Running an ANCOVA is almost but not exactly like running
Running an ANCOVA is almost (but not exactly) like running the following two-step analysis:
First, predict Y (the dependent variable) from X1 (the covariate), and take the residuals from this regression; this residual is denoted by X*.
Second, run an ANOVA on X* to see if the mean on X* differs across levels of A, the group membership variable.
How is the two-step analysis described here different from what happens when you run an ANCOVA?
Running an ANCOVA is almost but not exactly like running