We began this chapter by introducing some basic concepts of experimental design. We saw that we carry out an experiment by setting the values of one or more factors before the values of the response variable are observed. The different values (or levels) of a factor are called treatments, and the purpose of most experiments is to compare and estimate the effects of the various treatments on the response variable. We saw that the different treatments are assigned to experimental units, and we discussed the completely randomized experimental design. This design assigns independent, random samples of experimental units to the treatments.

We began studying how to analyze experimental data by discussing one-way analysis of variance (one-way ANOVA). Here we study how one factor (having p levels) affects the response variable. In particular, we learned how to use this methodology to test for differences between the treatment means and to estimate the size of pairwise differences between the treatment means.

Sometimes, even if we randomly select the experimental units, differences between the experimental units conceal differences between the treatments. In such a case, we learned that we can employ a randomized block design. Each block (experimental unit or set of experimental units) is used exactly once to measure the effect of each and every treatment. Because we are comparing the treatments by using the same experimental units, any true differences between the treatments will not be concealed by differences between the experimental units.

The last technique we studied in this chapter was two-way analysis of variance (two-way ANOVA). Here we study the effects of two factors by carrying out a two-factor factorial experiment. If there is little or no interaction between the two factors, then we are able to separately study the significance of each of the two factors. On the other hand, if substantial interaction exists between the two factors, we study the nature of the differences between the treatment means.