Skeptic said:
(sigh)
This is one of the "factoids" that are often presented in favor of a "huge" difference between blacks and whites in IQ, but it shows more of the ignorance of those who promote it.
When a statistician says that a certain difference is "large" as opposed to "small", he means something like "a difference this size between populations is easily detected even with a relatively small sample from the two populations." It does NOT mean that the effect is absolutely "large" in terms of actual units (as opposed to SDs), let alone that whatever difference exists is of any practical importance.
For instance, suppose that every single white person had an IQ of exactly 100, and every single black person had an IQ of exactly 99. Mathematically speaking, the difference between the two is not 1, or 10, but literally an infinite number of standard deviations (since the SD of both populations is exactly 0). This is, indeed, a "huge" difference for a statistician, in the sense that there is an absolute, 1:1, correlation between race and IQ in this case: one's race totally determines what one's IQ is. So? It would still be still a tiny difference both absolutely (one IQ point) and practically (in terms of differences in "real life" performance).
The one SD difference in IQ, even if real--which is doubtful--might be "huge" in Cohen's statistical sense and still "tiny" or "insignificant" in any practical sense, in the same way that an EXTRA LARGE coke bottle can fit in a SMALL refrigirator. (mis)quoting Cohen in this way is merely using words from one context in another context, with the clear intent of making the IQ difference between blacks and white look as "important" as possible. [/B]
Skeptic.
I believe cohen's intent in suggesting those guidelines was to do precisely what you claim is ignorant-- to have some guideline for determining when an effect size has practical value / is large in the "sense" I've been talking about.
In fact, the effect size removes one big problem with p values-- they correlate with sample size. So, like your example above, you could have "highly significant" results, but the effect size is so small the results have NO practical value.
See cohen's example on the "significant" relationship between height and IQ in kids. This correlation really exists! But it has no practical value-- raising a kid's iq 30 points would require we increase his/her height by something like 12 feet!
Here are the facts (I'll back them with cites if you require) you tell me whether the black / white mean IQ difference has any practical significance:
1) Replicated since WW I, in literally 100's (if not 1000s) of studies, the black mean is around 85, the white mean is 100.
2) Since the standard deviation of an IQ test is 15, the effect size (d) is 1.0
Based on the effect size of 1.0, we know:
3) About 84% of blacks score below the white mean (100) on an IQ test. Only about 2% of blacks score 115 or higher on an IQ test.
4) Given the above effect size, pick any important variable that correlates with IQ. E.g., suppose we pick job performance, which correlates .5 with IQ.
Suppose we set the cutoff score for selection at 115, one standard deviation above the IQ grand mean.
We'd hire about 16% of the white applicants, but only about 2% of the black applicants. Extreme adverse impact.
Would it be legal? Yes, because the test is a valid predictor of job performance for both whites and blacks.
So, here you have a situation where the effect you imply is tiny (and that I am ignorant for suggesting otherwise) results in a bias such that 8 times as many whites (proportionally) are hired over blacks.
Yeah, this is a trivial effect.
Now, substitute job performance for graduate GPA (another correlation around .5). So, why is it we need affirmative action for minorities if we want them fairly represented in higher education?
Then substitute job performance for income (a smaller correlation of .30). 10% of the variance in how much money you make is determined by your IQ. Factor in the race difference and tell me an effect size of 1.0 is trivial.