PROPHET StatGuide: Analysis of Covariance (ANCOVA)--Comparing simple linear regression lines

Analysis of covariance (ANCOVA) combines features of simple linear regression with one-way analysis of variance Both a quantitative variable X and an ANOVA grouping variable are used to describe the measurement (Y) variable.

Simple linear regression fits a straight line to X-Y data. One-way analysis of variance fits a mean to each group. One-way analysis of covariance fits a straight line to each group of X-Y data, such that the slopes of the lines are all equal. This fitted model may then be used to test the null hypotheses:


The X variable is also known as a covariate, or as a concomitant variable.

Analysis of covariance controls for X to make a more precise test of whether the treatment (group) means (intercepts) are equal. It can also be used to study the linear relationship between X and Y for each group.


To properly analyze and interpret the results of analysis of covariance (ANCOVA), you should be familiar with the following terms and concepts:

Failure to understand and properly apply analysis of covariance (ANCOVA) may result in drawing erroneous conclusions from your data. If you are not familiar with these terms and concepts, you may wish to consult with a statistician. You may also want to consult the following references:

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Last modified: March 27, 1997

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