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I have three groups with very small sample sizes (6 obs per each group). In order to use ANOVA I just want to make sure that the equality of variances is satisfied, as Levene's test does not have very good power for small sample sizes, I was wondering what is the right criteria value for rule of thumb (checking the equality of variances/ Max variance/ min variance).

Based on the following like, if the ratio of variances is more than 3 then we can reject the equality of variances:

https://data.library.virginia.edu/a-rule-of-thumb-for-unequal-variances/

But Based on this link (Keppel's ratio rule of thumb) if the ratio of variances is more than 9 then the equality of variances should be rejected.

http://www.theanalysisfactor.com/newsletter/October-2017.html

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    $\begingroup$ You cannot expect various "rules of thumb" to be completely the same: by definition, they are rough and approximate. These differ due to implicit assumptions about the sizes of the datasets and the expected consequences of erring in judgment. The "right criterion" has to depend on your circumstances, the nature of your data, and your analytical objectives. Please, then, provide some specifics in your post. $\endgroup$ – whuber♦ Aug 29 '18 at 15:55
  • $\begingroup$ @ whuber, thanks for the comment, In order to use Anova, I want to test the equality of variances among three groups with very small sample sizes (6 per group). I donot know I should use the rule of Thumb based on Keppel's suggestion or Dean and Voss's suggestion. $\endgroup$ – stat Aug 29 '18 at 17:20
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    $\begingroup$ The first thing to check is whether it would make a difference. For instance, if you still get significant results with a Kruskal-Wallis test or after finding a transformation of the variable that equalizes the variances, you can have some confidence that things are ok. Bootstrapping, although attractive, may be less informative just because the dataset is so small. These considerations suggest you haven't asked the question you are concerned about, which is what to do about this ANOVA. $\endgroup$ – whuber♦ Aug 29 '18 at 17:24
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So you want to use anova with small sample size. Questions about that has been asked&answered here before, see this list.

With three groups and only 6 obs per group you essentially cannot test if assumptions holds, so lacking strong prior information (maybe from experience with that kind of data) that variance is constant, it might be better not to make that assumption. So find a robust alternative that do not make that assumption, more detailed advice can be found from the list above. See also the comments above by @whuber.

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