This is a rather interesting Minute Physics video. It is tackling what is known as the Simpson Paradox. What is interesting is that it is applying it to an example where on first glance, there appears to be no form of statistical bias, but when viewed another way, it seems that there is.
What is interesting here is that several years ago, I mentioned of an AIP study examining universities in the US that have very small number of physics faculty and how many of those that do not have a single female faculty member. The result found that, statistically, this is what is expected based on the number of female physics PhDs, meaning that we can't simply accuse these schools (and hiring of female physicist in general) of bias against female physicists. This Minute Physics video appears to provide an illustration of what is expected statistically without imposing even any bias to the sample.
Again, I'm not saying that female physicists and faculty members do not face unfair or more challenges in their career when compared to male physicists. But illustrations such as these should also be considered so that we tackle problems that are real and meaningful and not chase something is not the source of the problem.