ANCOVA (Analysis of Covariance)

ANCOVA (Analysis of Covariance) extends ANOVA (Analysis of Variance) by statistically controlling one or more nuisance variables—called covariates—to better isolate the true effect of group differences.

In practice, ANCOVA combines an ANOVA with a regression.

Example

Imagine you want to compare three study methods (Groups A, B, and C) on exam performance. You also know that prior knowledge (e.g., a pre-test score) affects the exam results. Without controlling for that, Group B might simply have higher pre-test scores—and thus better results—not because Method B is more effective.

Key Points at a Glance

ANOVA vs. ANCOVA

• ANOVA only compares group means of a dependent variable (e.g., exam score).
• ANCOVA additionally adjusts for one or more covariates (e.g., pre-test score).

When to Use

When you want to compare groups but know that another variable (covariate) also influences the outcome.

Benefit

Greater statistical power, since part of the variance is explained and removed before testing group differences.

Assumptions

• Linear relationship between the covariate and the dependent variable
• Equal slopes (the covariate–outcome relationship is similar across groups)
• Independent residuals

In short: ANCOVA lets you compare groups more fairly by correcting for unwanted influences and focusing on the “true” group effect.

You can also run an ANCOVA online with numiqo—try our ANCOVA Calculator.