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"As you work toward providing everyone a fully enriched environment, differences in performance are increasing due to innate (in)abilities."

I don't know if you are referring to within group differences or between group differences here, but I can address the point either way.

In an ideal world where everyone has the fully enriched environment, we still would have the between group cultural preferences. I personally consider myself fortunate to have not been raised in the Chinese cultural environment with respect to educational pressure. Maybe other cultural groups, such as American black people, don't want to conform to the white upper middle class cultural expectations for educational achievement. But if we imagine a situation in which all cultural groups have roughly equivalent values regarding educational performance, I would expect the following:

1. There would still be individual (within group) differences in motivation.

2. Setting this aside for the purposes of this discussion, the innate differences between individuals and groups would be much more clearly revealed than they are now, and we would be able to say more accurately what they are. Based on your comments, I assume that you are more interested in between group differences.

It is certainly possible that American whites, blacks, Chinese, etc., would not have equal mean performances academically. It is impossible to determine whether the mean differences would be greater or less than they are now.

With respect to individual differences within groups, I would expect that many people could improve their performances, but everyone would be limited by whatever is maximally achievable with a human brain. This would tend to reduce the range of individual scores on tests like the SAT.

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Sorry for my typo—meant to say "...increasingLY due to innate..."

Agree it doesn't particularly matter whether looking at inter- or intra-group differences. Heritability due to genetic factors increases once you equalize environmental (i.e. non-genetic) factors. I would think cultural environments would tend to become more similar than different once enrichment becomes more universally the norm. I have no issues with the remainder of your analysis. Thanks for posting.

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In thinking further, the range might not change much because the people at the far left tail of the distribution are severely impaired, and many of them already receive specialized services. With improved nutrition and so on, there might be fewer people at the lowest end of the ability distribution, but some of the most impaired people would still anchor that end of the range. I would predict that mean scores for the entire population would rise, as well as mean scores for the ethnic subgroups. This would shift the highest part of the bell shape to the right, indicating actual improvement in ability population-wide. If this were to occur, psychometricians would probably adjust the tests, so that the average score would be 100 again, but this number would be the equivalent of 110 (or whatever) on the first version of the test.

Thanks for the dialogue, Richard.

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