Using Cliff's Delta as a Non-Parametric Effect Size Measure: An Accessible Web App and R Tutorial

Effect sizes are important because they are an accessible way to indicate the practical importance of observed associations or differences. Standardized mean difference (SMD) effect sizes, such as Cohen's d, are widely used in education and the social sciences -- in part because they are relatively easy to calculate. However, SMD effect sizes assume normally distributed data, whereas most data in these fields are ordinal and/or non-normal. In these situations, SMD effect sizes can be biased, and a non-parametric measure such as Cliff's [delta] is more appropriate. This paper provides a practical guide on how to calculate Cliff's [delta]. First, we present a conceptual overview and a worked example. Then we present two methods of calculating Cliff's [delta]: (1) a web-based Shiny application developed to accompany this paper (https://cliffdelta.shinyapps.io/calculator; suitable for all users), and (2) an R tutorial (suitable for R users). This is intended to provide researchers and practitioners with an appropriate and accessible effect size measure for non-normal data.