-life situations. You’ll need to figure out what your hypothesis is from the problem. This can be a little trickier than just figuring out what the accepted fact is. With word problems, you are looking to find a fact that is nullifiable (i.e. something you can reject).
A researcher thinks that if knee surgery patients go to physical therapy twice a week (instead of 3 times), their recovery period will be longer. Average recovery times for knee surgery patients is 8.2 weeks.
The hypothesis statement in this question is that the researcher believes the average recovery time is more than 8.2 weeks. It can be written in mathematical terms as: H 1 : μ > 8.2
Next, you’ll need to state the null hypothesis . That’s what will happen if the researcher is wrong . In the above example, if the researcher is wrong then the recovery time is less than or equal to 8.2 weeks. In math, that’s: H 0 μ ≤ 8.2
Ten or so years ago, we believed that there were 9 planets in the solar system. Pluto was demoted as a planet in 2006. The null hypothesis of “Pluto is a planet” was replaced by “Pluto is not a planet.” Of course, rejecting the null hypothesis isn’t always that easy— the hard part is usually figuring out what your null hypothesis is in the first place.
The one sample z test isn’t used very often (because we rarely know the actual population standard deviation ). However, it’s a good idea to understand how it works as it’s one of the simplest tests you can perform in hypothesis testing. In English class you got to learn the basics (like grammar and spelling) before you could write a story; think of one sample z tests as the foundation for understanding more complex hypothesis testing. This page contains two hypothesis testing examples for one sample z-tests .
Watch the video for an example:
A principal at a certain school claims that the students in his school are above average intelligence. A random sample of thirty students IQ scores have a mean score of 112.5. Is there sufficient evidence to support the principal’s claim? The mean population IQ is 100 with a standard deviation of 15.
Step 1: State the Null hypothesis . The accepted fact is that the population mean is 100, so: H 0 : μ = 100.
Step 2: State the Alternate Hypothesis . The claim is that the students have above average IQ scores, so: H 1 : μ > 100. The fact that we are looking for scores “greater than” a certain point means that this is a one-tailed test.
Step 4: State the alpha level . If you aren’t given an alpha level , use 5% (0.05).
Step 5: 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 6: If Step 6 is greater than Step 5, reject the null hypothesis. If it’s less than Step 5, you cannot reject the null hypothesis. In this case, it is more (4.56 > 1.645), so you can reject the null.
Watch the video for an example of a two-tailed z-test:
Blood glucose levels for obese patients have a mean of 100 with a standard deviation of 15. A researcher thinks that a diet high in raw cornstarch will have a positive or negative effect on blood glucose levels. A sample of 30 patients who have tried the raw cornstarch diet have a mean glucose level of 140. Test the hypothesis that the raw cornstarch had an effect.
*This process is made much easier if you use a TI-83 or Excel to calculate the z-score (the “critical value”). See:
You can use the TI 83 calculator for hypothesis testing, but the calculator won’t figure out the null and alternate hypotheses; that’s up to you to read the question and input it into the calculator.
Example problem : A sample of 200 people has a mean age of 21 with a population standard deviation (σ) of 5. Test the hypothesis that the population mean is 18.9 at α = 0.05.
Step 1: State the null hypothesis. In this case, the null hypothesis is that the population mean is 18.9, so we write: H 0 : μ = 18.9
Step 2: State the alternative hypothesis. We want to know if our sample, which has a mean of 21 instead of 18.9, really is different from the population, therefore our alternate hypothesis: H 1 : μ ≠ 18.9
Step 3: Press Stat then press the right arrow twice to select TESTS.
Step 4: Press 1 to select 1:Z-Test… . Press ENTER.
Step 5: Use the right arrow to select Stats .
Step 6: Enter the data from the problem: μ 0 : 18.9 σ: 5 x : 21 n: 200 μ: ≠μ 0
Step 7: Arrow down to Calculate and press ENTER. The calculator shows the p-value: p = 2.87 × 10 -9
This is smaller than our alpha value of .05. That means we should reject the null hypothesis .
