THE MEAN AND VARIANCE OF χ2, WHEN USED AS A TEST OF HOMOGENEITY, WHEN EXPECTATIONS ARE SMALL

=N(E i) N. ij (8s tj) Fisher (1922) showed that when every si and tj was sufficiently large, x2 has the usual distribution, with (m 1) (n 1) degrees of freedom. Thus its mean is (mr-1) (n-I ), its variance 2(m1) (n-1). Haldane (1937, 1938, 1939) investigated the exact values of the moments of x2 when expectations are small, in (m x n)-fold tables with men or m(n 1) degrees of freedom, but did not attempt the present problem. This had previously been done by Cochran (1936), in the