Missives from a fly bottle
barang dot sg
Last revised 31 August 2017
29. Simpson’s paradox

A strange and mysterious disease is going around and only two physicians are willing to treat it.

One of them is a lonesome Chinese acupuncturist; the other a certain western doctor.

No one knows which of these two physicians is better, so patients flock to them basically at random.

After a while, the following statistics emerge:

Western doctor
50 men treated – 40 cured
100 women treated – 20 cured

Chinese acupuncturist
200 men treated – 150 cured
100 women treated – 10 cured

The western doctor tends to cure 80% of men and 20% of women that are inflicted with the disease, whereas the Chinese acupuncturist tends to cure just 75% of men and 10% of women. So the western doctor seems to be better.

But, at second glance, the Chinese acupuncturist tends to cure 53% of all his patients, whereas the western doctor tends to cure only 40% of his. So the Chinese acupuncturist now seems to be better.

How can this be?

Named after Edward H. Simpson, who drew wide attention to this “paradox” in the 1950s.