Comparing Mean Response When There Are Three or More Treatments

Abstract

From the experimenter’s point of view, the primary function of this chapter is to provide methods which extend the comparison of treatment or group means beyond two treatments or groups. The statistical approach must not only accommodate this aim, but must do so in the most effective way possible. This leads to the need for methodology which incorporates the effect of employing experimental designs (which are used to control the level of non-treatment or extraneous variation). Much of the content of this chapter is devoted to rules for correctly selecting and applying methodology for designed experiments. The chapter has the following format:

• Section 15.2 is devoted to identification and description of designs;

• Section 15.3 describes the methods of model and data checking;

• Sections 15.4 to 15.6 document the construction of statistical methods for application with common designs;

• Section 15.7 describes the analysis and interpretation when there is a factorial arrangement of treatments; and

• Section 15.8 provides the methodology for comparison of treatments in pairs and in groups.