Mathematical Statistics

10 Analysis of Covariance (ANCOVA)

10.1 Introduction

Analysis of covariance (ANCOVA) as a branch of applied statistics covers several objectives. In any case, the observations are influenced by at least two factors. At least one of these factors has several levels, by which the material is classified into classes. At least one further factor is a regressor in a regression model between different variables in the model and called a covariable or a covariate. One branch of the ANCOVA is to test whether the influence of the covariable is significant and as the case may be to eliminate it.

If the factor is qualitative (not numeric), this target can be achieved simply by blocking and using analysis of variance (ANOVA). Another branch of the ANCOVA is to estimate the parameters of the regression model within the classes of the classification factor.

If we have just one classification factor and one covariable, then we have four models of the ANCOVA:

• Model I–I: Levels of the classification factor fixed and model I of regression
• Model I–II: Levels of the classification factor fixed and model II of regression
• Model II–I: Levels of the classification factor random and model I of regression
• Model II–II: Levels of the classification factor random and model II of regression

In statistical (theoretical) textbooks, mainly model I–I was presented. However, in applications and in many examples, exclusively cases are found for which model I–II must be used. The results found for model I–I ...