On collapsibilities of Yule’s measure

Simpson’s paradox reminds people that the statistical inference in a low-dimensional space probably distorts the reality in a high one seriously.To study the paradox with respect to Yule’s measure, this paper discusses simple collapsibility, strong collapsibility and consecutive collapsibility, and presents necessary and sufficient conditions of them.In fact, these conditions are of great importance for observational and experimental designs, eliminating confounding bias, categorizing discrete variables and so on.