In ANCOVA, what is the name of the assumption that the relationship between the covariate and the outcome is the same across different treatment levels?

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

Answer: (A)

The main concept being tested is that in ANCOVA the covariate should influence the outcome in the same way across all treatment groups, meaning the regression slopes are equal across groups. This is called homogeneity of regression slopes. When this assumption holds, you can adjust for the covariate and compare group means on the outcome as if the covariate’s effect is the same regardless of treatment. If the relationship between the covariate and the outcome differs by group, the adjustment would depend on the group, which means the ANCOVA model with a single slope is inappropriate and you’d need to include an interaction term or analyze groups separately. The other options—homogeneity of variance (equal spread of residuals across groups), homogeneity of covariance matrices (multivariate context), and normality (residuals’ distribution)—pertain to different assumptions and do not specify the covariate’s effect across treatment levels.