IMPORTANT - Just talk about the concept. Don't include formulas or tables. Short answer is fine.

Question:

Imagine that you ran a one-way ANOVA where the factor had three levels and the outcome was continuous. Imagine that you ran an ANCOVA using the same factor and outcome variable with the addition of a covariate. How would you know whether the ANOVA or ANCOVA model was a better fit of your data by comparing the output provided by the respective analyses (Hint: think about the statistics that use a ratio of signal to noise)? Given what circumstance(s) would you decide to use an ANOVA instead of an ANCOVA?