This chapter aims to show you how to compute the Analysis of Variance F ratio for the simplest possible design: one-factor, between-subjects with two levels. The basic equations can also be extended so that designs with three or more levels can also be analysed. As a reminder, the word factor is equivalent to independent variable while level refers to the different conditions of the factor. By convention, in a single-factor two-level experiment, the factor is designated by the letter A, while its two levels are designated A) and A 2 . NB These labels are just statisticians' shorthand, and should never be used as labels in a formal report. Meaningful names should be used instead. If a second independent variable is added, that factor is designated B by statisticians, and then the third factor is designated as C, and so on. Before beginning, here are some reminders of the notation which will be used. At the end of the chapter, some of the notation will be simplified, so bear this in mind while working through the examples:
X will only be used in order to give examples of equations; it stands for either a single arbitrary number or an entire set of numbers, depending on the example.