Experimental Design and Data Analysis for Biologists

In Chapter 10, we described a technique for reducing the residual or unexplained variation in an experiment by grouping experimental units into spatial or temporal blocks. Another approach to reducing the residual variation is to measure one or more concomitant continuous variables for each experimental unit along with the response variable. These concomitant variables, or covariates, are usually considered as continuous predictor variables, with the one or more factors being categorical predictors. A linear models analysis of this design is sometimes called an analysis of covariance (ANCOVA), where the effect of the covariate on the response variable is removed from the unexplained variability by regression analysis. The final ANCOVA tests the difference between factor level means, adjusted for the effect of the covariate.

Another use of ANCOVA is to compare the slopes and/or intercepts of two or more regression lines, although this use is less common. We will cover basic methods for ANCOVA in this chapter, but also pay particular attention to complex designs and situations with regression slopes that are heterogeneous between the factor levels (see also Figure 12.1).

Single factor analysis of covariance (ANCOVA)

The simplest ANCOVA design is one analogous to a single factor ANOVA where we have a single categorical predictor variable (factor). In addition to a single continuous response variable, we also record the value of a continuous covariate from each experimental or sampling unit.