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StatsMiniBlog: Will Rogers Phenomenon

21 Nov, 14 | by Bob Phillips

20140205-091454.jpgThe American humorist, Will Rogers, was reported to have said (of the migration of folk from Oklahoma to California):

When the Okies left Oklahoma and moved to California, they raised the average intelligence level in both states

While this is a deeply unkind comment reinforcing geographical stereotypes, it does a neat job of capturing an epidemological paradox. If you re-define group definitions, you can make both groups averages improve (survival, or IQ) without changing one jot the overall truth. Such a phenomenon must be guarded against when re-defining risk groups, for example on the basis of new diagnostic technologies, and seeing ‘group based’ benefits.

To take it pictorially:

If we have two risk groups, and individuals with good (80%), moderate (50%) and poor survival (10%), we can split them like this:


The overall survival rate is 50%; the low risk group ~70% and high risk group ~20%.

If, by better diagnostic technology, we split the orange patients out and plop them in the high risk group this happens:


The low risk group improves, now ~80% and high risk group also improves, now 30%. Despite our increasing surival rates in both low and high risk groups, theĀ overall survival rate is unchanged at 50%.

We’ve done nothing.

The Will Rogers phenomenon is subtle, but real. Beware when reading comparisons across time and between different groups. Is some thing really going on?

– Archi


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