Skip to main content
Cross Validated

You are not logged in. Your edit will be placed in a queue until it is peer reviewed.

We welcome edits that make the post easier to understand and more valuable for readers. Because community members review edits, please try to make the post substantially better than how you found it, for example, by fixing grammar or adding additional resources and hyperlinks.

Required fields*

10
  • 2
    $\begingroup$ I should explain what a "method for choosing a test" might be - introductory texts often use flowcharts. For unpaired data, maybe: "1. Use some method to check if both samples are normally distributed (if not go to 3), 2. Use some method to check for unequal variances: if so, perform two-sample t-test with Welch's correction, if not, perform without correction. 3. Try transforming data to normality (if works go to 2 else go to 4). 4. Perform U test instead (possibly after checking various assumptions)." But many of these steps seem unsatisfactory for small n, as I hope my Q explains! $\endgroup$ Commented Oct 29, 2014 at 16:01
  • 2
    $\begingroup$ Interesting question (+1) and a brave move to set up a bounty. Looking forward for some interesting answers. By the way, what I often see applied in my field is a permutation test (instead of either t-test or Mann-Whitney-Wilcoxon). I guess it could be considered a worthy contender as well. Apart from that, you never specified what you mean by "small sample size". $\endgroup$ Commented Nov 4, 2014 at 1:09
  • 3
    $\begingroup$ It is not clear to me why one would assert that nonparametric tests (rank sum or sign rank) would require symmetry? $\endgroup$ Commented Nov 5, 2014 at 22:36
  • 4
    $\begingroup$ @Silverfish " if the results are seen as a statement about location" That is an important caveat, as these tests are most generally statements about evidence for H$_{0}: P(X_{A} > X_{B}) =0.5$. Making additional distributional assumptions narrows the scope of inference (e.g. tests for median difference), but are not generally requisites for the tests. $\endgroup$ Commented Nov 6, 2014 at 3:09
  • 2
    $\begingroup$ It might be worth exploring just how "flawed" the "95% power for the Wilcoxon" reasoning is for small samples (in part it depends on what, exactly, one does, and how small is small). If for example, you're happy to conduct tests at say 5.5% instead of 5%, should that be the nearest suitable achievable significance level, the power often tends to hold up fairly well. Once can of course - at the "power calculation" stage before you collect data - figure out what the circumstances may be and get a sense of what the properties of the Wilcoxon are at the sample sizes you're considering. $\endgroup$ Commented Oct 22, 2015 at 22:07