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Adjusted vs Unadjusted Means
Understanding ANCOVA
Analysis of Covariance (ANCOVA) is a statistical technique that combines ANOVA and regression:
- Purpose: Compare group means while controlling for one or more continuous covariates
- Covariate: A continuous variable correlated with the dependent variable (e.g., baseline scores, age)
- Adjusted means: Group means after statistically removing the effect of the covariate
- Power gain: By removing covariate-related variance, ANCOVA increases statistical power
- Key assumption: Homogeneity of regression slopes - groups must have parallel regression lines
- Model: Y = μ + Group + β(Covariate) + ε
- F-test: Tests if adjusted group means differ significantly
- Applications: Pre-post studies, controlling confounders, increasing precision in experiments
- Caution: Covariate should not be affected by the treatment (use baseline values, not post-treatment)