> If the noise in polygenic scores is random, all that will do is reduce correlations. Random measurement error always reduces the ability to observe relationships. To be clear, I do not know enough about polygenic scores to judge one way or another how the noise "works" vis-a-vis the entire analysis.
That's correct, it is a flaw of the entire analysis, not the PGS in isolation. Yes, the polygenic score, when used to define 'genetic intelligence', will be biased towards zero and will miss a lot of the genetic intelligence. What then happens is the video-game playing becomes a measure of intelligence (genetic or otherwise), capturing what the polygenic score (and other covariates) miss. The logic then works in reverse: the reduced correlation is precisely why the residual confounding works. The worse your 'measurements' are at measuring the underlying trait, the more wiggle room there is for your 'outcomes' to actually be correcting the 'measurements' and not vice versa. See "Statistically Controlling for Confounding Constructs Is Harder than You Think" https://journals.plos.org/plosone/article?id=10.1371/journal... , Westfall & Yarkoni 2016. (More examples: https://www.gwern.net/notes/Regression )
What OP shows is not that video game playing causes IQ, but IQ causes video game playing. The choice to play video games (or not play them, because you are bad at learning) is an additional 1-item long IQ test and helps corrects for the error.
(And we do in fact know that video gaming & IQ correlate, so nothing new there. We also know from all the brain training randomized experiments that the causal arrow doesn't run in the direction they want it to run. OP is very wrong, including in claiming that the Flynn effect justifies believing in their effect - it actually is a criticism of their claimed causal relationship between IQs have been steady or falling even as video gaming increased massively.)
That's correct, it is a flaw of the entire analysis, not the PGS in isolation. Yes, the polygenic score, when used to define 'genetic intelligence', will be biased towards zero and will miss a lot of the genetic intelligence. What then happens is the video-game playing becomes a measure of intelligence (genetic or otherwise), capturing what the polygenic score (and other covariates) miss. The logic then works in reverse: the reduced correlation is precisely why the residual confounding works. The worse your 'measurements' are at measuring the underlying trait, the more wiggle room there is for your 'outcomes' to actually be correcting the 'measurements' and not vice versa. See "Statistically Controlling for Confounding Constructs Is Harder than You Think" https://journals.plos.org/plosone/article?id=10.1371/journal... , Westfall & Yarkoni 2016. (More examples: https://www.gwern.net/notes/Regression )
What OP shows is not that video game playing causes IQ, but IQ causes video game playing. The choice to play video games (or not play them, because you are bad at learning) is an additional 1-item long IQ test and helps corrects for the error.
(And we do in fact know that video gaming & IQ correlate, so nothing new there. We also know from all the brain training randomized experiments that the causal arrow doesn't run in the direction they want it to run. OP is very wrong, including in claiming that the Flynn effect justifies believing in their effect - it actually is a criticism of their claimed causal relationship between IQs have been steady or falling even as video gaming increased massively.)