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In two-way contingency tables we sometimes find that frequencies along thediagonal cells are relatively larger(or smaller) compared to off-diagonalcells, particularly in square tables with the common categories for the rowsand the columns. In this case the quasi-independence model with an additionalparameter for each of the diagonal cells is usually fitted to the data. Asimpler model than the quasi-independence model is to assume a commonadditional parameter for all the diagonal cells. We consider testing thegoodness of fit of the common diagonal effect by Markov chain Monte Carlo(MCMC) method. We derive an explicit form of a Markov basis for performing theconditional test of the common diagonal effect. Once a Markov basis is given,MCMC procedure can be easily implemented by techniques of algebraic statistics.We illustrate the procedure with some real data sets.

A Markov Basis for Conditional Test of Common Diagonal Effect in Quasi-Independence Model for Square Contingency Tables