A Test of Significance for the Homophily Index

A technique for directly determining the statistical significance of the homophily index has been developed in the process of evaluating data on friendship choices among student dentists.2 The technique is simple and yields reasonably accurate estimates of significance, even for as few as ten choices per attribute. As described by James Coleman,3 the computation of the index of homophily demands that the data on the round of choices within a given sample be conceived of as arranged in a 2 X 2 table. This is illustrated in Figure 1. The cells record the number of choices given by possessors of a particular attribute to those who share and those who do not share this attribute. For example, if a chooser with characteristic C1 selects an individual with characteristic C2, this is recorded as a component of X3. The index comprises a means of measuring the extent to which choosers with one attribute tend to overchoose or underchoose individuals with the same attribute as compared to their choices of individuals with the alternate attribute. Note that ml is the total number of choices made by individuals in the sample who have characteristic C1, and not the number of individuals with such characteristics. The numbers of individuals are given as n1 and n2 for those who have C1 type and C2 type characteristics, respectively; thus ni + n2= N, the sample size. A separate index is computed for two types of choice situations: where choosers overchoose their attribute similars and where choosers underchoose attribute similars. These two situations are defined by