Discussion
Which one of the following non-parametric test is analogous to the chi-square test of goodness of fit ?
Answer: B
The non-parametric analogue of the chi-square goodness-of-fit test is the Kolmogorov-Smirnov test.
Both test whether a sample comes from a specified distribution. The one-sample Kolmogorov-Smirnov statistic is the largest gap between the empirical distribution function and the hypothesised distribution function, \(D_{n} = \sup_{x} |F_{n}(x) - F_{0}(x)|\), and it works with ungrouped data.
The Mann-Whitney and median tests compare two samples' locations, and the Wilcoxon (signed-rank) test is about a location or paired difference; none of them tests goodness of fit to a given distribution.
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