I have one group of six raters who scored recordings of two separate six-person groups of participants, each group under separate conditions. While the participants were divided into two independent groups, the ordinal data came from the same group of raters. Due to the small sample size (i.e. 12 ordinal scores to compare both participants), which test could I run. I've read that I'd need at least 20 scores to run a Wilcoxon... Thank you for your time and consideration in answering this question!
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It is not true that 20 scores are necessary for a Wilcoxon signed rank test. Significance by conventional standards is even achievable given your sample size. Consider a simple example in r:
Given x=1:6;y=2:7, wilcox.test(y,x,paired=T) results in V = 21, p = .02. Hence the test you have in mind may be suitable enough. You could also consider resampling methods like permutation or bootstrap tests, but there's not a lot of statistical power in a sample of 12 regardless of the test.
answered Jul 4, 2014 at 7:34
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1$\begingroup$ Thank you for the answer! I'm a little confused, though, as another member posted that it wouldn't be wise to use the Wilcoxon signed rank test to test pair differences with ordinal data: @Scortchi (stats.stackexchange.com/a/47230/49494). Anyway, there's no statistician I can speak to in person about my (unnecessarily complicated) study that is familiar with non-parametric statistics in SPSS, so I appreciate the feedback! $\endgroup$– sb415Jul 7, 2014 at 17:34
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$\begingroup$ @sb415: interesting point. I don't usually advocate this, but you could make the explicit assumption that your rating options are spaced equally (more or less) along a latent, continuous dimension that they represent. This is how people usually gloss over Scortchi's point when averaging Likert ratings across several items of a questionnaire; it's called classical test theory. Evidently the sign test is the alternative, but given the size of your sample, I doubt it is powerful enough. $\endgroup$ Jul 7, 2014 at 21:40