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Which nonparametric or parametric test should I use?

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Choosing between the sign test, 1-Sample Wilcoxon test, and 1-sample t-test

  • If the distribution is not severely skewed and the sample size is greater than 20, use the 1-sample t-test.
  • If the distribution is approximately symmetric and you have a relatively small sample, use the 1-Sample Wilcoxon test.
  • If you are sampling from a non-symmetric population and you have a small sample, use the sign test.

Choosing between the Mood's median/Kruskal-Wallis test and the one-way ANOVA

Suppose you want to use a hypothesis test to compare medians of two or more populations whose distributions have the same shape and equal variance.
  • If the populations being sampled are normally distributed or each sample is greater than 20, use the one-way ANOVA.
  • If the populations being sampled are severely skewed and you have small samples, use the Mood's median or the Kruskal-Wallis test.

(Normal populations are symmetric; thus, a test for equality of medians is also a test for equality of means.)

Choosing between the two-sample Mann-Whitney test and the pooled t-test

  • If your samples have similar sample sizes or you have some evidence the population have approximately the same variances then use a pooled t-test. In cases where the normality assumption may not be valid you can still use the pooled t-test if your samples are large enough.
  • If you are sampling from nonnormal populations with the same shape and spread and your samples are relatively small, use the Mann-Whitney test.
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