X²and its components as tests of normality for grouped data

Abstract

We consider testing for an unobservable normal distribution with unspecified mean and variance. It is only possible to observe the counts in groups with boundaries specified before sighting the data. On the basis of a small power study we recommend the usual X 2 test be used as an omnibus test, augmented by informal examination of the first two non-zero component of X 2 . We also recommend use of maximum likelihood and method of moments estimation.