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Abstract:
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Consider partitioning a data set into n mutually exclusive segments, and within each segment computing a pair of subtotals. One can form n within-segment ratios, and one can also sum over all segments to form the global ratio. Our particular interest is the case where we compare two groups, e.g. an experiment versus its control group or the current time point versus some time in the past. Any overall change might be the result from changes within segment, from shifts in the relative sizes among the segments (shifts in "mix"), or some combination of the above. To distinguish between such metric and mix changes, we present two closely related decompositions, one on an additive scale, the other using percent relative change, and their associated plots. The approach draws from econometric price index theory and throws new light on Simpson's paradox.
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