One-Way ANCOVA (covariate-adjusted)

Verified

ANOVA

Independently verified. Every statistic this test reports has been re-derived against an independent reference — never the library the pipeline itself calls — the rendered output was read back in a browser, and the result is locked with a committed regression suite.

Run this test straight away on a free built-in teaching dataset — no data of your own needed — or bring your own. Either opens the guided workspace: variable setup, assumption diagnostics, results with effect sizes and confidence intervals, figures, and APA-ready reporting.

Loading teaching datasets…

Or use your own dataset

Loading your datasets…

Compares group means on a continuous DV while statistically controlling for ONE OR MORE continuous covariates.

The covariate adjustment reduces residual error variance, INCREASES power on the group F-test, and removes confounding from baseline differences in non-randomised designs. Reports the adjusted group means (estimated marginal means) with 95% CIs, the group F-test on adjusted means, the covariate regression slope, and η²p / partial-η² effect size. Critically requires the homogeneity-of-regression-slopes assumption — covariate × group interactions must be NS for the adjusted comparisons to be interpretable.

Worked example

Do teaching methods differ in exam score after controlling for prior ability?

Exam score is compared across three methods while adjusting for a pre-test covariate (prior ability) — ANCOVA gives a fairer comparison than raw means.

Result

After adjusting for prior ability, the methods still differed, F(2, 86) = 9.39, p < .001, partial η² = .18; the flipped classroom had the highest adjusted mean.

How you'd report it (APA)

An ANCOVA showed teaching method affected exam score after controlling for prior ability, F(2, 86) = 9.39, p < .001, partial η² = .18.

Try it yourself: Load this ready-made sample and follow the run above.

When to use it

  • Experimental design with baseline covariate
    Three teaching methods compared on final exam score, controlling for prior GPA.
  • Quasi-experimental with confound control
    Compare job performance across 3 departments, controlling for years of experience.

When NOT to — use instead

Hypotheses

H₀: the adjusted population means of the DV are equal across IV groups, after removing the linear effect of the covariate.
Hₐ: at least one adjusted mean differs from the others.

Parameter tested: adjusted population means {μ_adj[i]} of the DV at the grand covariate mean

Assumptions (and what to do if they fail)

No significant outliers on the DV within each groupmedium

Check: Inspect per-group boxplots of the DV.

If violated: Outliers distort within-group variance and the covariate-adjusted F-test.

Model residuals are approximately normally distributedmedium

Check: Shapiro-Wilk on residuals.

If violated: Non-normal residuals can inflate the F-test's Type I error rate.

Homogeneity of variance on the DV across groups (Levene's test)medium

Check: Levene's p > .05 → variances homogeneous.

If violated: Unequal variances inflate F-test Type I error.

Linear relationship between the DV and the covariate within each groupmedium

Check: Per-group scatter with linear fit; verify no obvious curvature.

If violated: Non-linear DV-covariate relationships produce biased adjusted means.

The slope of the DV on the covariate is the same across IV groups (no IV × covariate interaction)high

Check: Interaction p > .05 → slopes homogeneous.

If violated: If slopes differ by group, the covariate effect depends on the IV and a single 'adjusted' comparison across groups is not meaningful.

Covariate balance / overlap across groupsmedium

Check: Covariate one-way ANOVA p > .05 → balanced.

If violated: Groups differ on the covariate.

Ready to run a One-Way ANCOVA (covariate-adjusted) on your own data?

Guided setup, automatic assumption checks, effect sizes, figures and an APA write-up.

Run this test →