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Sample size for nonparametric tests

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The problem of choosing sample size for data to be analyzed by nonparametric tests

Nonparametric tests are used when you are not willing to assume that your data come from a Gaussian distribution. Commonly used nonparametric tests are based on ranking values from low to high, and then looking at the distribution of sum-of-ranks between groups. This is the basis of the Wilcoxon rank-sum (test one group against a hypothetical median), Mann-Whitney (compare two unpaired groups), Wilcoxon matched pairs (compare two matched groups), Kruskal-Wallis (three or more unpaired groups) and Friedman (three or more matched groups).

When calculating a nonparametric test, you don't have to make any assumption about the distribution of the values. That is why it is called nonparametric. But if you want to calculate necessary sample size for a study to be analyzed by a nonparametric test, you must make an assumption about the distribution of the values. It is not enough to say the distribution is not Gaussian, you have to say what kind of distribution it is. If you are willing to make such an assumption (say, assume an exponential distribution of values, or a uniform distribution) you should consult an advanced text or use a more advanced program to compute sample size.

A useful rule-of-thumb

Most people choose a nonparametric test when they don't know the shape of the underlying distribution. Without making an explicit assumption about the distribution, detailed sample size calculations are impossible. Yikes!

But all is not lost! Depending on the nature of the distribution, the nonparametric tests might require either more or fewer subjects. But they never require more than 15% additional subjects if the following two assumptions are true:

You are looking at reasonably high numbers of subjects (how high depends on the nature of the distribution and test, but figure at least a few dozen)

The distribution of values is not really unusual (doesn't have infinite tails, in which case its standard deviation would be infinitely large).

So a general rule of thumb is this (1):

 If you plan to use a nonparametric test, compute the sample size required for a parametric test and add 15%.


Erich L. Lehmann, Nonparametrics : Statistical Methods Based on Ranks, Revised, 1998, ISBN=978-0139977350, pages 76-81.

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