Precision and power in the analysis of social structure using associations

I develop guidelines for assessing the precision and power of statistical techniques that are frequently used to study nonhuman social systems using observed dyadic associations. Association indexes estimate the proportion of time that two individuals are associated. Binomial approximation and nonparametric bootstrap methods produce similar estimates of the precision of association indexes. For a mid-range (0.4-0.9) association index to have a standard error of less than 0.1 requires about 15 observations of the pair associated, and for it to be less than 0.05, this rises to 50 observations. The coefficient of variation among dyads of the proportion of time that pairs of individuals are actually associated describes social differentiation (S), and this may be estimated from association data using maximum likelihood. With a poorly differentiated population (S ∼ 0.2), a data set needs about five observed associations per dyad to achieve a correlation between true and estimated association indexes of r = ∼0.4. It requires about 10 times as much data to achieve a representation with r = ∼0.8. Permutation tests usually reject the null hypothesis that individuals have no preferred associates when S² × H > 5, where H is the mean number of observed associations per individual. Thus most situations require substantial numbers of observations of associations to give useful portrayals of social systems, and sparse association data inform only when social differentiation is high.