Statistical findings on subgroups belong to the most popular and simple forms of knowledge we encounter in all domains of science, business, or even daily life. We are told such messages as: Unemployment rate is overproportionally high for young men with low educational level, young poor women are infected with AIDS at a much higher rate than their male counterparts, lung cancer mortality rate ...

If N is a nontrivial proper normal subgroup of a finite group G then N and G/N are smaller than G. While it is false that G can be completely reconstructed from knowledge of N and G/N (see Example 1.1 below), it is nevertheless a standard technique in finite group theory to prove theorems about finite groups by induction on the size of the group and thereby use information about the smaller gro...

In the analysis of randomized controlled trials (RCTs), treatment effect heterogeneity often occurs, implying differences across (subgroups of) clients in treatment efficacy. This phenomenon is typically referred to as treatment-subgroup interactions. The identification of subgroups of clients, defined in terms of pretreatment characteristics that are involved in a treatment-subgroup interactio...