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A variety of methods are provided to estimate and visualize
distributional differences in terms of effect sizes. Particular emphasis
is upon evaluating differences between two or more distributions across
the entire scale, rather than at a single point (e.g., differences in
means). For example, Probability-Probability (PP) plots display the
difference between two or more distributions, matched by their empirical
CDFs (see Ho and Reardon, 2012; <doi:10.3102/1076998611411918>), allowing
for examinations of where on the scale distributional differences are
largest or smallest. The area under the PP curve (AUC) is an effect-size
metric, corresponding to the probability that a randomly selected
observation from the x-axis distribution will have a higher value
than a randomly selected observation from the y-axis distribution.
Binned effect size plots are also available, in which the distributions
are split into bins (set by the user) and separate effect sizes (Cohen's
d) are produced for each bin - again providing a means to evaluate the
consistency (or lack thereof) of the difference between two or more
distributions at different points on the scale. Evaluation of empirical
CDFs is also provided, with  built-in arguments for providing annotations
to help evaluate distributional differences at specific points (e.g.,
semi-transparent shading). All function take a consistent argument
structure. Calculation of specific effect sizes is also possible. The
following effect sizes are estimable: (a) Cohen's d, (b) Hedges' g,
(c) percentage above a cut, (d) transformed (normalized) percentage above
a cut, (e)  area under the PP curve, and (f) the V statistic (see Ho,
2009; <doi:10.3102/1076998609332755>), which essentially transforms the
area under the curve to standard deviation units. By default, effect sizes
are calculated for all possible pairwise comparisons, but a reference
group (distribution) can be specified.

Daniel Anderson

psd: Pooled Standard Deviation

Description

Usage

Arguments