I am now trying to use the non-parametric Kruskal wallis H test instead. But I have problems in reporting the violation of the assumptions in APA style.

Below are the results of the tests

Tests of Normality:

Shapiro-Wilk:

Group 1: df = 140 p = .096

Group 2: df = 182 p = .001

Group 3: df = 59 p = .124

Test of homogeneity of variances

Levene statistic = 3.02 df1 = 2 df2 = 378 p = .021

It will be nice if you guys can suggest other methods to deal with these violations of assumptions too!

Thanks a bunch!