Bayesian hypothesis testing helps to answer the question: Can the results from a test or survey be repeated? Why do we care if a test can be repeated? Let’s say twenty people in the same village came down with leukemia. A group of researchers find that cell-phone towers are to blame. However, a second study found that cell-phone towers had nothing to do with the cancer cluster in the village. In fact, they found that the cancers were completely random. If that sounds impossible, it actually can happen! Clusters of cancer can happen simply by chance . There could be many reasons why the first study was faulty. One of the main reasons could be that they just didn’t take into account that sometimes things happen randomly and we just don’t know why.
It’s good science to let people know if your study results are solid, or if they could have happened by chance. The usual way of doing this is to test your results with a p-value . A p value is a number that you get by running a hypothesis test on your data. A P value of 0.05 (5%) or less is usually enough to claim that your results are repeatable. However, there’s another way to test the validity of your results: Bayesian Hypothesis testing. This type of testing gives you another way to test the strength of your results.
Traditional testing (the type you probably came across in elementary stats or AP stats) is called Non-Bayesian. It is how often an outcome happens over repeated runs of the experiment. It’s an objective view of whether an experiment is repeatable. Bayesian hypothesis testing is a subjective view of the same thing. It takes into account how much faith you have in your results. In other words, would you wager money on the outcome of your experiment?
Traditional testing (Non Bayesian) requires you to repeat sampling over and over, while Bayesian testing does not. The main different between the two is in the first step of testing: stating a probability model. In Bayesian testing you add prior knowledge to this step. It also requires use of a posterior probability , which is the conditional probability given to a random event after all the evidence is considered.
Many researchers think that it is a better alternative to traditional testing, because it:
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Think about something strange and unexplainable in your life. Maybe you get a headache right before it rains, or maybe you think your favorite sports team wins when you wear a certain color. If you wanted to see whether these are just coincidences or scientific fact, you would form a hypothesis, then create an experiment to see whether that hypothesis is true or not.
But what is a hypothesis, anyway? If you’re not sure about what a hypothesis is--or how to test for one!--you’re in the right place. This article will teach you everything you need to know about hypotheses, including:
So let’s get started!
Merriam Webster defines a hypothesis as “an assumption or concession made for the sake of argument.” In other words, a hypothesis is an educated guess . Scientists make a reasonable assumption--or a hypothesis--then design an experiment to test whether it’s true or not. Keep in mind that in science, a hypothesis should be testable. You have to be able to design an experiment that tests your hypothesis in order for it to be valid.
As you could assume from that statement, it’s easy to make a bad hypothesis. But when you’re holding an experiment, it’s even more important that your guesses be good...after all, you’re spending time (and maybe money!) to figure out more about your observation. That’s why we refer to a hypothesis as an educated guess--good hypotheses are based on existing data and research to make them as sound as possible.
Hypotheses are one part of what’s called the scientific method . Every (good) experiment or study is based in the scientific method. The scientific method gives order and structure to experiments and ensures that interference from scientists or outside influences does not skew the results. It’s important that you understand the concepts of the scientific method before holding your own experiment. Though it may vary among scientists, the scientific method is generally made up of six steps (in order):
You’ll notice that the hypothesis comes pretty early on when conducting an experiment. That’s because experiments work best when they’re trying to answer one specific question. And you can’t conduct an experiment until you know what you’re trying to prove!
After doing your research, you’re ready for another important step in forming your hypothesis: identifying variables. Variables are basically any factor that could influence the outcome of your experiment . Variables have to be measurable and related to the topic being studied.
There are two types of variables: independent variables and dependent variables. I ndependent variables remain constant . For example, age is an independent variable; it will stay the same, and researchers can look at different ages to see if it has an effect on the dependent variable.
Speaking of dependent variables... dependent variables are subject to the influence of the independent variable , meaning that they are not constant. Let’s say you want to test whether a person’s age affects how much sleep they need. In that case, the independent variable is age (like we mentioned above), and the dependent variable is how much sleep a person gets.
Variables will be crucial in writing your hypothesis. You need to be able to identify which variable is which, as both the independent and dependent variables will be written into your hypothesis. For instance, in a study about exercise, the independent variable might be the speed at which the respondents walk for thirty minutes, and the dependent variable would be their heart rate. In your study and in your hypothesis, you’re trying to understand the relationship between the two variables.
