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. 
Kris Duszak and Jan Vrbik
math.ST stat.TH