An Application of the Kolmogorov-Smirnov Test for Normality with Estimated Mean and Variance

Psychologists often have occasion to test whether their obtained data could reasonably have been drawn from a normal population. In his important paper, Massey (1951) hinted that potentially, the Kolmogorov-Smirnov test might be useful in this regard though he cautioned that the distribution of the relevant statistic (D) was unknown when the mean and variance of the population were unknown and had to be estimated from the sample. Preliminary data reported by Massey implied (Rosenthal, 1967, p. 519) that in testing for normality, Ds only .7 as large as those tabulated (by Massey, Table 1; Siegel, 1956, Table E)