Collapsibility
Sander Greenland · Wiley StatsRef: Statistics Reference Online · 2014
Abstract Consider theI × J × Kcontingency table representing the joint distribution of three discrete variables,X,Y, andZ, theI × Jmarginal table representing the joint distribution ofXandY, and the set of conditionalI × Jsubtables (strata) representing the joint distributions ofXandYwithin levels ofZ. A measure of association ofXandYis said to bestrictly collapsibleacross Z if it is constant across the conditional subtablesandthis constant value equals the value obtained from the marginal table. Noncollapsibility (violation of collapsibility) is sometimes referred to as Simpson's paradox after a celebrated article by Simpson, but the same phenomenon had been discussed by earlier authors, including Yule. The termcollapsibility, however, seems to have arisen later in the work of Bishop and colleagues.