Most of us learned ANOVA in one class and ran into ANCOVA in some papers. If you google them, what you find would often say things like “Analysis of variance is designed to be used with interval-ratio level variables and is a powerful tool for analyzing the most sophisticated and precise measurements you are likely to encounter…”, but give vague answers when pressed.

Here is a summary of all these confusing methods including ANOVA, ANCOVA, MANOVA & MANCOVA.

	Compare	By	Example
One-way ANOVA	1 continuous response variable	1 categorical variable	comparing test score by religion
Two-way ANOVA	1 continuous response variable	2 or more categorical variables	comparing test score by both religion and race
ANCOVA	1 continuous response variable	1 categorical variable and 1 continuous variable	comparing test score by both religion and ‘number of hours working’
One-way MANOVA	2 or more continuous response variables	1 categorical variable	comparing test score and annual income by religion
Two-way MANOVA	2 or more continuous response variables	2 or more categorical variables	comparing test score and annual income by both religion and race
MANCOVA	2 or more continuous response variables	1 categorical variable and 1 continuous variable	comparing test score and annual income by both religion and ‘number of hours working’