# Can you analysis likert scale data with ANCOVA? what are the alternative when Kruskal-wallis is also not appropriate

We have conducted a trial with 30 participants, each participant given different intervention (Intervention A, Intervention B and Intervention C). The aim of the study is to compare the effectiveness of three interventions.

At baseline (T0), 6 weeks (T1) and 12 weeks (T2) participants assessed their conditions using a 5 point likert scale (1. No pain; 2.Slight discomfort; 3.Slight pain, 4.moderate pain, 5.severe pain)

I have attempted to analysis the outcomes using Kruskal-Wallis and ANCOVA on different occasions however: (1) Kruskal-Wallis is not appropriate as it looks at the degree of change from baseline to follow-up within each group, rather than comparing the findings across the groups at follow-up, adjusting for any baseline differences; (2) ANCOVA considers for baseline differences however it also treats the data as continuous variable.

Any advice would be highly appreciated.

• Use Repeated Measures ANOVA, with timepoint as within-subject variable. – Joseph Apr 23 '18 at 11:23

Your situation is ideal for the generalization of the Kruskal-Wallis test: the proportional odds ordinal logistic model. With that model you can adjust for covariates, avoid problematic change scores, and analyze the ordinal response directly while handling even extreme clumping in the data. The prop. odds model has as many intercepts as you have distinct values of $Y$, less one. For a start see my RMS course notes. But this deals with the non-repeated-measures part of your issue. To handle repeated measures you have three choices: Bayesian hierarchical prop. odds model (e.g.. R brms package), mixed effects classical proportional odds model (e.g., R ordinal package), or fit the regular prop. odds univariate model on a tall and thin dataset and correct after-the-fact for within-subject correlation (e.g., R rms package lrm, orm, and robcov functions).