I'm trying to determine whether I should be using an ANOVA or a non-parametric test. My DV is rating of confidence on a Likert scale (1-5), and 4 categorical IVs (n = 496).
Data distribution within each IV was non-normal, all Shapiro-Wilk tests p < .001, and Levene's test was significant for 2 of the 4 IVs. Also, there are 13 outliers (which were scores of 5 on the Likert scale). After excluding outlier cases, only 1 IV had a significant Levene's test - IV participant sex, in which the groups sizes were very unequal (70% female).
Conducting an ANOVA with and without outliers finds similar results, equality of variance, no interactions, 1 significant factor (with outliers), 2 significant factors (without outliers). Using a kruskal-wallis test also produces the same results as the ANOVA.
I'm not sure of the most appropriate analysis to use, parametric or non-parametric? Have I violated too many assumptions for the ANOVA?
Any advice is much appreciated, thanks.