If your question is about normality you should not rely on tests to decide about using or not parametric tests.

I strongly advise you to assess histograms of quantitative variables to make your decision, stratifying them for each categorical variable.

As concerning your question about post-hoc analysis, I believe you are referring to ANOVA, in which case I consider Tukey post-hoc as a good option. I can explain why, if that’s interesting for you.

Hello Girum,

First, be sure that you're checking normality for model residuals (difference between observed DV value and that estimated by the final, fitted model), and not for all cases combined on the raw DV scores.

Second, choose your method for judging whether or not normality is satisfied (is it the K-S test? some other test, like Shapiro-Wilk? a visual quantile-quantile plot of scores vs. the target/normal distribution? looking at sheer size of skew and/or kurtosis? comparing skew and/or kurtosis to their respective standard error?), and stick with it.

Third, if you'd like a robust analytic method that allows you to discard worries about normality, do consider using bootstrap/resampling methods. Many statistical packages include this as an option.

Finally, for post hoc tests, assuming that one is justified given your data, these also can be run via bootstrap estimation. However, I'd suggest you consider something like the Benjamini-Hochberg method in preference to a very low-powered method such as the Tukey HSD. See this link for more information: https://www.statisticshowto.com/benjamini-hochberg-procedure/

Good luck with your work.

Dear David Morse,

I have got very interesting advice for my work. Thank you very much!

Dear Edgar Mesquita,

Thank you for your helpful advice!

From your question it is not easy to deduce what the data is all about. What is your dependent variable and what are your independent variables. Is the dependent variable nominal, ordinal or scaled? Please clarify