October 5, 2017

Strength of evidence and type of evidence

The last 127 people to win a Nobel Prize for Physics have been men. Various people have calculated probabilities for this under a model where the true probability each time is 50:50.  Those probabilities are very small: they start with 37 zeros. Now, as people who analyse coincidences will tell you, there’s potential for cherry-picking. Gender of Nobel Laureates in Physics isn’t the only possible comparison.  On the other hand, if the comparison were picked from a thousand million billion trillion competing comparisons, the probability would still be tiny. The hypothesis that the committee chooses people at random for the Nobel Prize in Physics is not statistically defensible.  In fact, even the hypothesis that the committee chooses people with physics PhDs at random isn’t statistically defensible.

The reason there’s still controversy is that ‘choosing people at random’ isn’t anyone’s claim about how the Nobel Prize in Physics works.  Roughly speaking, there are three explanations for it just being given to women:

  1. Physics is too hard for women, who should just stick to biostatistics
  2. Women don’t get many opportunities to lead really ground-breaking physics research, because science is sexist
  3. The Nobel Committee for Physics (or the people eligible to nominate) are less likely to choose women who have contributed just as much

The p-value with a ridiculous number of zeros doesn’t provide any basis for assessing how important the three explanations are.  You need more data — and a different type of data.

So, for example, it’s relevant that Lise Meitner was nominated 29 times for the prize (and 19 times for the Chemistry prize) and didn’t win, but that Otto Hahn did win for their joint work. It’s relevant that Chieng-Shieng Wu was nominated 7 times and that a prize was awarded for the discovery she worked on. It’s relevant that Vera Rubin received lots of other prizes and awards and was routinely mentioned as a possible Nobelist — we don’t yet know how often she was nominated because there’s a 50-year secrecy rule.

Personally (though I’m not a physicist) I think that explanation 1 can be largely discounted and explanation 2 has to stretch a lot to cover the situation, so explanation 3 is looking plausible. But the numbers with 37 zeroes aren’t a relevant summary of the data.

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Thomas Lumley (@tslumley) is Professor of Biostatistics at the University of Auckland. His research interests include semiparametric models, survey sampling, statistical computing, foundations of statistics, and whatever methodological problems his medical collaborators come up with. He also blogs at Biased and Inefficient

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Comments

  • avatar
    Joseph Delaney

    “Physics is too hard for women, who should just stick to biostatistics”

    This seems to imply that Biostatistics is easier than physics, which I am not sure that I would agree without a lot more evidence. I have worked with people in both fields over a checkered career, and I don’t see any tendency for the median physicist to a lot sharper than the median biostatistician.

    Now maybe this is different at the very tails of the distribution. But I am skeptical. There are some very bright people in biostatistics.

    I am also generally skeptical about sex-based ability arguments. The potential for reverse causality concerns me greatly when using them to explain differences in outcome. These outcomes could also be explained by systemic gender bias. Maybe not in all cases, but I would want some serious data to rule this explanation out. If anything, my prior is for the gender bias over the innate ability, given the clear history of discrimination that women have faced over history. So I am in agreement about the plausibility of explanation #1.

    And none of this is to disagree with your larger point that the data is not well summarized by that specific test. It is more of a gut reaction to innate ability arguments, in general, especially when looking at the tails (neither the median nor the exceptional physicist is winning a Nobel prize, but only the elite).

    2 months ago