Minimal effect sizes do not imply minimal effects for differences in long-tailed distributions

ABSTRACT

Long-tailed distributions can distort findings, influence statistical tests, and result in small effect sizes. This research note proposed a definition of long-tailed distributions (i.e., SD/M ≥ 1) and developed an alternative formulation of the Cohen’s d effect size based on percent differences. Three hypotheses were examined: (a) waterfowl hunter harvest distributions tend to be long-tailed distributions, (b) differences in the means of two long-tailed distributions have minimal (d < .2) effect sizes unless the percent difference exceeds 20%, and (c) a minimal effect size does not necessarily imply that the difference in means should be ignored. Data obtained from 29 (1990–2018) annual waterfowl surveys in Illinois (n = 45,978) supported all three hypotheses. Statistical and managerial implications are discussed.

KEYWORDS:

• Long-tailed distributions
• effect size
• Cohen’s d
• duck harvest distributions