Chi-Squared Goodness-of-Fit Tests: Cell Selection and Power

Abstract

To use the Pearson chi-squared statistic to test the fit of a continuous distribution, it is necessary to partition the support of the distribution into k cells. A common practice is to partition the support into cells with equal probabilities. In that case, the power of the chi-squared test may vary substantially with the value of k. The effects of different values of k are investigated with a Monte Carlo power study of goodness-of-fit tests for distributions where location and scale parameters are estimated from the observed data. Allowing for the best choices of k, the Pearson and log-likelihood ratio chi-squared tests are shown to have similar maximum power for wide ranges of alternatives, but this can be substantially less than the power of other well-known goodness-of-fit tests.

Keywords:

• Pearson chi-squared statistic
• log-likelihood ratio chi—squared statistic
• small sample power
• EDF tests
• Shapiro—Wilk test
• rectangle test