Analysis of covariance
Analysis of covariance (ANCOVA) is a general linear model with a continuous outcome variable (quantitative, scaled) and two or more predictor variables where at least one is continuous (quantitative, scaled) and at least one is categorical (nominal, non-scaled). ANCOVA is a merger of ANOVA and regression for continuous variables. ANCOVA tests whether certain factors have an effect on the outcome variable after removing the variance for which quantitative predictors (covariates) account. The inclusion of covariates can increase statistical power because it accounts for some of the variability.
Assumptions
Like any statistical procedure, the interpretation of ANCOVA depends on certain assumptions about the data entered into the model. For instance, the F-test assumes that the errors[1] are normally distributed and homoscedastic.
Since ANCOVA is a method based on linear regression, the relationship of the dependent variable to the independent variable(s) must be linear in the parameters.
Simplifying assumption (not necessary to run ANCOVA): homogeneity of regression which says that the relationship between the covariate and the dependent variable should be similar across all groups of the independent variable.
Power considerations
While the inclusion of a covariate into an ANOVA generally increases statistical power by accounting for some of the variance in the dependent variable and thus increasing the ratio of variance explained by the independent variables, adding a covariate into ANOVA also reduces the degrees of freedom. Accordingly, adding a covariate which accounts for very little variance in the dependent variable might actually reduce power.
See also
- MANCOVA (Multivariate analysis of covariance)
References
External links
- Examples of all ANOVA and ANCOVA models with up to three treatment factors, including randomized block, split plot, repeated measures, and Latin squares
- One-Way Analysis of Covariance for Independent Samples
- Use of covariates in randomized controlled trials by G.J.P. Van Breukelen and K.R.A. Van Dijk (2007)
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