Heterogeneity among chromosomes was found to be a highly significant source of variation for association proportions, while culture, slide, and observer were negligible sources of variation for association proportions although important for numbers of associations. The consequences of these results for tests of group differences are discussed. It seems evident that each pair of acrocentric chromosomes has its own characteristic probability of entering into association. This is presumably a combination of the probability for each individual member of the pair, a proposition easily tested utilizing acrocentric chromosomes carrying polymorphisms which allow each member of the pair to be individually recognized. A mathematical theory for pairwise satellite association was developed and shown to fit observations on banded chromosomes. While we found very significant heterogeneity among individuals in the frequency with which different chromosomes entered into associations, there was no significant evidence for preferential association between any particular chromosomes, either heterologous or homologous. This finding in our material of apparently random associations between different chromosomes is contrary to claims made by other investigators and should be tested on other material. No correlation was found between the phenotype of the chromosome, as judged by cytogenetic polymorphisms, and its probability of association.