MONOTONE BOUNDS ON THE CHI-SQUARED APPROXIMATION TO THE DISTRIBUTION OF PEARSON'S XSTATISTICS12

Monotone bounds, depending on the underlying multinomial probabilities and the sample size, are given for the chi-squared approximation to the distribution of Pearson's statistic for goodness of fit for simple hypotheses. These bounds apply to the distribution of a single statistic and to the joint distribution of two statistics associated with the margins of a two-way table, in both the central and non-central cases.