Reply #109: It's statistically significant.

[Donald Ian Rankin]

I don't know what you mean by "you can make practically anything statistically significant with 100,000 subjects" - that's a large enough sample to effectively eliminate random errors (whether or not you think the study systematic bias depends on what you interpret it as, but provided you don't try and read it as something it isn't I suspect it's pretty free of that, too).

To give you and idea, assume that IQ is normally distributed with mean 100 and standard deviation 50 (it isn't, but that's a weaker claim than I need), and that that's true for both men and women. Then the average difference in IQ will be the sum of the IQs of 50,000 men - 50,000 women divided by 50,000.

This will be normally distributed with mean 0 and variance 0.01. The probability that that will be greater than 4 is... well, I can't find a lookup table that goes that far, but the odds of a study finding this great a difference in averages if there isn't a difference in distributions is unbelievably minute.

It's not a *big* differene at all - the odds of a given woman having a lower IQ than a given man are only very, very slightly less that 0.5 (note: this is not actually strictly deducible from the fact that women have a slightly lower average, but it's areasonably safe assumption given what we know about IQ), but they *are* less than 0.5; the study is statistically significant.