In Defense of Low Correlations
By Bryan Caplan
An interesting side discussion from “The Power of Personality” defends the practical importance even small correlations:
Walter Mischel (1968) argued that personality traits had limited utility in predicting behavior because their correlational upper limit appeared to be about .30. Subsequently, this .30 value became derided as the ”personality coefficient.” …
Should personality psychologists be apologetic for their modest validity coefficients? Apparently not, according to Meyer and his colleagues (Meyer et al., 2001), who did psychological science a service by tabling the effect sizes for a wide variety of psychological investigations and placing them side-by-side with comparable effect sizes from medicine and everyday life. These investigators made several important points. First, the modal effect size on a correlational scale for psychology as a whole is between .10 and .40, including that seen in experimental investigations… Second, the very largest effects for any variables in psychology are in the .50 to .60 range, and these are quite rare (e.g., the effect of increasing age on declining speed of information processing in adults). Third, effect sizes for assessment measures and therapeutic interventions in psychology are similar to those found in medicine. It is sobering to see that the effect sizes for many medical interventions–like consuming aspirin to treat heart disease or using chemotherapy to treat breast cancer–translate into correlations of .02 or .03. [emphasis mine]
Now you might take a Hansonian view of this: Just say, “Medicine is as useless as personality,” instead of “Personality is as useful as medicine!” But should you?
[A] modest correlation between a personality trait and mortality or some other medical outcome, such as Alzheimer’s disease, would be quite important… In terms of practicality, the .03 association between taking aspirin and reducing heart attacks provides an excellent example. In one study, this surprisingly small association resulted in 85 fewer heart attacks among the patients of 10,845 physicians (Rosenthal, 2000). Because of its practical significance, this type of association should not be ignored because of the small effect size.
For aspirin, this is a pretty convincing argument. For chemo, not so much. The difference, of course, is that an aspirin a day is painless, but chemo is horrible. If this estimate of the medical benefits of chemo for breast cancer is correct, then I really wonder how many women would do it.
The bottom line: For costless and near-costless actions, small beneficial correlations are enough to justify changing your behavior. If you find a lottery ticket for a free lunch, you might as well hang on to it. But you shouldn’t count on finding such lottery tickets with any frequency. In the real world, beneficial changes usually have a steep price, and a lot of “free lunches” are just scams.