SECTION 3.3 Summary

• In an experiment, we impose one or more treatments on the experimental units or subjects. Each treatment is a combination of levels of the explanatory variables, which we call factors.
• The design of an experiment describes the choice of treatments and the manner in which the subjects are assigned to the treatments.
• The basic principles of statistical design of experiments are control, randomization, and replication.
• The simplest form of control is comparison. Experiments should compare two or more treatments in order to avoid confounding the effect of a treatment with other influences, such as lurking variables.
• Randomization uses chance to assign subjects to the treatments. Randomization creates treatment groups that are similar (except for chance variation) before the treatments are applied. Randomization and comparison together prevent bias, or systematic favoritism, in experiments.
• You can carry out randomization by giving numerical labels to the subjects and using a table of random digits to choose treatment groups.
• Replication of each treatment on many subjects reduces the role of chance variation and makes the experiment more sensitive to differences among the treatments.
• Good experiments require attention to detail as well as good statistical design. Lack of realism in an experiment can prevent us from generalizing its results.
• In addition to comparison, a second form of control is to restrict randomization by forming blocks of subjects that are similar in some way that is important to the response. Randomization is then carried out separately within each block.
• Matched pairs are a common form of blocking for comparing just two treatments. In some matched pairs designs, each subject receives both treatments in a random order. In others, the subjects are matched in pairs as closely as possible, and one subject in each pair receives each treatment.