*61*

A paired samples t-test is used to compare the means of two samples when each observation in one sample can be paired with an observation in the other sample.

This tutorial explains how to conduct a paired samples t-test in Python.

**Example: Paired Samples T-Test in Python**

Suppose we want to know whether a certain study program significantly impacts student performance on a particular exam. To test this, we have 15 students in a class take a pre-test. Then, we have each of the students participate in the study program for two weeks. Then, the students retake a test of similar difficulty.

To compare the difference between the mean scores on the first and second test, we use a paired samples t-test because for each student their first test score can be paired with their second test score.

Perform the following steps to conduct a paired samples t-test in Python.

**Step 1: Create the data.**

First, weâ€™ll create two arrays to hold the pre and post-test scores:

pre = [88, 82, 84, 93, 75, 78, 84, 87, 95, 91, 83, 89, 77, 68, 91]post = [91, 84, 88, 90, 79, 80, 88, 90, 90, 96, 88, 89, 81, 74, 92]

**Step 2: Conduct a Paired Samples T-Test.**

Next, weâ€™ll use the ttest_rel() function from the scipy.stats library to conduct a paired samples t-test, which uses the following syntax:

**ttest_rel(a, b)**

where:

**a:Â**an array of sample observations from group 1**b:Â**an array of sample observations from group 2

Hereâ€™s how to use this function in our specific example:

import scipy.stats as stats #perform the paired samples t-test stats.ttest_rel(pre, post) (statistic=-2.9732, pvalue=0.0101)

The test statistic is **-2.9732Â **and the corresponding two-sided p-value isÂ **0.0101**.

**Step 3: Interpret the results.**

In this example, the paired samples t-test uses the following null and alternative hypotheses:

**H _{0}:Â **The mean pre-test and post-test scores are equal

**H _{A}:**The mean pre-test and post-test scores areÂ

*not*equal

Since the p-value (**0.0101**) is less than 0.05, we reject the null hypothesis. We have sufficient evidence to say that the true mean test score is different for students before and after participating in the study program.