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Dennis Lendrem
Dennis Lendrem
Making Data Make Sense
Posted in Business / Industries / Pharmaceuticals

Stigler's Law and Simpson's Paradox

Jan. 19, 2012 1:55 pm
No scientific discovery is named after its original discoverer.
Stephen Stigler

Stigler's Law was formulated by the sociologist Robert K. Merton. Stephen Stigler deliberately called this law Stigler's Law to illustrate this law in action.

Simpson's Paradox is another example of Stigler's Law in action. The paradox occurs when a correlation present in different groups is reversed when the groups are combined. Let's take a look at an example.

In Figure 1 if we look at the death rates in two clinics - Clinic A and Clinic B - we can see that the death rate is higher in Clinic B for both those patients with active cancer and those thought to be in remission. However, if we combine the numbers for patients with active cancer and patients in remission then the death rate appears to be higher in Clinic A.

Figure 1: Numbers surviving and death rates in two clinics for patients in remission, patients with active cancers, and for the two combined. The red bars represent the percentage of patients dying in the two clinics. When each category - active and remission - is considered separately then Clinic B has the higher death rate. However, when the two categories are combined the conclusions are reversed.


Special thanks to Emily for the data.Public Domain

Sadly, Simpson's Paradox is often observed in the unthinking analysis of medical and social statistics. And it is observed even more frequently in politics. Depending upon the selection or presentation of the data and how honestly it is presented Simpson's Paradox allows the same dataset to be used to draw opposing conclusions.

So what has this got to do with Stigler's Law?

Well, you guessed, the chap who first discovered Simpson's Paradox wasn't called Simpson. The name Simpson's Paradox was introduced by Colin Blyth in 1972. Edward Simpson's paper describing the paradox was written in 1951 and the paradox was first described by the statisticians Karl Pearson in 1899 and Udny Yule in 1903.

Another result for Stephen Stigler.


Colin R. Blyth (June 1972). "On Simpson's Paradox and the Sure-Thing Principle". Journal of the American Statistical Association 67: 364–366.

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