How to Conduct a Paired Samples T-Test

Numerous statistical tests are employed in data science and machine learning to compare and identify differences between variables or data elements. The majority of these tests are hypothesis tests, in which the variables are defined and the link between them is inferred based on the many tests being run. To compare the means of various groups of the categorical variable, another sort of statistical test that is utilized is the t-test.

What is T-Test?

A form of statistical test called the t-test is used to compare the means of various groups of categorical variables. It is employed to see if there is a difference between the groups. It can also be used to choose features for model training. In this case, the features are chosen and rejected based on the acceptance and rejection of the hypothesis as determined by the p and t values.

To find the difference, we essentially take the mean of each group or category of the categorical variables and compare it using the t-test.

The null hypothesis is rejected in this case and it is assumed that there is a difference between the means of the several groups that are being compared. The t valley is also calculated in this case and is compared with the crucial t value.

When it comes to the normal t-test, the null and alternate hypotheses are rejected and accepted based on the calculation of the individual means of the various groups, which is subsequently utilized to determine the t value for the test and aid in conducting hypothesis testing.

What is Paired Sample T-Test?

The means of the several groups are likewise compared using the paired Samples t-test; however, in this case, the difference in means is computed rather than the group means separately.

Said another way, it’s the test we apply when we have paired samples and wish to examine the rate at which the mean of a given variable changes between two groups. First, the t value is computed, followed by the difference in the group means.

Simply put, the paired t-test is applied in situations where there are paired or related sets of categorical variables—that is, when the data are associated by some action, event, or intervention.

On the other hand, the normal t-test is employed when there are two distinct sets of categorical variables that are unrelated to one another.

Workflow for Conducting the Paired T-Test

Let us discuss the various steps involved in conducting the paired t-test step by step.

Define Hypothesis

Any hypothesis test should begin with the definition of the hypothesis. Here, the alternative and null hypotheses are defined. The t value, which is obtained at the conclusion of the test, determines whether the hypotheses are accepted or rejected.

Gather the Paired Data

Since we are doing a paired t-test in this instance, the data would be paired data, or data samples that have been paired and gathered from the same event category. The same object or the same subject may provide the data, but the time periods may vary.

Compute the Differences

We will now compute the difference between the values of the various groups for every pair of observations. Thus, we shall have a value for each group’s specific observation index, and the difference between these values is computed for each observation.

Find the mean of the differences

We will use the means of these differences now that we have the difference in the group observations’ values. In this phase, the standard deviation will also be determined.

Find the T Value

The following formula is used to find the t value in this step:

T: Mean Difference/Sqrt (S^2/n) is the hypothesized difference.

Find the Critical T values

The crucial value for the t must be determined next. Here, the crucial t value for the samples is obtained by utilizing the significance level and the degree of freedom.

Interpret the Result

Compare the test findings now; the null hypothesis is rejected if the calculated t value is greater than the critical t value. In this case, the normal computed t value and the critical t values are calculated.


This article covered the t-test and the paired t-test, as well as the definition, applications, and methodology of each test, along with samples of the corresponding code. This post will make the paired t-test easier to comprehend and will demonstrate how to use it to compare various variable groups.


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