I have an independent variable with 4 levels. Lets say Group A, B, C and D. When i see for the normality in my dependent variables, i can see, some dependent variables are normal in Group A, B and C but not in D (Shapiro-Wilk Test, p<0.05), Some variables shows normality for Group A and C but not for Group B and D and like wise for all possible combinations. According to the assumption, the dependent variable should be normally distributed in each of the groups.
What should i do in this case where some groups shows normality and some do not. Shall i continue with the traditional ANOVA or need to use Non-parametric alternative? Please suggest.