, SOLUTION MANUAL INTRODUCTION
The end-of-the-chapter exercises have been designed to achieve several ends: (1) to illustrate the
use of techniques demonstrated in the text, thereby more effectively giving the students an
understanding of what they've read; (2) to extend the application of the techniques beyond what
was explicitly presented in the text, and (3) to probe further the theoretical principles upon which
the techniques are based. With over 50 years of teaching experience between us, we have come to
appreciate more those texts which do more than focus almost exclusively on repetitious drill in
their exercises, and we have sought to provide the kind and selection of exercises we most
appreciate when we do the teaching.
The difficulty of the exercises varies from fairly simple (but not trivial) to fairly
challenging. Many exercises require nothing more than a hand calculator, and some, not even that.
The more calculation-intensive exercises can be done with Excel, and, for tutorial purposes, we
suggest that is what the student does. The quickest way to do many exercises is with a statistical
software package, and some of that is encouraged. We remind the reader of the shortcoming of
"blindly" plugging into SPSS® or JMP®; the point of doing the exercises is to help master the
material, not to get the answers.
We have found the writing of the text and the solution manual to be a very demanding and
very rewarding undertaking. We hope you find reading and studying our book to be less demanding
and even more rewarding. If you care to share your comments, we would be receptive to having
them.
1
, Table of Contents
CHAPTER 2 – ONE-FACTOR DESIGNS AND THE ANALYSIS OF VARIANCE.......................................3
CHAPTER 3 – SOME FURTHER ISSUES IN ONE-FACTOR DESIGNS AND ANOVA ................ 13
CHAPTER 4 – MULTIPLE-COMPARISON TESTING.................................................................................... 23
CHAPTER 5 – ORTHOGONALITY, ORTHOGONAL DECOMPOSITION, AND THEIR ROLE IN
MODERN EXPERIMENTAL DESIGN ................................................................................................................ 48
CHAPTER 6 – TWO-FACTOR CROSS-CLASSIFICATION DESIGNS....................................................... 59
CHAPTER 7 – NESTED, OR HIERARCHICAL, DESIGNS............................................................................ 75
CHAPTER 8 –DESIGNS WITH THREE OR MORE FACTORS: LATIN-SQUARE AND
RELATED DESIGNS ................................................................................................................................................. 85
CHAPTER 9 - TWO-LEVEL FACTORIAL DESIGNS ....................................................................................... 98
CHAPTER 10 – CONFOUNDING/BLOCKING IN 2K DESIGNS.................................................................. 106
CHAPTER 11 – TWO-LEVEL FRACTIONAL-FACTORIAL DESIGNS .................................................... 112
CHAPTER 12 – DESIGNS WITH FACTORS AT THREE LEVELS ............................................................. 127
CHAPTER 13 – INTRODUCTION TO TAGUCHI METHODS ...................................................................... 136
CHAPTER 14 – INTRODUCTION TO SIMPLE REGRESSION ..................................................................... 142
CHAPTER 15 – MULTIPLE LINEAR REGRESSION ..................................................................................... 147
CHAPTER 16 – INTRODUCTION TO RESPONSE-SURFACE METHODOLOGY ................................... 152
CHAPTER 17 – INTRODUCTION TO MIXTURE DESIGNS ........................................................................ 157
2
, 1 CHAPTER 2 – ONE-FACTOR DESIGNS AND THE ANALYSIS OF VARIANCE
2
2.1
Treatment
1 2 3
(C = 3)
6 6 11
Replications 3 5 10
(R = 4) 8 4 8
3 9 11
Column means 5 6 10
Grand Mean 7
SSBc = 4 5 − 7 2 + 6−7 2 + 10 − 7 2 = 4 4 + 1 + 9 = 56
SSW = 6−5 2 + 3−5 2 + 8−5 2 + ⋯ + 11 − 10 2 = 38
𝐹𝑐𝑎𝑙𝑐 = 56 2 38 9 = 6.632
Alternatively, using Excel, we have
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 56 2 28 6.632 0.017 4.257
Within Groups 38 9 4.222
Total 94 11
Yes, there is sufficient evidence of differences is sales due to the level of the treatment; Fcalc =
6.632 is well within the rejection region; thus, we reject H0. 16
3
The end-of-the-chapter exercises have been designed to achieve several ends: (1) to illustrate the
use of techniques demonstrated in the text, thereby more effectively giving the students an
understanding of what they've read; (2) to extend the application of the techniques beyond what
was explicitly presented in the text, and (3) to probe further the theoretical principles upon which
the techniques are based. With over 50 years of teaching experience between us, we have come to
appreciate more those texts which do more than focus almost exclusively on repetitious drill in
their exercises, and we have sought to provide the kind and selection of exercises we most
appreciate when we do the teaching.
