# What is the intuition behind (M)ANCOVA and when/why should one use it?

As per my understanding here's the what/why/when of the following hypotheses tests in a crude sense:

• t-test: Used when comparing means between two samples
• ANOVA (one way): Used when you have one dependent variable and one independent (i.e., categorical) variable and you wish to analyze the 'means' (i.e., effects) across multiple groups. Simply stated, multi-way t-tests in essence.
• ANOVA (two way): Similar to one-way except you have two independent (i.e., categorical) variables
• MANOVA: ANOVA with multiple dependent variables
• ANCOVA: ??
• MANCOVA: ??

Intuitively, the concepts/intuition behind (M)ANOVA makes sense and I understand when/how to apply it and why is it necessary. I've just overly simplified my understanding about them above. However, I lack the similar intuition behind (M)ANCOVA.

• *ANCOVAs allow for both continuous and categorical variables. You can also have $n$-way versions, not just two-way. – Dimitriy V. Masterov Oct 25 '13 at 1:13