Goodness-of-Fit Tests

Abstract

Goodness-of-fit techniques are essential for determining whether hypothetical models fit observed data. When at all reasonable, exact tests are preferred to either nonasymptotic or, especially, asymptotic tests. In addition, the structures of these tests yield entirely different detection capabilities for varying alternatives. A selection of techniques is considered for both discrete and continuous data, along with examples and simulations intended to emphasize the differences in detection capabilities. The discrete data tests are further partitioned into exact tests (including Fisher’s exact test) and approximate tests (including those based on the Pearson (1900) X2 and Zelterman (1987) statistics) . Specific concerns regarding these discrete data tests are described. Continuous data tests due to Greenwood—Moran (Greenwood, 1946; Moran, 1947), Kendall—Sherman (Kendall, 1946; Sherman, 1950), Kolmogorov (1933), Smirnov (1939a), and Fisher (1929) are included. Simulated comparisons of the Kendall—Sherman and Kolmogorov tests are given.