The difficulty of the exercises varies from fairly simple (but not trivial) to fairly
challenging. Many exercises require nothing more than a hand calculator, and some, not even that.
The more calculation-intensive exercises can be done with Excel, and, for tutorial purposes, we
suggest that is what the student does. The quickest way to do many exercises is with a statistical
software package, and some of that is encouraged. We remind the reader of the shortcoming of
"blindly" plugging into SPSS® or JMP®; the point of doing the exercises is to help master the
material, not to get the answers.
We have found the writing of the text and the solution manual to be a very demanding and
very rewarding undertaking. We hope you find reading and studying our book to be less demanding
and even more rewarding. If you care to share your comments, we would be receptive to having
them.
1
, Table of Contents
CHAPTER 2 – ONE-FACTOR DESIGNS AND THE ANALYSIS OF VARIANCE.......................................3
CHAPTER 3 – SOME FURTHER ISSUES IN ONE-FACTOR DESIGNS AND ANOVA ................ 13
CHAPTER 4 – MULTIPLE-COMPARISON TESTING.................................................................................... 23
CHAPTER 5 – ORTHOGONALITY, ORTHOGONAL DECOMPOSITION, AND THEIR ROLE IN
MODERN EXPERIMENTAL DESIGN ................................................................................................................ 48
CHAPTER 6 – TWO-FACTOR CROSS-CLASSIFICATION DESIGNS....................................................... 59
CHAPTER 7 – NESTED, OR HIERARCHICAL, DESIGNS............................................................................ 75
CHAPTER 8 –DESIGNS WITH THREE OR MORE FACTORS: LATIN-SQUARE AND
RELATED DESIGNS ................................................................................................................................................. 85
CHAPTER 9 - TWO-LEVEL FACTORIAL DESIGNS ....................................................................................... 98
CHAPTER 10 – CONFOUNDING/BLOCKING IN 2K DESIGNS.................................................................. 106
CHAPTER 11 – TWO-LEVEL FRACTIONAL-FACTORIAL DESIGNS .................................................... 112
CHAPTER 12 – DESIGNS WITH FACTORS AT THREE LEVELS ............................................................. 127
CHAPTER 13 – INTRODUCTION TO TAGUCHI METHODS ...................................................................... 136
CHAPTER 14 – INTRODUCTION TO SIMPLE REGRESSION ..................................................................... 142
CHAPTER 15 – MULTIPLE LINEAR REGRESSION ..................................................................................... 147
CHAPTER 16 – INTRODUCTION TO RESPONSE-SURFACE METHODOLOGY ................................... 152
CHAPTER 17 – INTRODUCTION TO MIXTURE DESIGNS ........................................................................ 157
2
, 1 CHAPTER 2 – ONE-FACTOR DESIGNS AND THE ANALYSIS OF VARIANCE
2
2.1
Treatment
1 2 3
(C = 3)
6 6 11
Replications 3 5 10
(R = 4) 8 4 8
3 9 11
Column means 5 6 10
Grand Mean 7
SSBc = 4 5 − 7 2 + 6−7 2 + 10 − 7 2 = 4 4 + 1 + 9 = 56
SSW = 6−5 2 + 3−5 2 + 8−5 2 + ⋯ + 11 − 10 2 = 38
𝐹𝑐𝑎𝑙𝑐 = 56 2 38 9 = 6.632
Alternatively, using Excel, we have
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 56 2 28 6.632 0.017 4.257
Within Groups 38 9 4.222
Total 94 11
Yes, there is sufficient evidence of differences is sales due to the level of the treatment; Fcalc =
6.632 is well within the rejection region; thus, we reject H0. 16
3
