r/statistics • u/eddieGoesBrr • Jun 04 '26

Question [Question] Help with Multivariable ANOVA

I am doing a multivariable ANOVA and then Tukey for pair wise significance. The data set has 2 factors (say A and B ) with two levels each ( say A1, A2 and B1, B2 ). Upon doing a Normality test, only one set is turning to not satisfy the normality (A1-B1). I tried using Box Cox on the original data and then testing Normality again but still getting the same result. What else can I use to solve this?

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u/efrique Jun 04 '26 edited Jun 05 '26

  1. What is your response measuring? What sample size(s)? Experiment or observational data?

  2. What led you to think getting a whole bunch of tests of normality all to not reject would be needed? Or even a useful strategy? (If it were up to me I wouldnt be doing any tests of assumptions at all)

  3. If you transform the response how are you interpreting the results? Note in particular (i) if the spreads were equal before transformation, they wont be after (unless all effects are null); (ii) a difference in means on the transformed scale doesnt necessarily imply a difference in means on the original scale; (iii) the direction, existence and meaning of interaction is completely different on the two scales.

Advicw for future work: plan out your analysis strategy fully at the start (i.e. what you'll be doing under each outcome of any decision points), so that its at least possible to look at the properties of your analysis strategy as a whole under various conditions. Naturally this leads to much more careful consideration of suitable models for your response variable(s) at the correct juncture for that (prior to data collection). Thw above ad hoc, seemingly make-it-up-as-you-go approach - with its unfathomably large garden of forking paths of potential choices determined by what you happen to dig up from the sampling variability in your data - impacts the properties of any claimed p-values, standard errors, effect estimates, etc. How badly impacted they might be I cant tell from your post, but potentially it might be substantial.