I'm pretty confused about the conditions in which I should use a parametric or a nonparametric test to compare the means of 2 (or more) populations and would be very grateful if someone would explain it to me.
I know that if the distribution of the sample is not normal, non-parametric (Wilcoxon, Kruskal-Wallis) should be used. It is assumed that the central limit theorem allows to use parametric if n> 30, generalized error because in any case they are n> 30 for each level of the factor. On the other hand, now it seems that CLT is questioned and that 30 cases does not guarantee normality.
When do we have to use one or the other?
If ANOVA requires homoscedasticity, why are post-hoc tests for unequal variances?
Many thanks
I know that if the distribution of the sample is not normal, non-parametric (Wilcoxon, Kruskal-Wallis) should be used. It is assumed that the central limit theorem allows to use parametric if n> 30, generalized error because in any case they are n> 30 for each level of the factor. On the other hand, now it seems that CLT is questioned and that 30 cases does not guarantee normality.
When do we have to use one or the other?
If ANOVA requires homoscedasticity, why are post-hoc tests for unequal variances?
Many thanks