Goodness-of-fit tests

hlee — Tue, 06 Oct 2009 18:49:39 +0000

When it comes to applying statistics for measuring goodness-of-fit, the Pearson χ² test is the dominant player in a race and the Kolmogorov-Smirnoff test statistic trails far behind. Although it seems almost invisible in this race, there are more various non-parametric statistics for testing goodness-of-fit and for comparing the sampling distribution to a reference distribution as legitimate race participants trained by many statisticians. Listing their names probably useful to some astronomers when they find the underlying assumptions for the χ² test do not match the data. Perhaps, some astronomers want to try other nonparametric test statistics other than the K-S test. I’ve seen other test statistics in astronomical journals from time to time. Depending on data and statistical properties, one test statistic could work better than the other; therefore, it’s worthwhile to keep the variety in one’s mind that there are other tests beyond the χ² test goodness-of-fit test statistic.

This is the list I can think of at the moment and each test is linked to wikipedia for more stories.

Wilkoxson Rank Sum test (also called the Mann–Whitney U, Mann–Whitney–Wilcoxon (MWW), or Wilcoxon–Mann–Whitney test)
Wilcoxon signed-rank test
Anderson-Darling test
Cramer- von Mises test
Shapiro-Wilks test
Siegel-Tukey test

Before my updates, I welcome your comments that can grow this list. Also, I’d appreciate if your comment includes an explanation when the nonparametric test of your recommendation works better and a little description of your data characteristics. And don’t forget to get the qq-plot prior to discussing implications of p-values from these test statistics.

The AstroStat Slog » tests

Goodness-of-fit tests