Improving Accuracy of Goodness-of-fit Test

It is well known that the approximate distribution of the usual test statistic of a goodness-of-fit test is chi-square, with degrees of freedom equal to the number of categories minus 1 (assuming that no parameters are to be estimated – something we do throughout this article). Here we show how to improve this approximation by including two correction terms, each of them inversely proportional to the total number of observations.