Which means that the probability that 2 randomly selected highly analytical people are both on the autism spectrum is 1 in 25 (compared to 1 in 1,600 in the general population).
1204 x 0.3 = 360 couples with children in the sample were both defined as highly analytical, so we have ~15 couples where both are on the autism spectrum. This may explain why any effect is too small to detect.
Obviously these are made up numbers and the actual boundaries of the categories are more fluid than that but this does seem like a plausible explanation.
If we take:
p(on autism spectrum) = 2.5%
And defining:
p(highly analytical) = 10% (i.e. the top 10% most analytical people)
Then we get (via good ol’ Bayes):
p(highly analytical|on autism spectrum) = 4 x p(on autism spectrum|is highly analytical)
For simplicity’s sake, let:
p(highly analytical|on autism spectrum) = 80%
so:
p(on autism spectrum|is highly analytical) = 20%
Which means that the probability that 2 randomly selected highly analytical people are both on the autism spectrum is 1 in 25 (compared to 1 in 1,600 in the general population).
1204 x 0.3 = 360 couples with children in the sample were both defined as highly analytical, so we have ~15 couples where both are on the autism spectrum. This may explain why any effect is too small to detect.
Obviously these are made up numbers and the actual boundaries of the categories are more fluid than that but this does seem like a plausible explanation.