esvis - Visualization and Estimation of Effect Sizes
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.
