Residuals of a 2x2 between-subjects factorial ANOVA are not normally distributed Dependent variable: Emotional impact – measured by two ordinal variables (questions) on a Likert scale [1 (Least) to 10 (Most)] A composite mean score of the two variables was created named meanEMOTION which became the DV.
IV1: Gender (Male, Female)
IV2: Relationship type (Stranger, In a relationship)
I would like to conduct a 2x2 between-subjects ANOVA but my model is not normally distributed.
The Shapiro-Wilk test for the residuals of my DV was significant for all of my factors. I worry this may affect my ANOVA results.
There are some posts related to this on this site but the answers are inconsistent and there does not seem to be an agreement. In general, some people on the internet suggest using different non-parametric tests while others suggest not doing anything. I have read in the Andy Field (Discovering statistics using IBM SPSS statistics) book that there isn't a non-parametric equivalent to a 2x2 factorial ANOVA. And some say that factorial ANOVA may be robust enough to deal with non-normally distributed residuals. Perhaps I do not have to do anything with it?
I'm attaching the outputs from the test of normality and residuals:











The nonparametric (actually semiparametric) alternative is the proportional odds ordinal logistic model, which handles Wilcoxon and Kruskal-Wallis tests as special cases but allows for interaction terms.  An overview and resources may be found here.
