## gender gaps

Two of my colleagues [and co-authors] at Dauphine, Elyès Jouini and Clotilde Napp, published a paper in Science last week (and an associated tribune in Le Monde which I spotted first) about explaining differences in national gender inequalities in maths (as measured by PISA) in terms of the degree of overall inequality in the respective countries. Gaps in the highest maths performer sex ratio. While I have no qualm about the dependency or the overall statistical cum machine learning analysis (supported by our common co-author Jean-Michel Marin), and while I obviously know nothing about the topic!, I leisurely wonder at the cultural factor (which may also partly explain for the degree of inequality) when considering that the countries at the bottom of the above graphs are rather religious (and mostly catholic). I also find it most intriguing that the gender gap is consistently reversed when considering higher performer sex ratio for reading, because mastering the language should be a strong factor in power structures and hence differences therein should also lead to inequalities…

### 5 Responses to “gender gaps”

1. Here are further comments from David Draper that were erased for an unclear reason [thanks, David!]:

the problem is that regressions like those illustrated in figure s1 are at the wrong level of the data hierarchy, which is actually students nested in countries

to begin to look seriously at issues of causality, we would need a data set with one row for each student; there would be one or more outcome variables y (e.g., math test scores, e.g., at different ages); if we think (e.g.) that gender and family income are on the causal path for achievement on math tests, they would become supposedly causal factors x; and we would have to identify, measure and account/adjust for a potential myriad of confounding factors z (these are variables, correlated both with y and with x, that may also reasonably be on the causal path)

you know as well as I do how difficult it is to arrive at valid causal conclusions with observational data; the difficulty doesn’t imply that we should abandon the effort; I applaud the work of the authors of the science paper, but their analysis is only a first step in a wider and more difficult challenge at the person level

the situation is precisely analogous to that of doll’s epidemiological research in the 1950s, in which he showed a correlation between
the percentage of adults in a country who smoked and the death rate in the country due to lung cancer; doll’s work was (highly) suggestive, but it had to be followed by careful studies at the person level to definitively pin down the causal story

2. I’m not convinced about the religion being a deciding factor at all. I’m wondering… why do we have to force the gender gap idea in everything?

• What exactly is your point about “forcing the gender gap”? The sex difference in high maths performances has been observed consistently and repeatedly over the past decades. In my opinion, it is interesting to see how it correlates with other societal indicators.

3. David Draper Says:

One of the main problems with analyses like that illustrated in Figure S1 above is that countries don’t perform well or poorly on math tests, students do; as epidemiologists have long understood, these are ecological correlations and regressions, with all of the pitfalls implied by that class of methods …

• Thanks, David. While this does not address your point, the picture is rather reductive of the paper contents, which cover a large range of (penalised) regressions. With national indicators, as you point out.

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