Analysis of covariance

Overview
Analysis of covariance (ANCOVA) is a general linear model with one continuous explanatory variable and one or more factors. ANCOVA is a merger of ANOVA and regression for continuous variables. ANCOVA tests whether certain factors have an effect 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
As any statistical procedure, ANCOVA makes certain assumptions about the data entered into the model. Only if these assumptions are met, at least approximately, ANCOVA will yield valid results. Specifically, ANCOVA, just like ANOVA, assumes that the dependent variable is normally distributed and homoscedastic. Further, since ANCOVA is a regression-based method, the relationship of the dependent variable to the independent variable(s) must be linear in the parameters, as in regression analysis.

Power considerations
While the inclusion of a covariate into a 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 (see below). Accordingly, adding a covariate which accounts for very little variance in the dependent variable might actually reduce power.

ANCOVA vs. block design
While for block design, subjects are first separated into homogeneous groups (blocks) based on the concomitant variable and those within a given block are then randomly assigned into the different treatment groups; for ANCOVA, Subjects are measured on the covariate(s) and are randomly assigned into the different treatment groups without regard for their scores/values on the covariate(s). Block design control the effect of covariates by design, and ANCOVA control the effect of covariate through statistical analysis (statistical control)