Screening 500 genes when none is truly linked

Question

A genetics lab tests 500 genes for association with a trait, using a 5% significance level for each gene. Suppose, for the sake of argument, that not a single gene is truly associated with the trait.

On average, how many genes will still test as "significantly associated" purely by chance?

Accepted Answer

One gene at a time. Testing a gene "at the 5% level" means a gene with no real link still has a 5% chance of looking associated by luck. That false-alarm rate applies to every gene independently of whether it is real. Five hundred genes. The expected number of false hits is simply the number of tests times the per-test false-alarm rate: 	ext{expected false positives} = m 	imes \alpha = 500 	imes 0.05 = 25. So about 25 genes would light up even though none is genuinely linked. Why biologists dread this. Twenty-five "hits" looks like a rich result, but here it is entirely noise. This is exac…

Screening 500 genes when none is truly linked

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