The best hypotheses start by asking the right questions . For instance, if you’ve observed that the grass is greener when it rains twice a week, you could ask what kind of grass it is, what elevation it’s at, and if the grass across the street responds to rain in the same way. Any of these questions could become the backbone of experiments to test why the grass gets greener when it rains fairly frequently.
As you’re asking more questions about your first observation, make sure you’re also making more observations . If it doesn’t rain for two weeks and the grass still looks green, that’s an important observation that could influence your hypothesis. You'll continue observing all throughout your experiment, but until the hypothesis is finalized, every observation should be noted.
Finally, you should consult secondary research before writing your hypothesis . Secondary research is comprised of results found and published by other people. You can usually find this information online or at your library. Additionally, m ake sure the research you find is credible and related to your topic. If you’re studying the correlation between rain and grass growth, it would help you to research rain patterns over the past twenty years for your county, published by a local agricultural association. You should also research the types of grass common in your area, the type of grass in your lawn, and whether anyone else has conducted experiments about your hypothesis. Also be sure you’re checking the quality of your research . Research done by a middle school student about what minerals can be found in rainwater would be less useful than an article published by a local university.
Once you’ve considered all of the factors above, you’re ready to start writing your hypothesis. Hypotheses usually take a certain form when they’re written out in a research report.
When you boil down your hypothesis statement, you are writing down your best guess and not the question at hand . This means that your statement should be written as if it is fact already, even though you are simply testing it.
The reason for this is that, after you have completed your study, you'll either accept or reject your if-then or your null hypothesis. All hypothesis testing examples should be measurable and able to be confirmed or denied. You cannot confirm a question, only a statement!
In fact, you come up with hypothesis examples all the time! For instance, when you guess on the outcome of a basketball game, you don’t say, “Will the Miami Heat beat the Boston Celtics?” but instead, “I think the Miami Heat will beat the Boston Celtics.” You state it as if it is already true, even if it turns out you’re wrong. You do the same thing when writing your hypothesis.
Additionally, keep in mind that hypotheses can range from very specific to very broad. These hypotheses can be specific, but if your hypothesis testing examples involve a broad range of causes and effects, your hypothesis can also be broad.
Now that you understand what goes into a hypothesis, it’s time to look more closely at the two most common types of hypothesis: the if-then hypothesis and the null hypothesis.
First of all, if-then hypotheses typically follow this formula:
If ____ happens, then ____ will happen.
The goal of this type of hypothesis is to test the causal relationship between the independent and dependent variable. It’s fairly simple, and each hypothesis can vary in how detailed it can be. We create if-then hypotheses all the time with our daily predictions. Here are some examples of hypotheses that use an if-then structure from daily life:
In each of these situations, you’re making a guess on how an independent variable (sleep, time, or studying) will affect a dependent variable (the amount of work you can do, making it to a party on time, or getting better grades).
You may still be asking, “What is an example of a hypothesis used in scientific research?” Take one of the hypothesis examples from a real-world study on whether using technology before bed affects children’s sleep patterns. The hypothesis read s:
“We hypothesized that increased hours of tablet- and phone-based screen time at bedtime would be inversely correlated with sleep quality and child attention.”
It might not look like it, but this is an if-then statement. The researchers basically said, “If children have more screen usage at bedtime, then their quality of sleep and attention will be worse.” The sleep quality and attention are the dependent variables and the screen usage is the independent variable. (Usually, the independent variable comes after the “if” and the dependent variable comes after the “then,” as it is the independent variable that affects the dependent variable.) This is an excellent example of how flexible hypothesis statements can be, as long as the general idea of “if-then” and the independent and dependent variables are present.
Your if-then hypothesis is not the only one needed to complete a successful experiment, however. You also need a null hypothesis to test it against. In its most basic form, the null hypothesis is the opposite of your if-then hypothesis . When you write your null hypothesis, you are writing a hypothesis that suggests that your guess is not true, and that the independent and dependent variables have no relationship .
One null hypothesis for the cell phone and sleep study from the last section might say:
“If children have more screen usage at bedtime, their quality of sleep and attention will not be worse.”
In this case, this is a null hypothesis because it’s asking the opposite of the original thesis!
