Typically, a T-test evaluates if there is any significant difference in the mean values of two experimental conditions. However, if the study design is *within participants, *an approach known as paired sample T-test (commonly known as repeated measures T-test) must be used.

A paired sample T-test, a statistical procedure is used to examine whether the mean difference between two sets of observations is zero. In this test, the sample or entity is measured twice resulting in the ‘pairs’ of observation.

Like many statistical tests, the paired sample T-test has two hypotheses: the null hypothesis and the alternative hypothesis.

- The
*null hypothesis*considers that the true mean difference between the paired samples is zero. Here, all the observable differences are explained by random variation. - On the other hand, the
*alternative hypothesis*assumes that the true mean difference between the paired samples is not equal to zero. This hypothesis takes one of several forms based on the expected finding.

However, if the direction of the difference is of no importance, then two-tailed hypothesis can be used. If not, an upper-tailed or lower-tailed hypothesis is used to improve the power of the test. Whereas the null hypothesis remains the same for all types of alternative hypothesis.

As a parametric procedure, this test makes several assumptions. Here the observations are stated as the differences between the 2 sets of values, and each assumption attributes to these values.

The assumptions of paired sample T-test include:

**Level of Measurement**

Since this test is made on the normal distribution, it requires the sample data to be numeric as well as continuous. The continuous data can take on any value within a wide range, whereas the discrete data can only take on a few values.

**Independence**

Although independence of observations is not testable, it can be assumed if the data collection procedure was random without any replacement.

**Normality**

Normality assumption can be tested using various tools such as a histogram. This assumption is considered to be met if the histogram shape looks similar to symmetric and bell-shaped.

**Outliers**

These values appear far away from the data. If not handled appropriately, outliers can lead to incorrect conclusions as they can bias the results. The best approach of dealing with them is to simply eliminate them.

**Example**

Some sports students were picked from the entire population**s** that have to examined for their long jump performance The objective to perform this test to validate whether or not training increases the performance.To check we will have to record all the before and after observations for training programme (i.e., the dependent variable is “standing high jump performance”, and the two similar groups are the standing high jump values “before” and “after” the 19-week training program).

Most often, researchers conduct paired sample T-test using SPSS as it is considered as the most reliable statistical tool. The steps explain how can we analyze our data using a paired T-test in SPSS, should not be outraged.

Following the six steps, the interpretation of the results is also commuted depending on the data analysis.

- From tool box select Analyze. Next click on Compare the means option. This is followed by selecting the paired samples T-test on menu

- The Paired-Samples T-Test box will appear. Here explain the SPSS what kind of variables need to be analyzed
- Assign the variables JP1 and JP2 within the paired box. The method by which we can achieve this:

(a) Click on variables and bring down variables in paired variable box

(b) Place each variable separately into the boxes.

- Adjust the confidence level limits and click on continue button to perform the test (choose exclude cases analysis by analysis)

- Click on continue button to return to the paired samples T-test dialogue box

6. Click on the OK button.

Upon performing the analysis, the next step is to interpret the results.

SPSS statistics produces 3 tables in the Output Viewer under the category “T-Test.” However, you need not examine all 3 tables, instead investigate only 2 among them: the paired samples statistics table and the paired samples test table.

**Paired sample statistics table**

The first table is where detailed statistics for your variables is generated.

**Paired sample test table**

The Paired Samples Test table is table were the outputs are summarized.

On analyzing the table, comment on statistical significance of the variables such as

1. Degree of freedom (T) = t value,

- p = P – value ( probability value)

This is followed by interpreting the findings. When interpreting the results utilize information from descriptive as well as inferential statistics.

The steps involved here are:

- Describe the pattern of the data by using the means & standard deviations from the output table.
- Report if any difference is significant
- Combine these information and interpret, summarize the findings

Now that you know how to perform paired T-test using SPSS, fold your sleeves and get going with the process.

How to determine the sample for this test?

Explain how to calculate the degree of freedom