Exact Simultaneous Comparisons with Control in an r × c Contingency Table

Let categorical data coming from a control group and ( r ‐ 1) treated groups be given in an r × c contingency table. A simultaneous test procedure of the ( r ‐ 1) hypotheses that the probabilities of all c categories do not differ between the i ‐th treated group and the control is derived. For small tables and small cell frequencies it is exactly performed by generation of all tables having the given marginal sums. If 2 categories or 2 groups only are given the asymptotic distribution of the test statistic is known; otherwise its distribution may be simulated if the computational expenditure of performing an exact test is too large. By means of a Monte Carlo study it is shown that this method meets its level more reliably and that it has a better power than others.