I have a question about Fst values based on mitochondrial DNA data. Someone claims that if the Fst value is close to 0, a significant p-value (P < 0.05) doesn’t make sense — because an Fst close to 0 implies no genetic differentiation between groups, so the p-value shouldn't be significant. They argue that while it is possible to observe a high Fst but a non-significant p-value due to a small sample size, the reverse — a low Fst but significant p-value — should not occur. They also asked why I can't understand their logic and whether there are any papers supporting my point. I'm not sure how to respond to that or how I should interpret their stance. Is this claim valid?
Caveat that I don't know what Fst, and personally my body doesn't use DNA for my genetics.
But it sounds like the "someone" doesn't really understand how a p-value works. Just as values far from zero can have a large p-value with a small sample size, values close to zero can still have a low p-value if the sample size is large or the variance is low.
For example, a one sample t-test (against a null of 0) on the following values leads a significant p-value (c. 0.01). You can make these as trivially close to 0 as you want, as long as the variability is also proportionately low.
(0.001, 0.002, 0.001, 0.002)
just to support Sal. For a one sample z-test z=(mu-0)/(sigma/sqrt(n)) the probability for mu to be 0 is nihil. Therefore, there exist at least one set of samples where both sigma and n are of such values that |z|>1.96 and thus p
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