[kmm]

> a 2013 study conducted in the Netherlands found that women were taller than their male partners in just 7.5 percent of cases

Isn't that entirely to be expected just because men are on average taller than women? As a very quick 'n dirty numerical check, if you pick pairs of numbers from two normal distributions with means that are 2 standard deviations apart, only in 7.8% of the cases will the number from the distribution with the lowest mean be larger than that from the other distribution. In real life male and female heights aren't exactly normally distributed with the same standard deviation and just a differing mean, but is the true expected number of such pairs really much higher than 7.5%, that the result is significant?

[bhedgeoser]

How did you calculate that? (7.8%)

[kmm]

Let's assume male heights are distributed according to a pdf p(x;μ,σ) for a given mean and standard deviation, and assume the female heights are identically distributed with a mean lower by two standard deviations p(x;μ-2σ,σ) (which seems to be reasonably accurate). For a given female height y, the odds a random man is smaller than her are given by the integral of p(x;μ,σ) where x goes from negative infinity to y. You then have to integrate this quantity where y ranges from negative infinity to positive infinity, with the measure p(y;μ-2σ,σ) dy.

It's easy to show this quantity is independent of either the mean or standard deviation, so I just numerically integrated it in Mathematica for a standard normal distribution, which again seems to be reasonably accurate for human heights.