ANOVA for a categorical variable with multiple levels and a continuous outcome measure

Why would you evaluate a prognostic factor with 4 categories to predict a continuous outcome using ANOVA and Fisher’s least significant difference procedure rather than a simple linear regression model +/- covariates?

What’s the ultimate goal of the analysis? Why jump immediately to a multiple comparison procedure?

They are attempting to predict if scores on an upper airway endoscopic exam in thoroughbred horses (done prior to racing career) are predictive of future performance based upon earnings in dollars. The scale has four categories based upon laryngeal function (1 is normal, 4- represents partial paralysis).

Im also wondering if the one way ANOVA is non-significant can you run post hoc comparisons between levels using t-tests which was done in this study?

I wouldn’t base any decisions on ‘significance’. I assume the 1-4 scale is a predictor. Optimally this would be treated as ordinal using a shrinkage prior as done in the R package brms for ordered factor predictors. But a simple approach is to treat it is categorical using 3 indicator variables, get some evidence that the variable (with 3 d.f.) is associated with Y, and get individual confidence intervals (better: simultaneous confidence intervals) for differences of interest.

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