Don’t reason from slopes unless you also know about the intercepts
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Don't reason from slopes unless you include enough discrete control variables in the regressions that produced them (e.g. dummy variable 1 for men, 0 for women)
I realize I am very late to the party, but I was thinking this when reading the article. You don't glean the insights this article discusses from paying attention to intercepts per se, but by making sure to include in your model important confounding variables, which in the cases discussed are all categorical variables.
While correlation coefficients are symmetric between X and Y, intercepts and slopes aren't. Since brain size is presumably a cause rather than a consequence of intelligence, you should have the slope and intercept of g as a function of brain size, rather than vice versa.
(Under a condition where men and women have exactly the same level of g, that would still reveal bias, of course.)
FWIW, I think there's a reluctance to engage seriously with these sorts of statistical concepts (in particular normal or other distributions with different means) because it could facilitate crimethink.
It is probably my tiny brain that is at fault but although I follow the argument I don’t understand the use of the word “intercept”. Does you mean there is no intercept, no brain size point at which smartness / dumbness flips regardless of sex?
Nah, it comes from playing around with regressions too much and forgetting what the layperson knows.
A linear equation has two components: the slope and the intercept.
In the equation y=5x+2, 5 is the slope and 2 is the intercept. The line crosses ('intercepts') the Y-axis at 2.
What he's saying is that two lines can have equal (or in real life, similar) slopes and different intercepts. In this case the sexes have the same slope (brain size changes by the same amount with regard to IQ) but different intercepts (men and women, on average, with the same IQ will have different brain sizes). The equation might be 5x+1 for women and 5x+3 for men.
The actual value of the intercept is going to be the number you get for the equation when you plug in zero for 'x'--this would be the brain size for someone with a zero IQ. This doesn't have much real-life application in this case but is sometimes relevant for other applications (for example, costs for driving to the store and buying x # of cartons of eggs--even if they're out of eggs and you returned empty-handed you still wasted money driving there).
I’d like to read something by you digging deeply into the M/F thing, addressing Lynn’s book, Emil’s SubStack article, Warne’s blog post, etc. Lynn has women at 98 SD 14, men at 102 SD 16, which if true seems to completely explain far right tail gaps. In opposition there is the National Scottish school children test that proved the sexes are “exactly equal.”
Very nicely written!
Insightful!
Don’t reason from slopes unless you also know about the intercepts
=
Don't reason from slopes unless you include enough discrete control variables in the regressions that produced them (e.g. dummy variable 1 for men, 0 for women)
I realize I am very late to the party, but I was thinking this when reading the article. You don't glean the insights this article discusses from paying attention to intercepts per se, but by making sure to include in your model important confounding variables, which in the cases discussed are all categorical variables.
While correlation coefficients are symmetric between X and Y, intercepts and slopes aren't. Since brain size is presumably a cause rather than a consequence of intelligence, you should have the slope and intercept of g as a function of brain size, rather than vice versa.
(Under a condition where men and women have exactly the same level of g, that would still reveal bias, of course.)
FWIW, I think there's a reluctance to engage seriously with these sorts of statistical concepts (in particular normal or other distributions with different means) because it could facilitate crimethink.
It is probably my tiny brain that is at fault but although I follow the argument I don’t understand the use of the word “intercept”. Does you mean there is no intercept, no brain size point at which smartness / dumbness flips regardless of sex?
https://en.wikipedia.org/wiki/Y-intercept
Nah, it comes from playing around with regressions too much and forgetting what the layperson knows.
A linear equation has two components: the slope and the intercept.
In the equation y=5x+2, 5 is the slope and 2 is the intercept. The line crosses ('intercepts') the Y-axis at 2.
What he's saying is that two lines can have equal (or in real life, similar) slopes and different intercepts. In this case the sexes have the same slope (brain size changes by the same amount with regard to IQ) but different intercepts (men and women, on average, with the same IQ will have different brain sizes). The equation might be 5x+1 for women and 5x+3 for men.
The actual value of the intercept is going to be the number you get for the equation when you plug in zero for 'x'--this would be the brain size for someone with a zero IQ. This doesn't have much real-life application in this case but is sometimes relevant for other applications (for example, costs for driving to the store and buying x # of cartons of eggs--even if they're out of eggs and you returned empty-handed you still wasted money driving there).
Thank you this is really helpful! My teeny brain could not make head or tails of the Wikipedia page explanation.
I didn't totally follow the egg example to be honest but all the rest, yes, so thanks!
Aren't IQ tests designed so that men and women score equally well on average?
They're designed to remove biased items and they do underemphasize specific skills, but I am referring to the latent variable g.
I’d like to read something by you digging deeply into the M/F thing, addressing Lynn’s book, Emil’s SubStack article, Warne’s blog post, etc. Lynn has women at 98 SD 14, men at 102 SD 16, which if true seems to completely explain far right tail gaps. In opposition there is the National Scottish school children test that proved the sexes are “exactly equal.”
On the docket.