THE GENERALIZED CHI(2) GOODNESS-OF-FIT TEST

Because the power of the chi2 goodness-of-fit test depends on sample size, small and unimportant departures from a specified theoretical distribution may be detected with large samples. To adjust for data with extremely large sample sizes, a generalization of the chi2-test was developed that tests for the equality of an observed and fitted distribution to within a specified amount. Procedures for estimating the true amount of lack of fit between two distributions and for a calculation of the power of the generalized chi2-test under specified alternatives were devised. These techniques were applied to the analysis of red blood cell volume distributions in healthy individuals and patients with anaemia. To be consistent with the physiology of red blood cell production, the explicit models examined were a single log-normal distribution and a mixture of two log-normal distributions.