Extending the complexity of experimental designs

With f-tests, we can compare two sets of data. There are other experimental designs which will require a comparison of more than two sets of data and that is when we need an analysis of variance (AoV or ANOVA). Traditional statistics books always get their knickers in a frightful twist trying to explain ANOVAs. It is difficult to imagine why, because they are actually quite minor extensions of the two-sample f-test. 

A factor is something that we manipulate as part of an experiment in order to see whether it alters the endpoint we are measuring. In the rifampicin/theophylline experiment (Chapter 6), the factor was rifampicin. We then say that the factor has a number of levels . This is the number of different possibilities for that factor. There were two levels for rifampicin - it was either administered or withheld. In the weight-loss experiment in the previous chapter, there was again just one factor (drug) and it also had two levels (used or not used). In fact, for any experiment that can be analysed by a t-test there is always one experimental factor for which there are just two levels - the simplest of all experimental designs. 

A factor is an aspect of our experimental design that will be deliberately altered to see how this affects the outcome. Each different possibility within a factor is a level . 

---