Simpson's Paradox and the Hot Hand in Basketball

Abstract

A number of psychologists and statisticians are interested in how laypersons make judgments in the face of uncertainties, assess the likelihood of coincidences, and draw conclusions from observation. This is an important and exciting area that has produced a number of interesting articles. This article uses an extended example to demonstrate that researchers need to use care when examining what laypersons believe. In particular, it is argued that the data available to laypersons may be very different from the data available to professional researchers. In addition, laypersons unfamiliar with a counterintuitive result, such as Simpson's paradox, may give the wrong interpretation to the pattern in their data. This paper gives two recommendations to researchers and teachers. First, take care to consider what data are available to laypersons. Second, it is important to make the public aware of Simpson's paradox and other counterintuitive results.

Key Words:

• Hot hand phenomenon
• McNemar's test
• Multiple analyses
• Simpson's paradox