I conducted a mixed ANOVA and Box'x test has been violated as well as some variables in Levene's test (most of them are non-significant though). My total sample is 90, with 30 participant in each group (I have three groups) . how should I proceed ?
PS: My data is interval ratio and not normally distributed
I would be more concerned with the non-normality of the data/residuals. Research suggests that with equal sample sizes and normally distributed data, violation of homogeneity (besides that, assessing the deviation vom homoscedasticity is also a question of power, therefore with large sample sizes Box and Levene test will be significant even with slight heteroscdasticity. So these tests are somewhat pointless) may not be very harmful. BUT you can never be sure, therefore you should consider using robust estimation techniques. Rand R. Wilcox published lots of books on this topic and he provides R codes within his WRS2 package for every technique he presents.
Wilcox, R. R. (2017). Modern Statistics for the Social and Behavioral Sciences: A Practical Introduction (2nd Ed). Boca Raton, FL: Chapman
Wilcox, R. R. (2017). Introduction to robust estimation and hypothesis testing (4th ed.). Academic press.
Wilcox, R. R. (2010). Fundamentals of Modern Statistical Methods: Substantially Improving Power and Accuracy, 2nd Edition. New York: Springer.
Values of ANOVA data are assumed to be normal distribution. It is one of the assumptions for its application.
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