On the importance of tail ratios for psychological science

Even small group-mean differences (whether combined with variance differences or not) or variance differences alone (absent mean differences) can generate marked and sometimes surprising imbalances in the representation of the respective groups compared in the distributional tail regions. Such imbalances in group representation, quantified as tail ratios, have general importance in the context of any threshold, susceptibility, diathesis-stress, selection, or similar models (including the study of sex differences), as widely conceptualized and applied in the psychological, social, medical, and biological sciences. However, commonly used effect-size measures, such as Cohen's d, largely exploit data information around the center of distributions, rather than from the tails, thereby missing potentially important patterns found in the tail regions. This account reviews the background and history of tail ratios, emphasizes their importance for psychological research, proposes a consensus approach for defining and interpreting them, introduces a tail-ratio calculator, and outlines future research agenda.