Conversely, if your if-then hypothesis suggests that your two variables have no relationship, then your null hypothesis would suggest that there is one. So, pretend that there is a study that is asking the question, “Does the amount of followers on Instagram influence how long people spend on the app?” The independent variable is the amount of followers, and the dependent variable is the time spent. But if you, as the researcher, don’t think there is a relationship between the number of followers and time spent, you might write an if-then hypothesis that reads:
“If people have many followers on Instagram, they will not spend more time on the app than people who have less.”
In this case, the if-then suggests there isn’t a relationship between the variables. In that case, one of the null hypothesis examples might say:
“If people have many followers on Instagram, they will spend more time on the app than people who have less.”
You then test both the if-then and the null hypothesis to gauge if there is a relationship between the variables, and if so, how much of a relationship.
If you’re going to take the time to hold an experiment, whether in school or by yourself, you’re also going to want to take the time to make sure your hypothesis is a good one. The best hypotheses have four major elements in common: plausibility, defined concepts, observability, and general explanation.
At first glance, this quality of a hypothesis might seem obvious. When your hypothesis is plausible, that means it’s possible given what we know about science and general common sense. However, improbable hypotheses are more common than you might think.
Imagine you’re studying weight gain and television watching habits. If you hypothesize that people who watch more than twenty hours of television a week will gain two hundred pounds or more over the course of a year, this might be improbable (though it’s potentially possible). Consequently, c ommon sense can tell us the results of the study before the study even begins.
Improbable hypotheses generally go against science, as well. Take this hypothesis example:
“If a person smokes one cigarette a day, then they will have lungs just as healthy as the average person’s.”
This hypothesis is obviously untrue, as studies have shown again and again that cigarettes negatively affect lung health. You must be careful that your hypotheses do not reflect your own personal opinion more than they do scientifically-supported findings. This plausibility points to the necessity of research before the hypothesis is written to make sure that your hypothesis has not already been disproven.
The more advanced you are in your studies, the more likely that the terms you’re using in your hypothesis are specific to a limited set of knowledge. One of the hypothesis testing examples might include the readability of printed text in newspapers, where you might use words like “kerning” and “x-height.” Unless your readers have a background in graphic design, it’s likely that they won’t know what you mean by these terms. Thus, it’s important to either write what they mean in the hypothesis itself or in the report before the hypothesis.
Here’s what we mean. Which of the following sentences makes more sense to the common person?
If the kerning is greater than average, more words will be read per minute.
If the space between letters is greater than average, more words will be read per minute.
For people reading your report that are not experts in typography, simply adding a few more words will be helpful in clarifying exactly what the experiment is all about. It’s always a good idea to make your research and findings as accessible as possible.
Good hypotheses ensure that you can observe the results.
In order to measure the truth or falsity of your hypothesis, you must be able to see your variables and the way they interact. For instance, if your hypothesis is that the flight patterns of satellites affect the strength of certain television signals, yet you don’t have a telescope to view the satellites or a television to monitor the signal strength, you cannot properly observe your hypothesis and thus cannot continue your study.
Some variables may seem easy to observe, but if you do not have a system of measurement in place, you cannot observe your hypothesis properly. Here’s an example: if you’re experimenting on the effect of healthy food on overall happiness, but you don’t have a way to monitor and measure what “overall happiness” means, your results will not reflect the truth. Monitoring how often someone smiles for a whole day is not reasonably observable, but having the participants state how happy they feel on a scale of one to ten is more observable.
In writing your hypothesis, always keep in mind how you'll execute the experiment.
Perhaps you’d like to study what color your best friend wears the most often by observing and documenting the colors she wears each day of the week. This might be fun information for her and you to know, but beyond you two, there aren’t many people who could benefit from this experiment. When you start an experiment, you should note how generalizable your findings may be if they are confirmed. Generalizability is basically how common a particular phenomenon is to other people’s everyday life.
Let’s say you’re asking a question about the health benefits of eating an apple for one day only, you need to realize that the experiment may be too specific to be helpful. It does not help to explain a phenomenon that many people experience. If you find yourself with too specific of a hypothesis, go back to asking the big question: what is it that you want to know, and what do you think will happen between your two variables?
We know it can be hard to write a good hypothesis unless you’ve seen some good hypothesis examples. We’ve included four hypothesis examples based on some made-up experiments. Use these as templates or launch pads for coming up with your own hypotheses.
