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I am comparing three groups of participants, who gave ratings during a certain test on a scale from $1$ to $4$ (with $0.25$ steps). I was planning to do an ANOVA, but realized that a thing such as the mean of ratings $1$, $2$, $2$ is $5/3$ and does not actually exist on my original scale.

Is my data ordinal then? Should I do a Friedman test instead?

I should maybe add that I consider the distance from $1$ to $2$ to be the same as from $2$ to $3$ etc. EDIT: actually, I am not sure if I should do that. Would the answer be any different?

annie
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  • "Consider the distance to be the same" - that's the exact definition of interval vs. ordinal. Unless you have very good reasons to prove that the intervals are the same, you shouldn't make that assumption. And for ratings given by participants, this assumption is known to be wrong. But see my answer below: it is unclear if you will get better answers by treating your data as the ordinal data it is, or if you pretend that it is interval. – rumtscho Jul 31 '16 at 11:37
  • In many cases there may only be a small issue in assuming that the intervals are approximately equal, but there's no need to do it if you don't think it's reasonable. – Glen_b Aug 03 '16 at 08:07

1 Answers1

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Your data is ordinal, yes. Self-reported ratings are ordinal in principle.

However, you need to seek further literature to decide which tests you can apply. Yes, I know of the "don't take the mean of ordinal data" principle. However, this is the theory. In reality, it can turn out that you are better off treating your data as if it were interval. See for example Lewis' paper on usability ratings I cite below.

That paper is specifically about usability ratings, and specifically about mean vs. median. You need to find literature which applies to your own case and decide. If there is no such literature, you can either treat the data as ordinal or as interval, but have to provide arguments for your choice, else your reviewers will likely (should!) raise an issue.

Lewis, J. R. (1993). Multipoint scales: Mean and median differences and observed significance levels. International Journal of Human-Computer Interaction, 5(4), 383–392. http://doi.org/10.1080/10447319309526075

rumtscho
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