I have Likert-scale data from an experiment with 5 conditions, each of which has a different treatment and one is a control group. The goal is to compare the effect of the treatment between the conditions.
I tested the normality of distributions with the Shapiro-Wilk test. The result shows that the data is not normally distributed. Therefore, I used a non-parametric equivalent to ANOVA, in this case, Kruskal-Wallis test.
But then I tested the homogeneity of variance with Levene's test. The result shows that the variances are homogeneous.
Considering the results from Shapiro-Wilk test (non-normal distribution) and the results from Levene's test (variances are homogeneous), should I use the non-parametric Kruskal-Wallis or ANOVA?