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I have a set of 15 perception questions asked before and after a course to the same group of 13 students. The responses are 0%, 20%, 40%, 60%, 80% and 100%. What is the best way to analyze them to test for significant difference?

Carl
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Bani
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2 Answers2

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I would use the Wilcoxon signed-rank test. That test does not depend on the distribution type, that is, it is a nonparametric test. Thus, that the data categories are ordinal should make no difference as the ranking procedure is also ordinal.

Other questions you might want to answer include nonparametric significance of difference of variance for which I would use Conover's squared ranks test.

Carl
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    Wilcoxon's signed-rank test as usually applied requires at least interval-level data - so that you can calculate differences before ranking them. (I imagine the OP might be happy to consider these as interval-level.) – Scortchi - Reinstate Monica Jul 30 '17 at 15:55
  • @Scortchi That is what I thought, too. – Carl Jul 30 '17 at 17:38
  • But you say in your answer "the data categories are ordinal". (I'm not sure why - there's not much information given about what they represent.) – Scortchi - Reinstate Monica Jul 30 '17 at 20:26
  • @Scortchi The responses are 0, 0.2, 0.4, 0.6, 0.8, and 1. Looked like ordinal, equidistant responses to me. In other words, they are also interval; $0.2*(i-1)$, where $i$ is 1 to 6. – Carl Jul 31 '17 at 00:18
  • @Scortchi Reason for my equivocation is that I think that ordinal is required for Wilcoxon, although interval is fine. I think that all that is required for Wilcoxon is one one mapping, i.e., a mapping that doesn't fold onto itself in a sort of not functional way. – Carl Jul 31 '17 at 00:24
  • All that's required is that the before-after comparisons are on at least an ordinal scale. The usual way of making the comparisons is to subtract 'before' values from 'after' values - which requires *those* values to be on at least an interval scale. – Scortchi - Reinstate Monica Jul 31 '17 at 14:21
  • BTW I just edited the Wikipedia article, which said the test requires merely ordinal data - just before giving an example where they calculate differences. (And I found my answer [here](https://stats.stackexchange.com/a/47230/17230) when I was Googling for a reference.) – Scortchi - Reinstate Monica Jul 31 '17 at 15:15
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Use paired t test to find whether there is significant difference between pre and post course

Sam Gladio
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