ANCOVA calculator: compare groups while controlling for a covariate.

What is an ANCOVA?

An analysis of covariance (ANCOVA) compares group means on an outcome while statistically controlling for a covariate, a continuous variable that also affects the outcome, such as a pre-test score. It removes the covariate's influence from the error term and adjusts the group means, giving a fairer and usually more powerful comparison.

Model

The group effect is tested by comparing the full model with a model that contains only the covariate (Type III). Adjusted means are the model's predictions for each group at the overall mean of the covariate.

Worked example: three teaching methods

24 students in three methods (A, B, C) with a pre-test as the covariate and a post-test as the outcome.

1. Check homogeneity of slopes: F(2, 18) = 0.17, p = .846, so the assumption holds.
2. Covariate: F(1, 20) = 32.10, p < .001, partial η² = .62.
3. Method, adjusted for pre-test: F(2, 20) = 12.60, p < .001, partial η² = .56.
4. Raw means were 38.59, 44.91 and 44.76; adjusted means are 37.65, 44.60 and 46.01.
5. After adjustment, method C has the highest post-test score.

Assumptions to check

• Independent observations
• Linear relationship between covariate and outcome in each group
• Homogeneity of regression slopes (no group × covariate interaction)
• Roughly normal residuals with similar variances across groups
• The covariate was measured before the treatment, so it is not affected by it

How to report it (APA style)

“After controlling for pre-test scores, there was a significant effect of teaching method on post-test scores, F(2, 20) = 12.60, p < .001, partial η² = .56. Adjusted means were 37.65 (A), 44.60 (B) and 46.01 (C).”

References

• Field, A. (2018). Discovering statistics using IBM SPSS Statistics (5th ed.). SAGE.
• Huitema, B. E. (2011). The analysis of covariance and alternatives (2nd ed.). Wiley.
• Maxwell, S. E., Delaney, H. D., & Kelley, K. (2018). Designing experiments and analyzing data (3rd ed.). Routledge.