In ANCOVA, which assumption states that the effect of the covariate on the outcome does not differ across treatment levels?

• A. Homogeneity of regression slopes
• B. Homogeneity of variance
• C. Homogeneity of covariance matrices
• D. Normality

Answer: (A)

The idea is that the covariate’s influence on the outcome is the same across treatment groups. In ANCOVA, you’re adjusting the outcome for the covariate by estimating a common slope—the relationship between the covariate and the outcome should be identical no matter which treatment level you’re looking at. This is known as homogeneity of regression slopes. If the covariate affects the outcome differently depending on the treatment, the slopes differ and there’s an interaction between the covariate and treatment; the simple ANCOVA model without an interaction term would then give biased adjusted means. In that case, you’d need to include the covariate-by-treatment interaction or use a model that allows different slopes.

For context, other assumptions like equal variances across groups (homogeneity of variance), equal covariance structures (relevant to MANOVA), or normality of residuals are separate considerations in related analyses, but they describe different ways data can behave rather than how the covariate’s effect varies by treatment.