Design and Analysis of Experiments, 9th Edition

CHAPTER 13Experiments with Random Factors

CHAPTER OUTLINE

1. 13.1 RANDOM EFFECTS MODELS
2. 13.2 THE TWO-FACTOR FACTORIAL WITH RANDOM FACTORS
3. 13.3 THE TWO-FACTOR MIXED MODEL
4. 13.4 RULES FOR EXPECTED MEAN SQUARES
5. 13.5 APPROXIMATE F-TESTS
6. 13.6 SOME ADDITIONAL TOPICS ON ESTIMATION OF VARIANCE COMPONENTS
   1. 13.6.1 Approximate Confidence Intervals on Variance Components
   2. 13.6.2 The Modified Large-Sample Method
7. SUPPLEMENTAL MATERIAL FOR CHAPTER 13
8. S13.1 Expected Mean Squares for the Random Model
9. S13.2 Expected Mean Squares for the Mixed Model
10. S13.3 Restricted versus unrestricted Mixed Model
11. S13.4 Random and Mixed Models with Unequal Sample Size
12. S13.5 Background Concerning the Modified Large-Sample Method
13. S13.6 Confidence Interval on a Ratio of Variance Components using the Modified Large-Sample Method

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

CHAPTER LEARNING OBJECTIVES

1. Understand the difference between fixed and random factors.
2. Know the difference between the inference spaces for fixed and random factors.
3. Understand the methods‐of‐moments (ANOVA) approach to estimate variance components.
4. Understand how the REML method for variance component estimation works.
5. Know how to analyze an experiment with both fixed and random factors.

13.1 Random Effects Models

Throughout most of this book we have assumed that the factors in an experiment were fixed factors, that is, the levels of the factors used by the experimenter were the specific levels of interest. ...