Which statistical procedure uses the F-statistic to test the overall fit of a linear model after accounting for covariates?

Which statistical procedure uses the F-statistic to test the overall fit of a linear model after accounting for covariates?

• A. ANOVA
• B. MANOVA
• C. Analysis of covariance
• D. Multiple regression

Answer: (C)

When you want to compare group means while removing the influence of continuous covariates, you use analysis of covariance. In ANCOVA, you fit a linear model that includes the covariates and the group factor. To determine if the groups differ after accounting for covariates, you compare the full model (covariates plus the group factor) to a reduced model that includes only the covariates. The F-statistic from this comparison tests whether adding the grouping variable significantly improves model fit. A significant F indicates that, after adjusting for covariates, there are real differences between groups; a non-significant F suggests any differences are explained by the covariates alone. This approach specifically targets the effect of group membership after removing covariate variance, which is why it’s the method described.

When you want to compare group means while removing the influence of continuous covariates, you use analysis of covariance. In ANCOVA, you fit a linear model that includes the covariates and the group factor. To determine if the groups differ after accounting for covariates, you compare the full model (covariates plus the group factor) to a reduced model that includes only the covariates. The F-statistic from this comparison tests whether adding the grouping variable significantly improves model fit. A significant F indicates that, after adjusting for covariates, there are real differences between groups; a non-significant F suggests any differences are explained by the covariates alone. This approach specifically targets the effect of group membership after removing covariate variance, which is why it’s the method described.