Simpson's Paradox

A common example of Simpson's Paradox involves the batting averages of players in professional baseball. It is possible for one player to hit for a higher batting average than another player during a given year, and to do so again during the next year, but to have a lower batting average when the two years are combined. This phenomenon can occur when there are large differences in the number of at-bats between the years. (The same situation applies to calculating batting averages for the first half of the baseball season, and during the second half, and then combining all of the data for the season's batting average.)

A real-life example is provided by Ken Ross and involves the batting average of two baseball players, Derek Jeter and David Justice, during the baseball years 1995 and 1996:

Simpson's Paradox