A Course in Statistics with R

Chapter 13Experimental Designs

Package(s): BHH2, AlgDesign, granova, multcomp, car, agricolae, phia

Dataset(s): olson, tensile, girder, Hardness, reaction, rocket, rocket_Graeco, battery, bottling, SP, intensity

13.1 Introduction

Experimental Designs, also known as Design of Experiments (DOE), is one of the most important pillars of statistics.

Section 13.2 will introduce the important principles of experimental design, beginning with an interesting real experiment. The first model of the experimental design will be deliberated in Section 13.3, and its extensions to the block design will be detailed in Section 13.4. An effective extension and important class of models of factorial design will be taken up in Section 13.5.

13.2 Principles of Experimental Design

Salsburg (2001) has written a very interesting and historical account in his book titled “The Lady Tasting Tea”. The first chapter, with the same title as the book, has this amazing story of a lady who declared in a cafeteria that she can clearly distinguish between two variants of tea: (i) tea poured into milk, and (ii) milk poured into tea. As Salsburg puts it “A thin, short man, with thick glasses and a Vandyke beard beginning to turn gray, pounced on the problem”, and a live experiment rolled on. The lady was then sent a sequence of different patterns of tea poured into milk cups and milk poured into tea cups. For each cup, the lady would have one sip following which she would declare the process she felt was the ...