ON A SHARED ALLELE TEST OF RANDOM MATING

Summary A simple random sample is observed from a population with a large number‘ K ’ of alleles, to test for random mating. Of n couples, n ijkl have female genotype ij and male genotype kl (i, j, k, l {1,…, A‘}). The large contingency table is collapsed into three counts, n 0 , n 1 and n 2 where n p is the number of couples with s alleles in common (s = 0,1, 2). The counts are estimated by np̂ o where n 0 , is the estimated probability of a couple having s alleles in common under the hypothesis of random mating. The usual chi‐square goodness of fit statistic X 2 compares observed (n s ) with expected (np̂) over the three categories, s = 0,1,2. An empirical observation has suggested that X 2 is close to having a chi‐square distribution with two degrees of freedom (X) despite a large number of parameters implicitly estimated in e . This paper gives two theorems which show that x is indeed the approximate distribution of X 2 for large n and K 1 “, provided that no allele type over‐dominates the others.