The page you linked only gives a weak argument (3 genes to give a normal distribution of colour in maize?) and no references to empirical observations of the distribution. The video on the page, talking about skin colour, does not claim anything about the distribution, beyond the fact that there is a continuous range. Even with all of the mixing that has taken place in the last few centuries, the world does not look to me like skin colour is normally distributed.
Even Fisher’s original paper on the subject says only “The great body of available statistics show us that the deviations of a human measurement from its mean follow very closely the Normal Law of Errors” near the beginning, then proceeds with pure mathematics.
I can think of several ways in which a polygenic trait might not be normally distributed. I do not know whether these ever, rarely, or frequently happen. Only a small number of genes involved. Large differences in the effects of these genes. Multiplicative rather than additive affect. The central limit theorem doesn’t work so well in those situations.
And the graph of raw scores in the OP is clearly not a normal distribution. Would you justify transforming it into a normal distribution because that is how the “real” thing “must” be distributed? That would render the belief in normal distributions untestable.
To what extent has that been empirically tested?
The page you linked only gives a weak argument (3 genes to give a normal distribution of colour in maize?) and no references to empirical observations of the distribution. The video on the page, talking about skin colour, does not claim anything about the distribution, beyond the fact that there is a continuous range. Even with all of the mixing that has taken place in the last few centuries, the world does not look to me like skin colour is normally distributed.
Even Fisher’s original paper on the subject says only “The great body of available statistics show us that the deviations of a human measurement from its mean follow very closely the Normal Law of Errors” near the beginning, then proceeds with pure mathematics.
I can think of several ways in which a polygenic trait might not be normally distributed. I do not know whether these ever, rarely, or frequently happen. Only a small number of genes involved. Large differences in the effects of these genes. Multiplicative rather than additive affect. The central limit theorem doesn’t work so well in those situations.
And the graph of raw scores in the OP is clearly not a normal distribution. Would you justify transforming it into a normal distribution because that is how the “real” thing “must” be distributed? That would render the belief in normal distributions untestable.