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%?
And the effect size of childhood sex-typed behavior on sexual orientation [is around _d_ ≈ 1.3](/papers/bailey-zucker-childhood_sex-typed_behavior_and_sexual_orientation.pdf), so I'll actually go with roughly similar numbers for L.
-I could easily be wrong about the specific numbers, but I'm confident that this is the correct _methodology_. (Assuming that predictions don't causally [or otherwise](https://arxiv.org/abs/1710.05060) affect the things being predicted—but how likely is _that?_) My old anxieties about committing heresy have dissolved in the knowledge that it is, really, just a math problem.
+I could easily be wrong about the specific numbers. (My gut expects a _skilled_ "gaydar operator" to be more reliable than _d_ ≈ 1.1, which could still be true if the published statistics are [deflated by the measurement error](/2019/Sep/does-general-intelligence-deflate-standardized-effect-sizes-of-cognitive-sex-differences/) of less perceptive raters?) But I'm confident that this is the correct _methodology_. (Assuming that predictions don't causally [or otherwise](https://arxiv.org/abs/1710.05060) affect the things being predicted—but how likely is _that?_) My old anxieties about committing heresy have dissolved in the knowledge that it is, really, just a math problem.
projects / Ultimately_Untrue_Thought.git / blobdiff