Cliff´s Delta Calculator: A non-parametric effect size program for two groups of observations

Abstract

The Cliff´s Delta statistic is an effect size measure that quantifies the amount of difference between two non-parametric variables beyond p-values interpretation. This measure can be understood as a useful complementary analysis for the corresponding hypothesis testing. During the last two decades the use of effect size measures has been strongly encouraged by methodologists and leading institutions of behavioral sciences. The aim of this contribution is to introduce the Cliff´s Delta Calculator software that performs such analysis and offers some interpretation tips. Differences and similarities with the parametric case are analysed and illustrated. The implementation of this free program is fully described and compared with other calculators. Alternative algorithmic approaches are mathematically analysed and a basic linear algebra proof of its equivalence is formally presented. Two worked examples in cognitive psychology are commented. A visual interpretation of Cliff´s Delta is suggested. Availability, installation and applications of the program are presented and discussed.

Short-Term Effects of Mulligan Mobilization With Movement on Pain, Disability, and Kinematic Spinal Movements in Patients With Nonspecific Low Back Pain: A Randomized Placebo-Controlled Trial

“…The clinical ES for between-group analysis was evaluated with a nonparametric ES, Cliff δ. 24 This score can range from − 1 to 1; where 1 indicates that all observations from the sham-SNAG group are greater than all observations from the real-SNAG group. Conversely, − 1 indicates that all observations from the sham-SNAG group are less than all observations from the real-SNAG group.…”

“…Finally, 0 indicates perfect overlap, with equality of observations between the groups. 24 Cliff δ is calculated with R software and is presented with a confidence interval (CI) of 95% and categorized in small, moderate, large, and very large ES. 24 We also ran an exploratory analysis for the secondary within-group hypothesis (between baseline and final evaluation) in the sham and real-SNAG group following the same statistical method described above but with a Wilcoxon signed rank test.…”

Triglycerides and glucose index: A useful indicator of insulin resistance

“…To compare mean values of parametric variables, a Student's t test, an ANOVA test, and Cohen's ''d'' to assess effect size 25 were used. Medians of nonparametric variables were compared using a Mann---Whitney test and Cliff's delta 26 to assess effect size. Correlation between the TyG index and the TG/HDL-C ratio was calculated using Spearman's rho.…”

Mobility, proprioception, strength and FMS as predictors of injury in professional footballers

“…Cliff's d has a possible range from −1 to +1; values of ±1 indicate absence of overlap between groups whereas a value of 0 means the groups overlap completely. Values close to ±1 tend to occur when p<0.05 is observed 32. Effect size estimates are useful when the scale of measurement (and hence the size of difference between groups) is not easily understood.…”