I'am doing a two-way ANOVA and each factor has 3 levels (so 9 cells in total). My data has 60 to 200 observations per cell. The data is pretty normal but heteroscedastic (Levene's test 0.003). The ratio of biggest to smallest group variance is 1.7. The goal is to detect a difference in means of size about 10% of variance. My questions are:
what is the impact of heterescedasticity on standard ANOVA? can I still use it? if yes, what is a reference for your answer?
is there any corrected (Welch slyle) two-way ANOVA for heteroscedastic data? if yes, could you provide a reference?
what are advantages/pitfalls of weighted ANOVA in this case?
is there a non-parametric test that can replace two-way ANOVA in this case?