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The Kolmogorov-Smirnov Test: Which Tables Should Be Used?

1968; SAGE Publishing; Volume: 23; Issue: 2 Linguagem: Inglês

10.2466/pr0.1968.23.2.466

1558-691X

Gordon M. Harrington,

Advanced Statistical Methods and Models

Massey (1951) provided tables the Kolmogorov-Smirnov test of goodness of fir any specified function. He pointed out that more conservative values would be required cases where the population was derived from sample values. Lilliefors (1967) provided the corrections tests of normality with a population of unknown mean and variance. Rosenthal (1968) pointed out the usefulness of these corrections and suggested, as an example, that on reevaluation of Harrington's (1967) report of p > .20, it should more appropriately be reported as p .10 and specifically pointed out the basis use of the Massey tables in preference to a correction such as that of Lilliefors. The note emphasized a fundamental point in choice of critical values this statistic which is reiterated here as a caution to others. Rosenthal suggests failure to employ the critical values of D tabulated by Lilliefors can lead to serious errors of inference. On the contrary, there is a choice between the two cables depending on the hypothesis tested, and errors of inference atttach to the inappropriate choice. The Massey tables test against a completely specified distribution. The Harrington note followed the latter approach and concluded for any specified normal distribution consistent with previous E-bias studies . . . D .lo). Thar is, if the E-bias effect exists, then one can accept these data as a sample from a normal population. Using the Lilliefors tables, as Rosenthal suggests, poses the question of the probability of drawing these sample values from some totally unknown normal distribution. If the target population is unknown, that is if there is no basis an hypothesis of E bias, this test is most appropriate, and one might do well to question the normality of the sample. In short, if one assumes the validity of reports of E bias, the Massey tables should be used. If one rejects the validity of these studies, Rosenthal's usage is appropriate.