Calculating components of the coefficient of relationship.
The coefficient of relationship by isonymy is Ri=sigma(n(n-1)/2(N(N-1)) in which n is the number of persons of each surname and N=sigma n. Dividing Ri into two components, one for the contribution of co-residence (family size) and the other for diversity of surnames among residences is achieved by letting a1 represent sigma n(n-1) for all residents, a2 represent sigma n(n-1) after eliminating all but one individual of any name at any residence, and b1 represent 2N(N-1) for all residents. Then the component for inter-residence diversity is a2/b1 and the component for relationship by co-residence (including the interaction) is (a1-a2)/b1. By the same logic it is possible to calculate separately the interaction component, but the additional information seems of limited importance.
Lasker
G W
GW
Wayne State University, Detroit, Michigan 48202, USA.
D005195:Family Relations; D005260:Female; D006801:Humans; D008297:Male; D008432:Mathematical Computing