Paired sample t-test is a statistical technique that is used to compare two population means in the case of two samples that are correlated. Paired sample t-test is used in ‘before after’ studies, or when the samples are the matched pairs, or the case is a control study. For example, if we give training to a company employee and we want to know whether or not the training had any impact on the efficiency of the employee, we could use the paired sample test. We collect data from the employee on a seven scale rating, before the training and after the training. By using the paired sample t-test, we can statistically conclude whether or not training has improved the efficiency of the employee. In medicine, by using the paired sample t-test, we can figure out whether or not a particular medicine will cure the illness.
Assumptions in Paired sample t-test:
1.The first assumption in the paired sample t–test is that only the matched pair can be used to perform the paired sample t-test.
2.In the paired sample t-test, normal distributions are assumed.
3.Variance in paired sample t-test: In a paired sample t-test, it is assumed that the variance of two samples is same.
4.Independence of observation in paired sample t-test: In a paired sample t-test, observations must be independent of each other.
Steps in the calculation of paired sample t-test:
1.Set up hypothesis: To calculate the paired sample t-test, first we have to set up the hypothesis. In a paired sample t-test, we set up two hypotheses. The first is null hypothesis, which assumes that the mean of two paired samples are equal. The second hypothesis in the paired sample t-test will be an alternative hypothesis, which assumes that the means of two paired samples are not equal.
2.Select the level of significance: In paired sample t-test, after making the hypothesis, we choose the level of significance. In most of the cases in the paired sample t-test, significance level is 5%, but in medicine, the significance level is set up at 1%.
3.Calculate the parameter: To calculate the parameter we will use the following formula for the paired sample t-test:
Where d bar is the mean difference between two samples, s² is the sample variance, n is the sample size and t is a paired sample t-test with n-1 degrees of freedom.
An alternate formula for paired sample t-test is:
4.Testing of hypothesis or decision making: After calculating the parameter, we will compare the calculated value with the table value. If the calculated value is greater than the table value, then we will reject the null hypothesis for the paired sample t-test. If the calculated value is less than the table value, then we will accept the null hypothesis in the paired sample t-test and say that there is no significant mean difference between the two paired samples in the paired sample t-test.
Paired sample t-test in SPSS:
Most statistical software performs this paired sample t-test. In SPSS, paired sample t-test is available under “analysis” in the menu option, and then in the “compare means” option. As we click on “paired sample t-test,” the following window will appear in SPSS:
Now, from the left side, we will select the first paired variable and drag it into the paired variables option, variable1, and then select the second paired variable and drag it in to the second variable place. From the “option” menu, we will select the “confidence interval” and then click on the “ok” button. After clicking the ok button, the result window will show the result for the paired sample t-test. The first two tables in SPSS for the paired sample t-test will show the descriptive statistics and the correlation between the paired variable. The next table will show the value of the paired sample t-test associated with their probability value. The table will look like the following table:
This table shows a paired sample t-test value associated with the p value and other statistics. By using the p value, we can make decisions about the pair of the sample mean. For instance, this table shows the P value for the pair BI and BI2— and their probability value is .896, which is greater than the significance level at 5%. In this example of the paired sample t-test, paired sample means are insignificant, or the mean of the two paired samples are equal.
