ANCOVA with all continuous variables

Question

I have the following variables:

• Psychological trait data collected at pre- and post-intervention
• Fitness data (e.g., weight in kg), collected at pre- and post-intervention

I am interested in seeing whether psychological trait at baseline (pre-intervention) explains change (e.g., weight loss) in the fitness from pre- to post-.

Is ANCOVA okay for this? The way I have it set up is:

• Dependent: Fitness post- (continuous)
• Independent: psychological trait pre- (continuous)
• Covariate: Fitness pre- (continuous)

My concern is that my independent variable (psychological trait pre-) is continuous, not categorical. Is it okay to proceed with this ANCOVA, or do I need to go with a different analysis method (that allows for testing a continuous independent variable's effect on change observed between two time points in the dependent variable)?

Answer 1

Instead of ANOVA use regression, which is the more general method: it's perfectly okay to do a regression with any mix of categorical and continuous variables. ANOVA is equivalent to a regression with categorical predictors, interactions and iid Normal errors.

Regression will most likely do for all your modeling needs. It's straightforward to relax some assumptions: you can let a predictor act smoothly but nonlinearly on the response using a spline transformation; you can use a generalized linear model (GLM) for a non-linear response; you can model correlations among responses/errors in several ways, eg. generalized least squares (GLS).