In class we discussed the importance of using non-parametric tests on ordered data (i.e. data from a subjective 1-to-10 scale). We talked about the variety of tests available, but I decided to make a handy flow chart for anyone who wants a quick reference of which test to chose.
As you see above, the first deciding factor is the number of factors. This weeds out your possibilities really quickly since you can only properly do one-factor non-parametric tests. For reasons that are really complicated, there simply isn't a way to do the equivalent of a two-way ANOVA for non-parametric data; signed-rank tests aren't made to produce enough information to have any meaningful analysis across multiple factors. A search through the internet shows that some people have attempted to develop multi-factor non-parametric tests, but statisticians have deeply contentious opinions on whether they work or not, so it's best just to avoid them. So, keep this in mind when designing studies that all non-parametric data should only be tested by one factor at a time.
Next, your test depends on the number of sample groups you want to compare. If you only have one group and want to compare to a set/expected value, then use the Wilcoxon signed rank test (non-parametric equivalent of a one-sample t-test). If you have two groups, you can use the Mann-Whitney U-test for unpaired samples (equivalent of unpaired t-test) or the Wilcoxon matched-pairs signed rank test for paired samples (equivalent of paired t-test). If you have three or more groups, there actually is a non-parametric equivalent of a one-way ANOVA! We didn't talk about it much in class, but it is called the Kruskal-Wallis test, which I will address in my next blog post. If you are making multiple planned comparisons, use the Dunn's test to correct for the multiple comparisons. If you are not making multiple comparisons, you can use the Fisher's LSD test.
Hope this flow chart helps my fellow visual learners out there!