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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.

j3ypi
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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.

Isabella Ghement
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  • Yes, great! Do you know any published resources proposing k = 4? – j3ypi May 22 '18 at 12:21
  • I don't, but found a mention to it here: https://stats.stackexchange.com/questions/41021/test-for-equal-variance – Isabella Ghement May 22 '18 at 15:09
  • See also http://www.theanalysisfactor.com/newsletter/October-2017.html, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3350940/ for sme fun reading. – Isabella Ghement May 22 '18 at 15:22
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    These slides mention that "Rule of thumb: the ratio of the largest to the smallest group variance should be 3:1 or less, but be careful, the more unequal the sample sizes the smaller the differences in variances which are acceptable". https://www.tcd.ie/medicine/neuropsychiatric-genetics/assets/pdf/2009_3_ANOVA.pdf – Isabella Ghement May 22 '18 at 15:23
  • So if I'd have equal sample sizes, k = 4 might be arguable? For my own research I would choose a different statistical test, but I actually asked for a fellow student of mine whos supervisor for her thesis is a pain with very limited understanding of statistics. – j3ypi May 22 '18 at 16:52
  • If you have "unequal" sample sizes, k=4 might be arguable. – Isabella Ghement May 22 '18 at 17:14