You are a student at PrepScholar University. When you walk around campus, you notice that, when the temperature is above 60 degrees, more students study in the quad. You want to know when your fellow students are more likely to study outside. With this information, how do you make the best hypothesis possible?
You must remember to make additional observations and do secondary research before writing your hypothesis. In doing so, you notice that no one studies outside when it’s 75 degrees and raining, so this should be included in your experiment. Also, studies done on the topic beforehand suggested that students are more likely to study in temperatures less than 85 degrees. With this in mind, you feel confident that you can identify your variables and write your hypotheses:
If-then: “If the temperature in Fahrenheit is less than 60 degrees, significantly fewer students will study outside.”
Null: “If the temperature in Fahrenheit is less than 60 degrees, the same number of students will study outside as when it is more than 60 degrees.”
These hypotheses are plausible, as the temperatures are reasonably within the bounds of what is possible. The number of people in the quad is also easily observable. It is also not a phenomenon specific to only one person or at one time, but instead can explain a phenomenon for a broader group of people.
To complete this experiment, you pick the month of October to observe the quad. Every day (except on the days where it’s raining)from 3 to 4 PM, when most classes have released for the day, you observe how many people are on the quad. You measure how many people come and how many leave. You also write down the temperature on the hour.
After writing down all of your observations and putting them on a graph, you find that the most students study on the quad when it is 70 degrees outside, and that the number of students drops a lot once the temperature reaches 60 degrees or below. In this case, your research report would state that you accept or “failed to reject” your first hypothesis with your findings.
Let’s say that you work at a bakery. You specialize in cupcakes, and you make only two colors of frosting: yellow and purple. You want to know what kind of customers are more likely to buy what kind of cupcake, so you set up an experiment. Your independent variable is the customer’s gender, and the dependent variable is the color of the frosting. What is an example of a hypothesis that might answer the question of this study?
Here’s what your hypotheses might look like:
If-then: “If customers’ gender is female, then they will buy more yellow cupcakes than purple cupcakes.”
Null: “If customers’ gender is female, then they will be just as likely to buy purple cupcakes as yellow cupcakes.”
This is a pretty simple experiment! It passes the test of plausibility (there could easily be a difference), defined concepts (there’s nothing complicated about cupcakes!), observability (both color and gender can be easily observed), and general explanation ( this would potentially help you make better business decisions ).
While watching your backyard bird feeder, you realized that different birds come on the days when you change the types of seeds. You decide that you want to see more cardinals in your backyard, so you decide to see what type of food they like the best and set up an experiment.
However, one morning, you notice that, while some cardinals are present, blue jays are eating out of your backyard feeder filled with millet. You decide that, of all of the other birds, you would like to see the blue jays the least. This means you'll have more than one variable in your hypothesis. Your new hypotheses might look like this:
If-then: “If sunflower seeds are placed in the bird feeders, then more cardinals will come than blue jays. If millet is placed in the bird feeders, then more blue jays will come than cardinals.”
Null: “If either sunflower seeds or millet are placed in the bird, equal numbers of cardinals and blue jays will come.”
Through simple observation, you actually find that cardinals come as often as blue jays when sunflower seeds or millet is in the bird feeder. In this case, you would reject your “if-then” hypothesis and “fail to reject” your null hypothesis . You cannot accept your first hypothesis, because it’s clearly not true. Instead you found that there was actually no relation between your different variables. Consequently, you would need to run more experiments with different variables to see if the new variables impact the results.
You’re about to give a speech in one of your classes about the importance of paying attention. You want to take this opportunity to test a hypothesis you’ve had for a while:
If-then: If students sit in the first two rows of the classroom, then they will listen better than students who do not.
Null: If students sit in the first two rows of the classroom, then they will not listen better or worse than students who do not.
You give your speech and then ask your teacher if you can hand out a short survey to the class. On the survey, you’ve included questions about some of the topics you talked about. When you get back the results, you’re surprised to see that not only do the students in the first two rows not pay better attention, but they also scored worse than students in other parts of the classroom! Here, both your if-then and your null hypotheses are not representative of your findings. What do you do?
This is when you reject both your if-then and null hypotheses and instead create an alternative hypothesis . This type of hypothesis is used in the rare circumstance that neither of your hypotheses is able to capture your findings . Now you can use what you’ve learned to draft new hypotheses and test again!
