Researchers are often interested in determining the effects of two or more controlled variables (factors) on a response measurement.

This chapter starts with the design and analysis of experiments with two factors. A well designed experiment that varies two factors is more efficient than two separate experiments involving single factors. More importantly, it allows the researcher to examine whether the two factors interact in their effect on the response.

Experiments with three or more experiments extend these ideas but it is harder to display the experimental data and to visualise models for the data. In experiments with four or more factors, the raw data cannot be plotted, so graphical and numerical summaries must be relied on for analysis.

A full factorial experiment with several controlled factors requires many experimental units (runs of the experiment) and can be prohibitively expensive. Experimental designs using fewer experimental units will be considered in the next chapter.