The paired t test assumes that you have sampled your pairs of values from a population of pairs where the difference between pairs follows a Gaussian distribution. If you want to test this assumption with a normality test, you need to go through some extra steps:

1.On the Options tab of the t test dialog, choose the option to graph the differences.

2.View the results table (part of the t test results) showing the differences. Click Analyze and choose Column statistics.

3.Choose the normality test(s) you want. We recommend D'Agostino's test. Note that none of the normality tests are selected by default, so you need to select at least one.

4.If the P value for the normality test is low, you have evidence that your pairs were not sampled from a population where the differences follow a Gaussian distribution. Read more about interpreting normality tests.

If your data fail the normality test, you have two options. One option is to transform the values (perhaps to logs or reciprocals) to make the distributions of differences follow a Gaussian distribution. Another choice is to use the Wilcoxon matched pairs nonparametric test instead of the t test.

Note that the assumption is about the set of differences. The paired t test does not assume that the two sets of data are each sampled from a Gaussian distribution, but only that the differences are consistent with a Gaussian distribution.