Bounds on the Size of the Likelihood Ratio Test of Independence in a Contingency Table

Bounds are obtained on the limiting size of the nominal level-α likelihood ratio test of independence in a r × c contingency table. The situations considered include sampling with both marginal totals random and with one margin fixed. Upper and lower bounds are obtained. The limiting size is greater than α when some marginal probabilities are small. As the degrees of freedom increase, the limiting size tends to 1 for all α-values.