A non-parametric test is used in the case of non-normality (and thus often with smaller groups). An explanation about non-parametric tests with info about the following tests:
0:00 – 15:45 over Mann-Whitney for two independent samples 15:45 – 23:00 over Wilcoxon signed rank test for related samples 23:00 – end over Kruskal-Wallis test for multiple independent samples
Look here for a video about the Friedmans test (non parametric version of repeated measures ANOVA):
How can you check the assumptions of Kruskal-Wallis? Look here and here.
