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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:

  1. what is the impact of heterescedasticity on standard ANOVA? can I still use it? if yes, what is a reference for your answer?

  2. is there any corrected (Welch slyle) two-way ANOVA for heteroscedastic data? if yes, could you provide a reference?

  3. what are advantages/pitfalls of weighted ANOVA in this case?

  4. is there a non-parametric test that can replace two-way ANOVA in this case?

kjetil b halvorsen
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AsyaM
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  • Perhaps these Q&A may help http://stats.stackexchange.com/questions/97098/practically-speaking-how-do-people-handle-anova-when-the-data-doesnt-quite-mee?rq=1 and http://stats.stackexchange.com/questions/28601/how-to-run-two-way-anova-on-data-with-neither-normality-nor-equality-of-variance?rq=1 – mdewey Dec 15 '16 at 14:31
  • Thanks for your comment, but it is most about one way anova, where I know Welch correction. But I'am searching for an answer about 2-way anova... – AsyaM Dec 15 '16 at 15:21
  • The second one is entitled How to run two-way ANOVA .. so i assumed it was about two-way ANOVA. – mdewey Dec 15 '16 at 15:30
  • Indeed, the second is about two-way anova, I see now.Tkank you. Still I can't find any reference for when using anova or answer on my "correction" question. Lots of people write "you can do anova" or "it is pretty robust" , "rule of thumb is biggest variance is 4 times smallest". But no reference provided. – AsyaM Dec 15 '16 at 17:47
  • Sorry you didn't get a real answer. I'm looking for the same thing, and I'll come back when I know more. – abalter May 24 '19 at 04:42
  • Check generalised least squares. You can model the variances same as you model the mean differences. – Heteroskedastic Jim Jul 02 '19 at 13:05

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