how do you show For example, let's say we have a group of 5 students who took a pre-test and post-test. Their scores were: Pre-test: 80, 85, 90, 95, 100 Post-test: 85, 90, 95, 100, 105 The differences are: 5, 5, 5, 5, 5 The mean of the differences is 5. The standard deviation of the differences is 0 (since all differences are the same). The t-statistic is undefined (since the standard deviation is 0, we can't divide by 0). In this case, we can conclude that there is a significant difference between the pre-test and post-test scores, as all students improved by 5 points on a graph