Monday, 19 December 2011

Statistical assumptions are not scientific assumptions

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It is worth noting that frequentist statistics are built on the assumption of no difference between groups (that two groups are assumed to be random samples from a single population). 

From this assumption, which has nothing whatsoever to do with reality (and is essentially an historical accident derived from the work of Ronald Fisher on crop yields), we tend to assume there is no difference between groups unless 'proven' otherwise. 

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Yet, in the case of human groups separated by scores of generations, and when looking at traits (such as 'g' - general intelligence and personality) which 

1. substantially affect reproductive success, and 

2. are substantially heritable - then this assumption of sameness is irrational. 

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In other words, it would make more sense, scientifically (as opposed to statistically) to expect to find important differences in cognitive abilities and dispositions (including their magnitude and distribution) between separated human populations. 

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Indeed, that was pretty much always the case in the past - people expected that 'strange' people would be different from themselves - often exaggerating the degree of difference to an absurd extent in travellers tales. 

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We have gone crazily far in the opposite direction and not only expect, but statistically assume that there are zero differences in the mean and standard deviation of traits, and that apparent differences are due to sampling biases - except when this probability is very (albeit arbitrarily) low.

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In practice, as we observe, there is never conclusive evidence to reject the 'null hypothesis' that all human populations everywhere are actually one population varying randomly and apparent differences are due to biased sampling - the null hypothesis can always be saved by ever more attention on real or imagined sampling errors - when people really want to save it.

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And failing to reject the null hypothesis is falsely assumed to be 'proving' no difference - yet it is nothing of the sort. It is merely the default assumption of statistics, which is an arbitrary - indeed non-scientific, assumption. 

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(Bayesian statistics claims to overcome this problem of frequentist statistics, but I think it leads to other problems and disagreements. In fact, common sense/ built-in human reason is enough to overcome the problem to the extent that it needs ot be overcome. .i.e The common sense that if things seem to be different, it is reasonable to proceed on the assumption they are different, until proven otherwise. This assumption of difference should not automatically be inverted, as it is with Leftism/ political correctness.)

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