1 Revision of your Introductory class

In experimental design and execution we manipulate, or choose, one or more variables and record the effect of this manipulation on another variable. The variables we manipulate are called explanatory or predictor variables and the other is called the response. These are also known as independent and dependent variables respectively.

Predictor, Explanatory, x and Independent: all terms used to describe the variables we choose.

Predicted, Response, y and Dependent: all terms used to describe the variable we measure.

When we plot data, the response variable goes on the y-axis and the explanatory variable goes on the x-axis. If we have two explanatory variables we need another way to visualise it. Often we might indicate the different values of a second explanatory variable with colour. The third explanatory variable can be displayed using different panels. See Figure 1.1.

Figure 1.1: Explanatory variables are placed on the x-axis and, if there is more than one, indicated with different colours (or shapes) and panels. The response variable is always on the y-axis.

In choosing between regression, t-tests, one-way ANOVA and two-way ANOVA we consider how many explanatory variables we have and whether they are continuous or categorical.

If we have one continuous explanatory variable we can apply a regression. If the explanatory variable is categorical with two groups (or levels) we have the choice of a t-test or a one-way ANOVA, but when there are more than two groups we must use a one-way ANOVA.

A two-way ANOVA is used when there are two categorical explanatory variables. See Figure 1.2.

Figure 1.2: Decision tree for choosing between single linear regression, t-tests, one-way ANOVA and two-way ANOVA.

These apparently different tests are, in fact, the same test. They have the same underlying mathematics, or to put it another way, they all follow the same model. That model is often known as the General Linear Model.