Effects May Both Increase or Decrease in the Long Term: A Statistical Illustration

Abstract

It has been argued that small effect sizes observed at a single instance should not be dismissed because they can often accumulate in the long term. This follows a classic argument by Abelson (1985). However, it has also been argued that such long-term accumulation is entirely speculative and need not happen. Using a simple statistical illustration, we show how restrictive Abelson’s assumptions are and argue that they are unlikely to be met in psychological research. This demonstrates that the Abelson example is unrealistically biased toward the accumulation of effect sizes; even small deviations can have large consequences for the long-term effect sizes. This is true even if no long-term counteracting mechanisms, such as habituation, are at play. Further, it is shown how long-term effect sizes may be smaller than those observed at a single time point. If the theoretical value of an effect lies in the long term, it should be examined in that long term, and not merely be the subject of speculation in the short term.