Plotting the cumulative deviation of a subgroup from the full population as a function of score
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Assessing whether a subgroup of a full population is getting treated equitably often involves assigning numerical "scores" to all individuals such that similar individuals get similar scores; matching via propensity scores is common, for example. Given such scores, equitable treatment could mean that individuals with similar scores attain similar outcomes independent of the individuals' memberships in the subgroup. The traditional graphical methods for visualizing inequities are known as "reliability diagrams" or "calibration plots," which bin the scores into a partition of all possible values, and for each bin plot both the average outcomes for only individuals in the subgroup as well as the average outcomes for all individuals in the full population; comparing the graph for the subgroup with that for the full population gives some sense of how the averages for the subgroup deviate from the averages for the full population. Unfortunately, real data sets contain only finitely many observations, limiting the usable resolution of the bins, and so the conventional methods can obscure important variations due to the choice of bins. Fortunately, plotting cumulative deviation of the subgroup from the full population sidesteps the problematic binning. The cumulative plots encode subgroup deviation directly as the slopes of secant lines for the graphs. Slope is easy to perceive even when the constant offsets of the secant lines are irrelevant. The cumulative approach avoids binning that smooths over deviations of the subgroup from the full population.
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