**Tags**

95% confidence interval, Gregory Clark, IQ, Neanderthals, polygenic scores, Richard Klein, standard error, Upper Paleolithic Revolution

Commenter “Some Guy” had some questions about polygenic scores for me. His questions are in block quotes with my answers directly below each one.

How good do you think polygenic scores will have to get before they start getting used on an individual level? Like within how many SDs of the true IQ/g/educational achievement?

If one’s polygenic score is extreme enough, it doesn’t have to be very accurate at all to give useful information. For example, let’s say you have several embryos to choose from and one has a polygenic education score of +5 SD. Even though such scores only predict 12% of the variance, because +5 SD is so extreme, you can be about 97% confident that embryo will grow up to be more educated than the average person (assuming he or she is raised in a society similar to the one from which the stats were derived).

One problem with polygenic scores is they don’t seem translate well from one culture to another, suggesting they’re more correlative than causal.

The uses I can think of is to identify children with high potential from poor backgrounds, or as an environmentally unbiased entrance “exam” for schools etc.

What I would like to see them be used for is to estimate the IQs of historical Geniuses like Albert Einstein and to estimate the IQs of ancient human populations. For example Richard Klein believes there was a major genetic change in human cognition that occurred about 50 kya that allowed us to suddenly spread from Africa, replace the Neanderthals, colonize the globe and create representational art. If we compared the polygenic scores of humans both before and after the upper Paleolitic revolution, we could test this idea. Similarly Gregory Clark believes rapid genetic evolution in Europe allowed the industrial revolution.

I would also love to see polygenic IQ scores for the Neanderthals, assuming they would be meaningful in a group that culturally and genomically distinct.

What sort of PGS-IQ correlation would result in polygenic scores that are say within 1 SD of the true IQ? I know you often calculate standard errors from correlations, mind sharing the formula/method?

Within 1 SD with degree of certainty? If you mean with 95% certainty, you would need a correlation of 0.85+ which I doubt will ever be achieved. Even the correlation between two different IQ tests is seldom that high.

The method is to square the correlation to get the percentage of the variance explained, and then subtract that value from 1 to see what percentage is left unexplained.

So for example a PGS that correlated 0.85 with IQ explains 72% of the IQ variance, thus leaving 28% unexplained.

The variance is defined as the standard deviation squared, so since the IQ standard deviation is set at 15, the variance is 225, and 28% of 225 is 63.

The square root of 63 is 7.9 which is what the standard deviation would be if everyone had the same PGS. This is also known as the standard error of the estimate. Now in a bell curve, 95% fall within 1.96 of the mean, so multiplying 7.9 by 1.96 tells us that 95% of say the UK, will have IQs within 15.5 points of the PGS prediction.

So if you have a PGS of +2 SD that correlates 0.85 with IQ, your IQ will likely be 0.85(2) = +1.7 or IQ 126, with a 95% confidence interval of 111 to 142. But of course we’re nowhere near seeing a 0.85 correlation.

To get the general public to really trust polygenic scores for IQ, I’d guess the accuracy would have to be within 5 points of the true score. Within 10 points would lead to people who actually differ by 20 points regularly ending up with the same polygenic score. Since 20 points tend to be the difference between leaders and followers, such errors would be highly noticeable.

I think if they achieved a correlation of 0.7 with IQ they’d be considered credible (especially if the predictive power was maintained across oceans and generations). That’s the correlation between different IQ type tests with each-other and these are routinely used to decide issues as important as who gets into an elite college, who gets excluded from the military, who gets diagnosed as disabled or gifted, and who gets sentenced to death by the courts.

By the way, what do you think about this argument against people who consider intelligence entirely environmental: If that really was the case, then disadvantaged people would NEVER be smarter than people with good backgrounds. So why even bother giving people from poor backgrounds a chance? 100% environmentalism leads to un-egalitarian conclusions, and is easily disproven by the existence of smart disadvantage people.

It’s prima facie absurd, but it wouldn’t necessarily lead to the conclusion that we shouldn’t give deprived people a chance. On the contrary it might lead to the conclusion that changing IQ is simply a matter of changing environments.