Probability in combined population can favor one solution, even if probability in separate populations favors another solution {Simpson's paradox} {Simpson paradox}. For example, for population A, solution 1 has probability 2/3 with N = 3, and solution 2 has probability 1/2 with N = 2. For population B, solution 1 has probability 3/4 with N = 4, and solution 2 has probability 5/7 with N = 7. For combined population, solution 1 has probability 5/7 with N = 7, and solution 2 has probability 6/9 with N = 9. Average of population averages is not necessarily combined population average, because some populations have more weight.
mediant fraction
Simpson's paradox follows from mediant fraction properties.
change
If probability of two outcomes varies in one population or set and does not vary in another set, expected outcome can reverse.
Mathematical Sciences>Logic>Paradox
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Date Modified: 2022.0224