[1] I say "his" because it seems like men are highly overrepresented in submitting falsified data. Obviously there are probably more men in science to start with, but consider that 30/30 of the most retracted scientists are men. https://retractionwatch.com/the-retraction-watch-leaderboard...
For these reasons, retractions are not a good measure of behavior.
Edit: this was in response to your comment before your edit
I agree retractions are an imperfect measure, but it's not like there is much more to go on.
Most importantly, the 30 people on this leaderboard who have dozens of retracted papers are not just people who got unlucky with sampling or made one mistake and had to retract a paper–they are those who repeatedly and knowingly faked data and then published it.
I don't disagree that the rate of misbehavior and gender balance of scientists differ internationally and would ideally be factored into an analysis.
But to play the game... maybe woman are more likely to get caught falsifying data before publication, because the evil patriarchy thinks woman cannot to science and thus more rigorously verifies their results? We for sure could come up with lots of other crappy explanations and theories.
If I were being pedantic [I guess I am :-) ], I'd probably say the best prior would be p =(n male scientists/number all scientists)
Overall I bet men are slightly more than 1/2, but even if it's an 80/20 split the p value for this would be many sigma.
Don't take my word for it, here's a couple lines of R code.
# vector of prior probabilities, natural choice is proportion of men
prop.men <- seq(0, 1, length.out=100)
# compute prob of observation (30/30) given prior probability
pvals <- dbinom(x=30, size=30, prob=prop.men)
plot(prop.men,
log10(pvals),
type="l", col="blue", lwd=2,
ylab="log10 pval for 30/30 offenders being men",
xlab="Baseline male percentage in science"
)
abline(h=log10(0.05), col="red", lwd=2, lty=2) # "significance" line
text(x=0.6, y=-30, lab="Below red line\nsignificant at α=0.05")
# since prob vector is 100 long, indices of entries returned here
# correspond to % men needed for this to have α > 0.05
which(pvals>0.05)
Of course this is a bit back-of-the-envelope done in 5 minutes, but you get the point.
EDIT: Please don't downvote statements of fact. My karma score pays the price for your momentary burst of dopamine.
http://itre.cis.upenn.edu/~myl/languagelog/archives/002748.h...