[SPSS - wilcoxon/paired t test] - not normally distributed data

Hello! I ran an analysis of my data of research into a repeated measures design and found the difference of both conditions to be not normally distributed.

When exlcuding data to make it normally distributed and thus use parametric tests, can we only exclude data that exceeds the limit of the z score +-3.29 (outliers), or can we exclude data that exceeds the 5% of data that goes up to Z score of +-2.58.

For an example, say 8% of my data goes up to +-2.58. Am I able to exclude the 3% so only 5% of my data is within the limits of +-2.58, or can I only exclude outliers (none)?

Thank you!


TS Contributor
If your sample sitze is lange enough, the t-test functions well even if the differences are not from a normally distributed population.

With kind regards

Hello! Unfortunately, my sample size is not large enough - so I cannot assume normality, that's why I was asking whether I can exclude extreme values as I have no outliers.


Super Moderator
Three comments:

1) Don't delete outliers just to achieve a particular distribution. Outliers include information too.
2) I know the Wilcoxon rank-sign test is commonly seen as the default non-parametric alternative to the paired t-test, but it actually tests quite a different null hypothesis. The paired t-test tests an hypothesis that the mean difference is zero; the Wilcoxon test tests a null hypothesis that if we randomly select a pair of observations from the population, then the probability that observation A will be greater than observation B is 50%. It cannot be interpreted as a test of equal means or equal medians unless you add the auxiliary assumption that the two distributions are identical.
3) You could use a paired permutation test as an alternative, which allows you to stick to testing a null hypothesis of equal means (as for the t-test), but without the normality assumption. You probably can't do this in SPSS, but can do in R.