Regression to the mean is just the fact that rare events tend to be followed by more typical or average ones.
A simple example would be the lotto winner today who plays again tomorrow. Chances are, tomorrow's ticket isn't gonna hit.
This is not because the "dice have memory" (that would be the gambler's fallacy), but just the opposite. Since playing the lottery today and tomorrow are independent events, and since the most common result when one plays is to lose, the rare event of actually winning yesterday will likely be followed by the more comment event of losing today. This is true even though winning yesterday has nothing to do with the odds of winning again today.
Perhaps a simpler example is to flip 10 coins all at once. Keep flipping them til all ten land heads.
Once they finally all land heads (the rare event...) flip em again just one more time. Chances are, you'll get about 5 heads / 5 tails (... will likely be followed by a more common or average one).
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I initially thought that regression to the mean would not occur with IQ, because the test's reliabilities are so large (upper .90s where 1.0 is perfect). 1- the reliability squared is the amount of error in a test (variance not due to the construct the test is measuring) so there's not much room for regression to the mean-- At least, I think.
I guess though you'd get regression to the mean when the parents are either very low or very high in IQ (the rare events). Even with a large chunk of the variance in IQ being genetic, the best bet would be the kids of very bright parents would have higher than average IQs, but IQs lower than their parents (due to regression to the mean).
Still though I think the effect would be small due to the high reliability and high hereditability of IQ.
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We've had many debates here on IQ and genes, I won't open that can o worms, but just some points for interested posters to consider:
1) One cannot deny that race differences exist on IQ tests. The data go back to WW I, and the differences have to be among the most replicated effects in all psychology. The differences are not trivial either (1 standard deviation, roughly, for blacks versus whites).
2) All I'm saying in 1 is that races differ in mean IQ. This is not a racist statement. It's a fact.
3) Racism potentially comes in to play when you try explaining WHY races differ in mean IQ.
It could be that IQ tests don't measure intelligence at all, but instead measure culture-- and thus are biased. This is a potential explanation for the gap that doesn't seem at all racist.
On the other hand, the GAP could be entirely driven by genes, with some races clearly "superior" to others (a potentially racist explanation for the difference).
4) The fairest conclusion right now is that no one knows why races differ in IQ.
Evidence for the genetic view is anything but conclusive.
That said, no one has been able to find variables in the environment that trully matter (meaning when one controls for these variables, the difference between races goes away). This isn't for lack of trying either. Just about everything one can think of in the environment that might matter has been studied / controlled for, and yet the race differences remain.
5) The differences are not due to test bias. "Test bias" has precise meaning in psychometrics, and is something that can be easily measured. In study after study after study, there is no bias-- IQ tests predict many important things, and they do so just as accurately for whites as for blacks (so much so that the EEOC allows employers to use IQ tests in selection, even though they exclude black applicants at a disproportionate rate!).
6) If you buy the methodology / logic behind identical twin studies, and the correlations (e.g.,) between foster kids and adopted parents (r=00), then the evidence for the hereditability of IQ is overhwelming. Again, perhaps one of the most replicated effects in psych, with between 50-75% of your IQ being determined by genes.
**I recently was debating a neuroscientist on this, who pointed my to a study suggesting that h2 estimates are flawed because they ignore the prenatal environment.
Her argument was it's the womb that matters. Clearly, this is an environmental variable, but (i still need to think about this) in the typical "identical twins reared apart" studies, the environmental effects of the womb would be confounded with the measure of H2. So, h2 would vastly overestimate the effects of genes on iq, were indeed the womb the key thing that matters when it comes to determining IQ.
Interesting argument-- I need to read more about it, but my initial reaction is that it's such a potentially compelling wrench in the engine to the standard genetic model, that unless there were some strong paradigm-shift inertia going on, I don't understand why this research isn't getting paramount attention in the area.
7) Damn this post is long. I wonder if anyone read it. Percocets make me chatty.