Although when I try to put numbers on it now, it's actually looking like I happened to get this one right: if 3% of men are gay, you need log<sub>2</sub>(97/3) ≈ 5 [bits of evidence](/2018/Oct/the-information-theory-of-passing/) to think that someone probably is. Is a sufficiently distinctive "gay voice" that much evidence—something you're 32 times more likely to hear from a gay man than a straight man?
-It looks like you have to go awfully far into the tail to get that sufficiently distinctive. Table 2 in Smyth _et al._'s ["Male Voices and Perceived Sexual Orientation"](/papers/smyth_et_al-male_voices_and_perceived_sexual_orientation.pdf) works out to [Cohen's _d_](/2019/Sep/does-general-intelligence-deflate-standardized-effect-sizes-of-cognitive-sex-differences/) ≈ 1.09. Assuming normality and equal variances for that effect size, you need to be 3.43 standard deviations out from the straight male mean in order to get that much evidence. (Because Φ(1.09 - 3.43)/Φ(-3.43) ≈ 32, where Φ is the [cumulative distribution function](https://en.wikipedia.org/wiki/Cumulative_distribution_function) of the normal distribution.)
+It looks like you have to go awfully far into the tail to get that sufficiently distinctive. Table 2 in Smyth _et al._'s ["Male Voices and Perceived Sexual Orientation"](/papers/smyth_et_al-male_voices_and_perceived_sexual_orientation.pdf) works out to [Cohen's _d_](/2019/Sep/does-general-intelligence-deflate-standardized-effect-sizes-of-cognitive-sex-differences/) ≈ 1.09. Assuming normality and equal variances for that effect size, you need to be 3.43 standard deviations out from the straight male mean in order to get that much evidence. (Because Φ(1.09 − 3.43)/Φ(−3.43) ≈ 32, where Φ is the [cumulative distribution function](https://en.wikipedia.org/wiki/Cumulative_distribution_function) of the normal distribution.)
I don't think Prof. H.'s voice was quite that extreme? Maybe it was only 2 or 2.5 standard deviations out, for a likelihood ratio of around 8–12.7, which is about 3–3.7 bits of evidence—which is an update from 3% to about 20–28%?
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