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I know the F-test determines if two samples are different based upon their variances, whilst the t-test determines if two samples are different based upon their mean (but include the variance, as standard deviation in the formula, unlike the F-ratio).

My research group uses a data mining tool based on calculating the F-ratio. Sections with high F-ratio are ranked highly, and then features are mined based upon the magnitude of the F-ratio. However, my advisor is telling me that the true indication of whether it is possible to discover a feature is if it passes a t-test. In other words, she says that in order for something to be significant in terms of the F-ratio, it must also pass the t-test. I always thought that these two were unrelated tests, and have different applications, and are used independently. Which is true?

Jimbo
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  • There are different ways to construct an "F ratio"?. I assume you're talking about the ANOVA case here. In a one-way analysis of variance, the following holds for the two test statistics: $F = t^2$, and they are asymptotically equivalent to [Wald tests](https://stats.stackexchange.com/a/60459/930). – chl Oct 14 '20 at 06:31
  • @chl Yes, i'm talking about the ANOVA case here for a 2 class comparison only. I had no idea about that relationship! This is something I'd like to bring up to my advisor. I found a derivation here on stack exchange and some other websources, I'm wondering if there are any papers or textbooks that demonstrate/explain this. – Jimbo Oct 14 '20 at 07:44

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It is not entirely clear what your research group is doing. The ANOVA is a generalization of the t-test for more than 2 groups. It's true that the the t-test and ANOVA differ in methodology, but in essence you wouldn't need to do a t-test if you already performed an ANOVA (assuming all the assumptions are met). If the assumptions are not met you could use a non-parametric test such as the Kruskal–Wallis ANOVA.

However, you mention the F-ratio in your question, which makes me wonder whether you are doing an ANOVA at all or just calculating the F-ratio (F-statistic), which is used in the ANOVA. If you are only calculating the F-ratio then you haven't performed an actual test, and something additional would need to be done to actually test whether these ratios (or means) are different, which I guess you could use a t-test but why not just use ANOVA?

user2974951
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  • let me clarify - usually our software only calculates the F-ratio, and we aren't actually performing any test. That "additiona" part of testing if the means are actually different is what I'm attempting to do. I think my advisor has it in her head that this is done by a t-test, rather than ANOVA is the more sensible and natural solution. We always run a two-class comparison only. – Jimbo Oct 14 '20 at 07:47