As far as I understand, the tails coming apart and the moment attribution are two different, superimposed problems. The tails coming apart is “Nigeria has the best Scrabble players in the world, but the persons with the richest English vocabulary in the world are probably not Nigerian”. The moment attribution is “the best Scrabble players in the world are Nigerian, but Nigerians are probably not the best Scrabble players in the world”. In the first case, we are talking about the distribution of country scores for two correlated variables, in the second we are talking about the distribution of individuals within a country for a single variable.
Also, thank you for bringing up Nigerian Scrabble, that would have made a somehow funnier example than NK’s math olympiads.
The tails coming apart is “Nigeria has the best Scrabble players in the world, but the persons with the richest English vocabulary in the world are probably not Nigerian”
No. The tails coming apart here would be “gameplaying of game A correlates with national variable B but the top players of game A are not from the top country on variable B”.
I say it’s borderline circular because while they aren’t the same explanation, they can be made trivially the same depending on how you shuffle your definitions to save the appearances. For example, consider the hypothesis that NK has exactly the same distribution of math talent as every other country of similar GDP, the same mean/SD/etc, but they have a more intense selection process recruiting IMO participants. This is entirely consistent with tails coming apart (“yes, there is a correlation between GDP and IMO, but it’s r<1 so we are not surprised to see residuals and overperformance which happens to be NK in this case, which is due to difference in selection process”), but not with the distributional hypothesis—unless we post hoc modify the distribution hypothesis, “oh, I wasn’t talking about math talent distributions per se, ha ha, you misunderstood me, I just meant, IMO participant distribution; who cares where that distribution difference comes from, the important thing is that the NK IMO participant distribution is different from the other countries’ IMO participant distributions, and so actually this only proves me right all along!”
As far as I understand, the tails coming apart and the moment attribution are two different, superimposed problems. The tails coming apart is “Nigeria has the best Scrabble players in the world, but the persons with the richest English vocabulary in the world are probably not Nigerian”. The moment attribution is “the best Scrabble players in the world are Nigerian, but Nigerians are probably not the best Scrabble players in the world”. In the first case, we are talking about the distribution of country scores for two correlated variables, in the second we are talking about the distribution of individuals within a country for a single variable.
Also, thank you for bringing up Nigerian Scrabble, that would have made a somehow funnier example than NK’s math olympiads.
No. The tails coming apart here would be “gameplaying of game A correlates with national variable B but the top players of game A are not from the top country on variable B”.
I say it’s borderline circular because while they aren’t the same explanation, they can be made trivially the same depending on how you shuffle your definitions to save the appearances. For example, consider the hypothesis that NK has exactly the same distribution of math talent as every other country of similar GDP, the same mean/SD/etc, but they have a more intense selection process recruiting IMO participants. This is entirely consistent with tails coming apart (“yes, there is a correlation between GDP and IMO, but it’s r<1 so we are not surprised to see residuals and overperformance which happens to be NK in this case, which is due to difference in selection process”), but not with the distributional hypothesis—unless we post hoc modify the distribution hypothesis, “oh, I wasn’t talking about math talent distributions per se, ha ha, you misunderstood me, I just meant, IMO participant distribution; who cares where that distribution difference comes from, the important thing is that the NK IMO participant distribution is different from the other countries’ IMO participant distributions, and so actually this only proves me right all along!”