Nonparametric Statistics with Applications to Science and Engineering with R, 2nd Edition

6Goodness of Fit

Believe nothing just because a so‐called wise person said it.

Believe nothing just because a belief is generally held.

Believe nothing just because it is said in ancient books.

Believe nothing just because it is said to be of divine origin.

Believe nothing just because someone else believes it.

Believe only what you yourself test and judge to be true.

paraphrased from the Buddha

Modern experiments are plagued by well‐meaning assumptions postulating that the data are distributed according to some “textbook” cumulative distribution function (CDF). This chapter introduces methods to test the merits of a hypothesized distribution in fitting the data. The term goodness of fit was coined by Pearson in 1902 and refers to statistical tests that check the quality of a model or a distribution's fit to a set of data. The first measure of goodness of fit for general distributions was derived by Kolmogorov (1933). Andrei Nikolaevich Kolmogorov (1905–1987), perhaps the most accomplished and celebrated Soviet mathematician of all time, made fundamental contributions to probability theory, including test statistics for distribution functions – some of which bear his name. Nikolai Vasil'yevich Smirnov (1900–1966), another Soviet mathematician, extended Kolmogorov's results to two samples.

In this section we emphasize objective tests (with ‐values) and later analyze graphical ...