Hi: I have a survey where respondents were asked to rank a series of statements in terms of how much they agreed with them. There were seven statements. So, for each of seven statements, each respondent has value that ranges from 1 to 7, depending on where they ranked that item. Two questions: first, should I conceive of this as an ordinal or an interval level variable. I'm inclined to think of it as an ordinal variable, because I'm not sure how meaningful a mean is in this context. It seems more intuitive to say the median ranking of this group of respondents' for this statement was 2, compared to 5 for a different group, rather than, say, 3.6 compared to 5.5, or whatever.
So, my first question is, is that sound logic?
The second question flows from this: If I do conceive of this as an ordinal level variable, rather than an interval, what statistical test can I use to test for difference in median values? I have read a little bit that refers to a Wilcoxon-Mann-Whitney test for difference in medians, but I'm not sure if that is proper for a cross-sectional survey of around 150 people at the same point in time.
Thank you for your suggestions
Best Answer
The Wilcoxon-Mann-Whitney is not a test for equality of medians, it's a test for one variable being stochastically larger than another ($P(X>Y)>P(Y>X)$). If you're using it as a location test, it's actually a test for a zero (population) median of pairwise differences.
If you make the additional assumption of identical distributions apart from a location shift then it will be a test of medians (but it would also be a test of means, as long as population means exist).
So that's seven numbers per respondent. What did you do with those 7 numbers?
If you just added the scores on each item, you already assumed the 7 items were interval scale when you did that.
If you can add a "2" and "6" and get the same result as when you got a "3" and "5", then everything needed for a mean to be meaningful was already assumed to be true.
If you find a median intuitive, that's fine, there's nothing stopping you working with medians -- that doesn't require you to assume it ordinal even though you already made it interval.
You can always consider a permutation test; it assumes exchangeability under the null, which is a somewhat stronger assumption than the Wilcoxon-Mann-Whitney needs.