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Remedial measures for violations of assumptions in ANOVA

A basic question when one suspects that the variances of the treatment groups may be unequal or the distribution of measurements may be non-normal, one question is: How to make up for unequal variance and/or nonnormality and still apply the ANOVA framework?

 
  1. Transformation of the response variable to make its distribution closer to normal and to stabilize the variance.
  2. When the departures are too extreme such that transformations do not work: use nonparametric tests instead of the usual F-test for testing the equality of means.

1.1 Variance stabilizing transformations