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I often read about a rule of thumb, one can apply if the test of equal variances returns a significant result. Depending on the source, the proposed maximal $F$ ratio varies between 1.5 and 4, which isn't particuarly surprising since it's only a rule of thumb.

But is there any paper suggesting this rule of thumb (preferably the one with the $F$ ratio of 4)? I can't find any. The test of homogenity of variances is in context of an assumption check for an ANOVA.

Thanks in advance! Otherwise it might get hard to justify this choice to the supervisor.

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Do you mean a rule of thumb involving the ratio of the maximum to minimum observed group variances being larger than a certain number k before we can conclude the assumption of homogeneity of variances is violated? If yes, the link http://data.library.virginia.edu/a-rule-of-thumb-for-unequal-variances/ mentions a book reference for k = 3 which was motivated by simulations, while also confirming that sample size influences how much faith we can put in this rule of thumb. The book reference is Design and Analysis of Experiments, by Dean and Voss, 1999, page 112.

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