Let's say that I want to know three training program effectiveness. Our independent variable is categorical variable (with three levels). Our response variable is after-train scores. Then I introduce a co-variate variable: before-training scores. I introduce a new response variable the score difference between after train and before train. (Y = after train score - before train scores)
Now I have two models in R
(1) one way anova, Y~training program (p-value 4.921e-11)
(2) ancova: after train ~ before train + train program (p-value 3.360e-11)
both output leads to same conclusion and very similar p-value.
Now, I'm confused which model to choose, what criteria should I look at to select a better model?