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To illustrate this idea, suppose that in the birth control pills example (2.5.2) the original population T includes both genders. Then P(Pregnancy|T.Male.Takes birth control pills) = P(Pregnancy|T.Male) = 0, while P(Pregnancy|T.Female. Takes birth control Equation editor pills) ≠ P(Pregnancy|T.Female) assuming that not all women in the population take birth control pills. In other words, if you are a male in this population, taking birth control pills is statistically irrelevant to whether you become pregnant, while if you are a female it is relevant. In this way we can capture the idea that taking birth control pills is explanatorily irrelevant to pregnancy among males but not among females.
To characterize the SR model Scientific software more precisely we need the notion of a homogenous partition. A homogenous partition of A is a set of subclasses or cells Ci of A that are mutually exclusive and exhaustive, where P(B|A.Ci) ≠ P(B|A.Cj) for all Ci ≠ Cj and where no further statistically relevant partition of any of the cells A, Ci can be made with respect to B - that is, there are no additional attributes Dk in A such that P(B|A.Ci) ≠ P(B|A.Ci.Dk).