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In their review of effect sizes of the Cohen’s d family, Goulet-Pelletier and Cousineau (2018) proposed several methods for generating confidence intervals for the unbiased standardized mean difference, g. Among them they proposed using degrees of freedom ν = 2(n − 1) instead of ν = (n − 1) for all paired samples designs that use a pooled standard deviation to standardize the mean difference (pooled paired samples) when calculating g and its confidence limits from a noncentral t distribution. Simulations demonstrate that the exact ν for a pooled paired samples design vary as a function of the population correlation ρ between 2(n − 1) at ρ = .0 and (n − 1) at ρ = 1.0. This affects the calculation of g and the selection of the appropriate noncentral t distribution for calculating the confidence limits. Using a sample r to estimate the unknown ρ causes a further deviation from the presumed noncentral t distribution evenwhen the ν are known. These facts adversely affect the coverage of the confidence intervals computed as recommended by the authors. These methods for calculating noncentral t confidence intervals should not be used as described with pooled paired samples designs. Noncentral t confidence intervals for either a two sample design or a paired samples design where the mean difference is standardized by the standard deviation of the difference scores are unaffected by this problem. An R script and C source code are provided.

the quantitative methods for psychology

Commentary on "A review of effect sizes and their confidence intervals, Part I: The Cohen's d family": The degrees of freedom for paired samples designs.