Learning causal graphs via nonlinear sufficient dimension reduction

From Sparse to Dense Functional Data in High Dimensions: Revisiting Phase Transitions from a Non-Asymptotic Perspective

Deep Nonparametric Quantile Regression under Covariate Shift

On the Optimality of Gaussian Kernel Based Nonparametric Tests against Smooth Alternatives

R Handbook: Two-sample Mann–Whitney U Test

Clear examples in R. Two-sample Wilcoxon-Mann–Whitney U Test; Effect size r; Freeman's theta; epsilon-squared; tau-b; Cliff's delta; Vargha-Delaney A; Exercises J

Effect Sizes for ANOVAs

Distribution Learning via Neural Differential Equations: A Nonparametric Statistical Perspective

Effect size measures in a two-independent-samples case with nonnormal and nonhomogeneous data - Behavior Research Methods

In psychological science, the “new statistics” refer to the new statistical practices that focus on effect size (ES) evaluation instead of conventional null-hypothesis significance testing (Cumming, Psychological Science, 25, 7–29, 2014). In a two-independent-samples scenario, Cohen’s (1988) standardized mean difference (d) is the most popular ES, but its accuracy relies on two assumptions: normality and homogeneity of variances. Five other ESs—the unscaled robust d (d r * ; Hogarty & Kromrey, 2001), scaled robust d (d r ; Algina, Keselman, & Penfield, Psychological Methods, 10, 317–328, 2005), point-biserial correlation (r pb ; McGrath & Meyer, Psychological Methods, 11, 386–401, 2006), common-language ES (CL; Cliff, Psychological Bulletin, 114, 494–509, 1993), and nonparametric estimator for CL (A w ; Ruscio, Psychological Methods, 13, 19–30, 2008)—may be robust to violations of these assumptions, but no study has systematically evaluated their performance. Thus, in this simulation study the performance of these six ESs was examined across five factors: data distribution, sample, base rate, variance ratio, and sample size. The results showed that A w and d r were generally robust to these violations, and A w slightly outperformed d r . Implications for the use of A w and d r in real-world research are discussed.