ANCOVA Calculator
Free ANCOVA online with covariate adjustment, adjusted treatment means, F tests and post-hoc options.
When to use it
Use one-way ANOVA with a continuous covariate (baseline yield, age, initial weight, pre-test score) that is correlated with the response. Adjusting for the covariate increases power and removes confounding when groups differ on the covariate by chance.
When NOT to use it
Do not use when the covariate is itself affected by the treatment (post-treatment confounding). Do not use when the slope of Y on X differs across groups (assumption of homogeneous slopes); test the treatment-by-covariate interaction first. Do not use when the covariate is measured with substantial error.
What you get
ANCOVA table partitioning Treatment, Covariate, Error; F and p for each; adjusted treatment means at the grand-mean covariate value with their SEs; the regression slope of Y on X (assumed common across groups); residual diagnostics; post-hoc letter display on adjusted means.
How to interpret the output
The treatment F in ANCOVA tests whether the treatment effect remains after controlling for the covariate. Adjusted means (least-squares means) are what you report as treatment effects, not the raw group means. If the covariate F is large, the covariate explains substantial variation that ANOVA without it would have lumped into error; the gain in power can be substantial.
Common pitfalls
- Skipping the homogeneous-slopes check (treatment by covariate interaction).
- Using a covariate that is influenced by the treatment.
- Reporting raw group means instead of adjusted means.
- Forgetting that the covariate must be measured before the treatment is applied or independently of it.
Try it in StatVeda
The ANCOVA (one covariate) engine runs entirely in the browser. No signup, no install, no data sent to a server. Paste your data, hit Run, copy the output.
Open ANCOVA (one covariate)References
- Snedecor, G. W. and Cochran, W. G. (1989). Statistical Methods, 8th edition. Iowa State University Press, Ames. Chapter 18.
- Cochran, W. G. (1957). Analysis of covariance: Its nature and uses. Biometrics, 13(3), 261 to 281.