Short-Cut Formulas for the Exact Partition of χ 2 in Contingency Tables

Recently, Lancaster (1949, 1950) and Irwin (1949) showed how x2 may be partitioned exactly into single degrees of freedom when expected frequencies are estimated from the data. In particular they considered the case of an r X s (r rows, s columns) contingency table in which the expected frequencies are computed from the marginal totals. Their work suggests several different methods of carrying out the necessary computations, some of which they...