It also doesn’t always happen. For instance if you have two pairs of parents that are far above the average in some partially-heritable trait, then their children will exhibit some regression to the mean and be less above average in the trait, but if the children pair off and have children of their own, then the children of the children will have the same expected trait level as the original children, i.e. no regression to the mean.
Let me check: you mean the grandchildren have the same ex ante expected height as the ex ante expected height of the children. Of course! (Just as the children have the same ex ante expected height as the parents’ ex ante expected height, which is now screened off by knowing their actual height.) But if you reset your expectations based on the observed children’s heights, you’ll still witness (on average) regression to the mean.
Let me check: you mean the grandchildren have the same ex ante expected height as the ex ante expected height of the children. Of course! (Just as the children have the same ex ante expected height as the parents’ ex ante expected height, which is now screened off by knowing their actual height.)
Yes, but in this case because you know the parents’ heights, the children’s ex ante expected height differs from the population mean.
But if you reset your expectations based on the observed children’s heights, you’ll still witness (on average) regression to the mean.
Though not towards the population mean but rather towards the ex ante expected height of the children.
It also doesn’t always happen. For instance if you have two pairs of parents that are far above the average in some partially-heritable trait, then their children will exhibit some regression to the mean and be less above average in the trait, but if the children pair off and have children of their own, then the children of the children will have the same expected trait level as the original children, i.e. no regression to the mean.
Let me check: you mean the grandchildren have the same ex ante expected height as the ex ante expected height of the children. Of course! (Just as the children have the same ex ante expected height as the parents’ ex ante expected height, which is now screened off by knowing their actual height.) But if you reset your expectations based on the observed children’s heights, you’ll still witness (on average) regression to the mean.
(If not this, I’d appreciate an explainer!)
Yes, but in this case because you know the parents’ heights, the children’s ex ante expected height differs from the population mean.
Though not towards the population mean but rather towards the ex ante expected height of the children.