In his 2008 book Impossible?, Julian Havil presents an argument offered in Massachusetts in 1854 contending that foreigners were more likely to be insane than native-born Americans. These figures were offered:

Whole Population
	Insane	Not Insane	Totals
Foreign-Born	625	229375	230000
Native-Born	2007	892669	894676
Totals	2632	1122044	1124676

The probability that a foreign-born person was deemed insane was 625/230000 = 2.7 × 10^-3, and for a native-born person the probability was 2007/894676 = 2.2 × 10^-3, which seems to support the claim.

But we get a different story when we divide the data by social hierarchy, into what were called the pauper and independent classes:

Pauper Class
	Insane	Not Insane	Totals
Foreign-Born	182	9090	9272
Native-Born	250	12513	12763
Totals	432	21603	22035

Independent Class
	Insane	Not Insane	Totals
Foreign-Born	443	220285	220728
Native-Born	1757	880156	881913
Totals	2200	1100441	1102641

In the pauper class the probability of a foreign-born person being deemed insane is 182/9272 = 0.02, which is the same as that for a native-born person (250/12763 = 0.02). And the same is true in the independent class, where both probabilities are 2.0 × 10^-3. Havil writes, “So, if an adjustment is made for the status of the individuals we see that there is no relationship at all between sanity and origin” (an example of Simpson’s paradox).