  When comparing two independent groups, shift functions are basically
techniques that compare multiple quantiles rather than a single measure of
location, the goal being to get a more detailed understanding of how the
distributions differ. Various versions have been proposed and studied. This
paper deals with extensions of these methods to main effects and interactions
in a between-by-between, 2-by-2 design. Two approaches are studied, one that
compares the deciles of the distributions, and one that has a certain
connection to the Wilcoxon-Mann-Whitney method. For both methods, we propose an
implementation using the Harrell-Davis quantile estimator, used in conjunction
with a percentile bootstrap approach. We report results of simulations of false
and true positive rates.
