# Paired Samples t-Test in SPSS: Step by Step

Paired samples t-test in SPSS is another popular form of inferential analysis. This method is used frequently in many types of research to prove the hypothesis.

Actually, this test is quite simple, really. The formulas and procedures to be used are easy to understand. Don’t worry if you are a statistics beginner. You’ll understand it quickly.

Although it seems very simple, the benefits of this test are enormous. Many research conditions can be answered using this test

For those of you who have research and struggle with the mean value, please read through.

## What is Paired Samples T-Test?

Paired samples t-test is a hypothesis testing conducted to determine whether the mean of the same sample group has a significant difference or not.

Paired samples t-test is another form of t-test which aims to test two means from those from the same sample group.

The t-test is performed using the t-distribution as the basis for the development of the test

Paired t-test is performed to test 2 conditions using the mean test statistic of paired objects.

Examples of frequently used uses:

1. Measurement of samples before and after different treatments or conditions. For example, a farmer wants to measure the height of the plant before being fertilized and after being fertilized whether it is significantly different or not.

2. Measurement of samples against two different times. For example, an analyst wants to find out whether there is a significant difference in fashion industry income before and after the Covid-19 pandemic.

3. Measurements are made on the same sample as two parts of the sample. For example, an ophthalmologist wants to find out if there is a significant difference in the patient’s eye condition between the left eye and the right eye.

The purpose of this test is to determine whether there is a statistically significant difference in the mean between the paired objects.

This test is also known as dependent t-test, repeated measures t-test, or paired t-test. It’s because we used the same unit of sample on two different condition or two different points of time or two related part of the same unit.

## The requirement of using Paired Sample t-Test

If you want to use paired samples t-test, these are the requirement:

• Statistical difference between two points in time
• Statistical difference between the two conditions
• Statistical difference between two measures
• Statistical differences between interconnected pairs

You need to remember: paired t-tests can only be used to compare means (means) for two groups of samples with two treatments that are related to a normal distribution.

The paired t test is not suitable for use under the following conditions:

• The data used are not paired
• The distribution used is not normal
• Comparing more than two groups
• Ordinal / rank data type

The truth is, you have to fulfill all of the list above. If you don’t, perhaps you have to use non-parametric statistical test.

Also, when you do outlier and normality testing, the variable that you use is the one that represents the difference between the paired values. Remember, don’t use the original values.

## The Test Statistics of Paired Samples t-Test

Once you’ve looked at the one-sample t-test formula, you shouldn’t have too much trouble with the paired t-test formula.

The test statistics used are as follows

Where:

Explanation:

## Example of Paired Samples t-Test in SPSS

Take a look at this Paired Samples t-test in SPSS. You will learn how to solve the problem quickly. If you have done the one-sample t-test in SPSS, it would be easier.

In this case, we would like to analyze whether there is a significant average difference between mathematics scores and sports scores of a group of students in favorite high schools.

By using the semester report, the data we get is as follows:

Perform hypothesis testing to determine whether the average scores of students’ mathematics and sports differ significantly or not.

The steps of using the paired t-test using SPSS software:

1. Input data used in the data view menu
2. Input variables used in the variable view menu
3. Select Analyze >> Compare Means >> Paired-Samples T-Test

4. Select the variable to be tested and click the arrow button

5. Select options to determine the confidence interval level, then click continue

6. Click Ok

On the output display page, you will see 3 tables as follows.

• The first table is paired sample statistical table that contains the average, number of samples, standard deviation, and standard error which I named column A
• The second table is paired sample correlation table that contains the number of samples, the values obtained, and the level of significance.
• The third table is paired sample test table that contains the statistical results of the paired t-test.

Based on the output above, allow me to summarize five important points we have to check:

• A. Mean value of sports score is 72.33
• B. Mean value of sports score is 92.20
• C. Correlation value of math score and sports score is 0.137. we can conclude that there is a positive but weak relationship between math scores and sports score.
• D. The difference in the mean value between sports score and math score is -17.96667. We can conclude that the students’ mean sports scores were lower than the mean math scores.
• E. P-value of the test is 0.000. We can conclude that there is  significant mean difference between math scores and exercise scores.

To explain the p-value in formal steps, let we use the hypothesis test procedure.

1. Determine the hypothesis formula

2. Define the significance level

3. Define the rejection criteria

Reject H0 if p-value < alpha (0.05)

4. The test statistics

5. Conclusion

Based on the SPSS output above (point E), it can be seen that the p-value is 0.00. It means, p-value < alpha. That means we have successfully rejected H0

Also, we can conclude several points:

• There is significant differences of mean value between math scores and sports scores.
• On average, the students’ sports scores were 17.69 points lower than their math scores.
• There is positive correlation between sports scores and math scores but it is so weak.

Conclusion

Paired samples t-test is a hypothesis test conducted to determine whether the mean value of the same sample group has a significant difference or not.

The criteria that you have to know if you want to use this test:

1. The sample is random
2. Types of data used are intervals and ratios
3. The two sample groups are from the same group and related
4. The data used are normally distributed or at least close to the normal distribution
5. There are no outliers or extreme value

The paired samples t-test is an extension of the t-sampling distribution test. You can use it in the case of a small sample, assuming the data is normally distributed.