A Comparison of the Pearson Chi-Square and Kolmogorov Goodness-of-Fit Tests with Respect to Validity

This paper compares the Pearson Chi-Square and Kolmogorov good-ness-of-fit tests with respect to validity under the following conditions: (1) the N independent observations are tabulated and arranged into k mutually exclusive groups that are equally probable under the hypothesis to be tested; and (2) both N and k are “small”; i.e., not greater than 50. A random sampling experiment was performed, and the results show that in general for the conditions considered, the Pearson test is more valid than the Kolmogorov test.