On collapsibilities of Yule's measure

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