
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.
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Doi:
10.20982/tqmp.16.4.p281
Fitts, Douglas A.
281294
Keywords:
noncentral t distributions
, parameter estimation
, simulation
Tools: R, C
(no sample data)
(Appendix)
In their review of effect sizes of the Cohen's d family, GouletPelletier 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 \nu = 2(n  1) instead of \nu = (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 \nu for a pooled paired samples design vary as a function of the population correlation \rho between 2(n  1) at \rho = .0 and (n  1) at \rho = 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 \rho causes a further deviation from the presumed noncentral t distribution even when the \nu 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 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.
