Design and Analysis of Experiments, 9th Edition

CHAPTER 4Randomized Blocks, Latin Squares, and Related Designs

CHAPTER OUTLINE

1. 4.1 THE RANDOMIZED COMPLETE BLOCK DESIGN
   1. 4.1.1 Statistical Analysis of the RCBD
   2. 4.1.2 Model Adequacy Checking
   3. 4.1.3 Some Other Aspects of the Randomized Complete Block Design
   4. 4.1.4 Estimating Model Parameters and the General Regression Significance Test
2. 4.2 THE LATIN SQUARE DESIGN
3. 4.3 THE GRAECO-LATIN SQUARE DESIGN
4. 4.4 BALANCED INCOMPLETE BLOCK DESIGNS
   1. 4.4.1 Statistical Analysis of the BIBD
   2. 4.4.2 Least Squares Estimation of the Parameters
   3. 4.4.3 Recovery of Interblock Information in the BIBD

SUPPLEMENTAL MATERIAL FOR CHAPTER 4

1. S4.1 Relative Efficiency of the RCBD
2. S4.2 Partially Balanced Incomplete Block Designs
3. S4.3 Youden Squares
4. S4.4 Lattice Designs

The supplemental material is on the textbook website www.wiley.com/college/montgomery.

CHAPTER LEARNING OBJECTIVES

1. Learn about how the blocking principle can be effective in reducing the variability arising from controllable nuisance factors.
2. Learn about the randomized complete block design.
3. Understand how the analysis of variance can be extended to the randomized complete block design.
4. Know how to do model adequacy checking for the randomized complete block design.
5. Understand how a Latin square design can be used to control two sources of nuisance variability in an experiment.

4.1 The Randomized Complete Block Design

In any experiment, variability arising from a nuisance factor can affect the results. Generally, we define a nuisance factor ...