friedman repeated measures analysis of variance on ranks

Friedman test is basically the non-parametric version of the repeated measures ANOVA, so you use it when your data doesn't follow a normal distribution or when you're working with ordinal data. Since you have the same group being measured at different time points or under different conditions, you're essentially ranking the scores for each participant across those conditions. It's super handy because it ignores the actual values and just looks at the ranks, which saves you a lot of headache when your data is all over the place.

When you run the calculation, you're looking for whether there's a significant difference between the conditions. The test statistic, often denoted as Q or Chi-square, is calculated using the formula 12 / (n * k * (k + 1)) * (sum of squares of rank totals) - 3 * n * (k + 1). Here, n is the number of subjects and k is the number of repeated measures. If your p-value comes out lower than 0.05, it means at least one of the conditions is different from the others, but it won't tell you exactly which pair is different.

If you find a significant result, you'll definitely need to follow up with post-hoc tests to pinpoint where the differences actually are. Most people just do pairwise Wilcoxon signed-rank tests with a Bonferroni correction to keep the error rate down. It can get a bit tedious if you have many conditions, but it's the standard way to make sure your findings are actually solid and not just some random noise in the data.