Aggregating Ratios

face of a prisoner

Sub-population count ratios do not aggregate linearly with sub-population weights. Suppose sub-population 1 has two types with count ratio r1. Suppose that these two types in sub-population 2 have count ratio r2. Suppose the count ratio of the sub-population 1 to sub-population 2 is p. Then simple algebra shows that the type count ratio within the combined population is (p(r1(r2+1)+r2(r1+1))/(p(r2+1)+r1+1)

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