The more comfortable you become with writing hypotheses, the better they will become. The structure of hypotheses is flexible and may need to be changed depending on what topic you are studying. The most important thing to remember is the purpose of your hypothesis and the difference between the if-then and the null . From there, in forming your hypothesis, you should constantly be asking questions, making observations, doing secondary research, and considering your variables. After you have written your hypothesis, be sure to edit it so that it is plausible, clearly defined, observable, and helpful in explaining a general phenomenon.
Writing a hypothesis is something that everyone, from elementary school children competing in a science fair to professional scientists in a lab, needs to know how to do. Hypotheses are vital in experiments and in properly executing the scientific method . When done correctly, hypotheses will set up your studies for success and help you to understand the world a little better, one experiment at a time.
If you’re studying for the science portion of the ACT, there’s definitely a lot you need to know. We’ve got the tools to help, though! Start by checking out our ultimate study guide for the ACT Science subject test. Once you read through that, be sure to download our recommended ACT Science practice tests , since they’re one of the most foolproof ways to improve your score. (And don’t forget to check out our expert guide book , too.)
If you love science and want to major in a scientific field, you should start preparing in high school . Here are the science classes you should take to set yourself up for success.
If you’re trying to think of science experiments you can do for class (or for a science fair!), here’s a list of 37 awesome science experiments you can do at home
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Ashley Sufflé Robinson has a Ph.D. in 19th Century English Literature. As a content writer for PrepScholar, Ashley is passionate about giving college-bound students the in-depth information they need to get into the school of their dreams.
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Persistent concerns with the vehicle’s propulsion systems mean Suni Williams and Butch Wilmore will return home next year in a SpaceX vehicle.
Nasa announced that two astronauts aboard the international space station will have their stay extended by several months and that they will return on a spacex capsule because of problems with the boeing starliner..
“NASA has decided that Butch and Suni will return with Crew 9 next February and that Starliner will return uncrewed. A test flight by nature is neither safe nor routine. And so the decision to keep Butch and Suni aboard the International Space Station and bring the Boeing Starliner home uncrewed is the result of a commitment to safety.” “I talked with Butch and Suni both yesterday and today. They support the agency’s decision fully, and they’re ready to continue this mission on board I.S.S. as members of the Expedition 71 crew. Their families are doing well. Their families understand, just like the crew members when they launch, there’s always an opportunity, there’s always a possibility that they could be up there much longer than they anticipate. So the families understand that. I’m not saying it’s not hard. It is hard. It’s difficult.”
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Two astronauts who have spent months aboard the International Space Station will have to stay there months longer after NASA decided on Saturday that they could not return on Boeing’s troubled Starliner space vehicle. They will return instead on a SpaceX capsule next year.
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Hypothesis Test Graph Generator. Note: After clicking "Draw here", you can click the "Copy to Clipboard" button (in Internet Explorer), or right-click on the graph and choose Copy. In your Word processor, choose Paste-Special from the Edit menu, and select "Bitmap" from the choices. Note: This creates the graph based on the shape of the normal ...
A null hypothesis that the metric is the same across our groups, so any difference we observe in our collected data must merely be statistical noise and an alternate hypothesis which says there is indeed some difference. We can then proceed to collect data for the two groups, estimate the metric of interest for them and see how compatible our ...
We'll perform the regular 1-sample t-test with a null hypothesis mean of 260, and then graphically recreate the results. How to Graph the Two-Tailed Critical Region for a Significance Level of 0.05. To create a graphical equivalent to a 1-sample t-test, we'll need to graph the t-distribution using the correct number of degrees of freedom ...
Step 7: Based on steps 5 and 6, draw a conclusion about H0. If the F\calculated F \calculated from the data is larger than the Fα F α, then you are in the rejection region and you can reject the null hypothesis with (1 − α) ( 1 − α) level of confidence. Note that modern statistical software condenses steps 6 and 7 by providing a p p -value.
Hypothesis testing is a scientific method used for making a decision and drawing conclusions by using a statistical approach. It is used to suggest new ideas by testing theories to know whether or not the sample data supports research. A research hypothesis is a predictive statement that has to be tested using scientific methods that join an ...
