Example: A group of 30 people rated their satisfaction levels of places A, B and C
- There are 3 dependent variables, which are the ratings of places A, B and C on a 5-point Likert scale
Running a Friedman's Test, we are able to understand if there is any significant difference in the mean ranks of the different groups (places). My question is, how is running a Friedman's Test different from running multiple Wilcoxon Signed-Rank Tests if we are doing multiple-to-one comparisons? (e.g. we are working for place A, and we want to see the differences in satisfaction levels vs place B and C).
I also understand that we can apply a Bonferroni correction to reduce Type 1 errors. So in this example: 0.05/2 as the different pairs are:
- A vs B
- A vs C
Could the multiple Wilcoxon Signed -Rank Tests be more suitable in this example compared to the Friedman's Test?
What do you want to know? Just whether they are different, or which one ranked highest, or something else? Have you graphed your data?
The test of Friedman is for independent samples while Wilcoxon signed rank test is for paired samples. It is important make clear that the test of Friedman is used when we have a randomized block design (two factors). For a completely randomized one-factor design (one factor) it is recommended the Kruskal-Wallis test (William Kruskal and W. Allen Wallis) to compare the medians of three or more populations with independent samples.
Those tests only express equality or difference in the treatments. If the test is rejected, it is possible to test pairs of means to see which ones are different, or if any is greater.
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