Rosalind Arden, Research Fellow at the Centre for Philosophy of Natural and Social Science (CPNSS), and Theodore Hill (Georgia Institute of Technology) have now published their new paper ‘Recurring Errors in Studies of Gender Differences in Variability’ in the journal ‘Stats’.
About the paper:
Charles Darwin noticed that in some species, in some traits, males were more variable than females. Since Darwin, many scholars have explored this phenomenon in different species, at different stages of development, and in diverse traits. Larry Summers, while President of Harvard, pointed out in 2005 that evidence suggests men are more variable than women in several traits. He hypothesised that this sex difference in variance could be one of several contributing factors to explain why more men than women work in some areas of science. A critical outcry followed his conjecture; the fuss got him fired. Much of the criticism was based on mistakes.
That men’s cognitive ability test scores are more variable than women’s is found in many but not all studies. More variance means the scores are more dispersed. It means that to a greater extent than among men, women’s test scores cluster towards the middle of the distribution. It also means that, being more dispersed, men’s test scores more than women’s are more often found in the extremes of the distribution. Men’s scores are more often found at the far-left tail (lower scores) and at the far-right tail (higher scores).
Why is this empirical question politicised? It has been clouded by controversy since if men’s scores have greater variance, that distributional difference may contribute to unequal numbers of men and women having preferences for, or being selected into, occupations or other opportunities that call on test scores at the very high tail where the asymmetry between the sexes may exist.
Because the empirical question has been politicised (mistakenly, in our view), papers that report the headline ‘greater male variability debunked’ tend to get widely circulated – the kind of glee we may feel when ‘our side’ wins.
We argue that several statistical errors are often made in exploring the question of greater male variability. We focus on one influential paper, which makes some of these mistakes. We argue for a cool empirical approach and for all of us to check ideology at the door as best we can while doing science.