Experimental Design and Data Analysis for Biologists

In this chapter, we will examine the relationship between two or more response variables and one or more categorical predictor variables. We are primarily interested in two research questions. First, are there differences between groups based on all the response variables taken together and, second, can we successfully classify observations, particularly new observations, into the correct group.

Multivariate analysis of variance (MANOVA)

There are many situations where we record more than one response variable from each sampling or experimental unit and where these units are allocated to or occur in treatment groups. Ecologists often record the abundances of many species from each sampling or experimental unit and physiologists commonly measure more than one variable (e.g. blood pressure, heart rate, etc.) on experimental animals. For example, Peckarsky et al. (1993) examined the sub-lethal responses of mayfly larvae in streams to three different predator treatments (no predator and normal food, no predator and reduced food, one predatory mayfly (Megarcys) and normal food). There were five response variables recorded for each mayfly: body mass, egg mass, percentage of eggs, total mass, and maturation time. Botanists and zoologists also often measure many morphological variables when describing organisms from different locations or to compare organisms that may or may not be taxonomically different.