I inherited a dataset with a very small sample size (n=3 per group) and three factors (primary insult x secondary insult x treatment). I intended to use a three-way ANOVA, but I was warned that this may not be the way to go, as statistical tests for assumptions of ANOVA (particularly normality) may yield false results.
What is the appropriate statistical test for this situation? I'm somewhat familiar with Friedman or Scheirer-Ray-Hare but am unclear about how to proceed. I'm currently using GraphPad Prism 8.0 at the request of my PI/junior investigator but have experience with R, so feel free to suggest solutions using either package. Thanks!
Hello Kathleen,
You could try the aligned ranks anova, which may be evaluated via R (see this link by another RG contributor, Salvatore Mangiafico: https://rcompanion.org/handbook/F_16.html). There are other possible tactics as well, using what I would call hybrid methods (due to Conover & Iman, or Puri & Sen).
The most obvious challenge, of course, is going to be the poor level of statistical power for any comparisons you might run, unless the differences are pretty profound in magnitude.
Good luck with your work!
Hello,
The Kruskal–Wallis test is appropriate for this situation. Please check the following link for using Kruskal-Wallis Test in R.
http://www.sthda.com/english/wiki/kruskal-wallis-test-in-r
It is important to note that your 3W ANOVA is mathematically equivalent to 1W ANOVA of your N1 X N2 X N3 factorial design if you take any combination of your design as a single treatment with the 3 replicates each. In this case you can perform Kruskal–Wallis one-way analysis of variance as Davoud suggested.
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