Analyzing 7-point items with parametric tests?

Question

I realize this question has been asked in various permutations (and I've reviewed the posts), but I can't find a good answer.

I have DVs that are 7-point Likert ITEMS. The items were presented horizontally with equal spacing 1 2 3...7 with verbal anchors corresponding to the bottom (1) and top (7) ends (disagree strongly to agree strongly).

Most of the analyses I want to do are repeated-measures type -- so I want to determine whether the degree of agreement with one item differs from another. So I'm wondering if I use RM ANOVA, or Friedman's, or is there another method I should be looking at? But I also want to do some multiple regression type analyses and tests of mediation.

The sample size is large > 2000.

The problem is that I can't find a good article/resource that backs me up one way or another. I know it is discrete data, but the way it is presented and the sample size makes me wonder if I can argue for doing parametric tests? I don't see how tests performed on ranks would be better, since there would be so many ties in this type of data. And then there is the big downside that I can't say one mean is higher than another...

I've read a few articles comparing t-tests to WMW but usually these simulations with very small samples so it is hard to know how it applies to my data. It seems that WMW may be marginally better if the data are severely non-normal, but I can't be sure I'm interpreting that correctly.

My 4 main DV's are not terribly out of shape but not perfectly normal...one is negatively skewed (mean 4.75, md 5), another is a bit flat so more approaching uniform.

Any guidance on what direction to take would be much appreciated. Particularly if there is any book or article that I could cite to justify my choice of method.

Thank you!

Answer 1

Welcome to the site.

With a Likert scale DV that has 7 options, you want some sort of ordinal analysis, you have no guarantee that the distance between 1 and 2 is the same as between 2 and 3 (or any other pair); with repeated measure data you want to account for the dependency in the data.

One method that does both is a nonlinear multilevel model. In SAS see PROC GLIMMIX (probably; might need NLMIXED). In R see nlme or lme4 (I believe both of those have options for ordinal dependent variables).

If you are willing to assume that the Likert scale is actually continuous (I don't generally recommend this, with only 7 points, but it could be OK), you would want a linear multilevel model (same libraries in R, but in SAS see PROC MIXED. RM ANOVA makes some pretty stringent assumptions, including sphericity (which includes compound symmetry and is unlikely to be met).