Browse 20+ hypothesis icon stock illustrations and vector graphics available royalty-free, or start a new search to explore more great stock images and vector art. Scientific Process Icon Set - hypothesis, analysis, etc. Hypothesis and guess RGB color icon. Explanation for phenomenon.
Hypothesis testing is a fundamental tool used in scientific research to validate or reject hypotheses about population parameters based on sample data. It provides a structured framework for evaluating the statistical significance of a hypothesis and drawing conclusions about the true nature of a population. Hypothesis testing is widely used in ...
Scientific Method. Ask a Question. Create a Hypothesis and Make a Prediction. Test Your Hypothesis. Analyze Your Data. Draw a Conclusion.
It seeks to explore and understand a particular aspect of the research subject. In contrast, a research hypothesis is a specific statement or prediction that suggests an expected relationship between variables. It is formulated based on existing knowledge or theories and guides the research design and data analysis. 7.
A hypothesis is an educated guess, based on observation. It's a prediction of cause and effect. Usually, a hypothesis can be supported or refuted through experimentation or more observation. A hypothesis can be disproven but not proven to be true. Example: If you see no difference in the cleaning ability of various laundry detergents, you might ...
Developing a hypothesis (with example) 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. Example: Research question.
Hypothesis. This will be your guess at how your experiment will turn out. What will happen? ... Put this scientific method graphic organizer to use! Have students design plastic bottle planters and test to see which works best. The Scientific Method. Download File. Download Now (309KB)
Formulating Hypotheses for Different Study Designs. Generating a testable working hypothesis is the first step towards conducting original research. Such research may prove or disprove the proposed hypothesis. Case reports, case series, online surveys and other observational studies, clinical trials, and narrative reviews help to generate ...
Get hypothesis test results and create a graph with this hypothesis testing calculator. Visit Statgraphics to learn about hypothesis testing in statistics.
A hypothesis, on the other hand, is a specific prediction about a new phenomenon that should be observed if a particular theory is accurate. It is an explanation that relies on just a few key concepts. Hypotheses are often specific predictions about what will happen in a particular study. They are developed by considering existing evidence and ...
We multiply the probabilities, as there is a 50% chance of the first coin coming up heads (in theory, one out of every two times the coin will be heads). Therefore, in the universe of first-coin-flip-heads, 1 out of ever 2 flips there will theoretically come up with a second head.
Hypothesis testing is a tool for making statistical inferences about the population data. It is an analysis tool that tests assumptions and determines how likely something is within a given standard of accuracy. Hypothesis testing provides a way to verify whether the results of an experiment are valid. A null hypothesis and an alternative ...
A hypothesis is a statement or proposition that is made for the purpose of testing through empirical research. It represents an educated guess or prediction that can be tested through observation and experimentation. A hypothesis is often formulated using a logical construct of "if-then" statements, allowing researchers to set up experiments to determine its validity. It serves as the ...
Hypothesis is a prediction of the outcome of a study. Hypotheses are drawn from theories and research questions or from direct observations. In fact, a research problem can be formulated as a hypothesis. To test the hypothesis we need to formulate it in terms that can actually be analysed with statistical tools.
The process of hypothesis testing involves two hypotheses — a null hypothesis and an alternate hypothesis. The null hypothesis is a statement that assumes there is no relationship between two variables, no association between two groups or no change in the current situation — hence 'null'. It is denoted by H0.
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.
Step 2: State the Alternate Hypothesis. The claim is that the students have above average IQ scores, so: H 1: μ > 100. The fact that we are looking for scores "greater than" a certain point means that this is a one-tailed test. Step 3: Draw a picture to help you visualize the problem. Step 4: State the alpha level.
Merriam Webster defines a hypothesis as "an assumption or concession made for the sake of argument.". In other words, a hypothesis is an educated guess. Scientists make a reasonable assumption--or a hypothesis--then design an experiment to test whether it's true or not.
The quote, opens new tab, purportedly made by Harris on Jan. 21, 2021, says: "These Trumpers think we care about the constitution.We have the power now, it's time to end this They really don't ...
A study adds strong evidence to the hypothesis that the asteroid that killed the dinosaurs came from a family of objects that originally formed well beyond the orbit of the planet Jupiter. Is ...