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.
Year: 2020
Type: editorial
Abstract: 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 = .0and (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 even when 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.
Author: Douglas A. Fitts
Institution: University of Washington
Language: English
Subfield: Statistics, Probability and Uncertainty
Field: Decision Sciences
Domain: Social Sciences
Open Access status: diamond
OpenAlex ID: W4254475121