Analysis of Messy Data, Volume II:

Researchers often do not analyze nonreplicated experiments statistically because they are unfamiliar with existing statistical methods that may be applicable. Analysis of Messy Data, Volume II details the statistical methods appropriate for nonreplicated experiments and explores ways to use statistical software to make the required computations feasible.

Preface

viii

Analyzing Two-Way Treatment Structures with One Observation Per Treatment Combination

1

(40)

Introduction

2

(1)

An Example

3

(1)

Model Definition and Parameter Estimation

4

(1)

What Can Be Done?

5

(1)

A Heuristic Test for Interaction

5

(2)

Tukey's Single-Degree-of-Freedom Test for Non-additivity

7

(6)

Two-Way Interaction Plots

13

(4)

Mandel's Bundle of Straight Lines Model

17

(12)

Comparing Mandel's Model and Tukey's Model

29

(2)

Generalized Interaction Models

31

(1)

Characteristic Root Test for Interaction

32

(9)

The Multiplicative Interaction Model

41

(9)

Model Definition and Parameter Estimation

42

(5)

Selecting an Appropriate Number of Terms to Describe the Interaction

47

(3)

More on the Analysis of Multiplicative Interaction Models

50

(14)

Estimating σ2

51

(1)

Tests On Main Effects

51

(1)

Inferences on the Interaction Parameters

52

(4)

Improved Estimation of σ2 in the Multiplicative Interaction Model

56

(4)

Simultaneous Tests on the α and γ's

60

(4)

Half-Normal Plots

64

(7)

Construction of Half-Normal Plots

65

(2)

Estimating σ from a Half-Normal Plot

67

(1)

Use of Half-Normal Plots in Interpreting Nonreplicated Experiments

68

(3)

Analyzing A Two-Way Treatment Structure in a Split-Plot Design with No Replications

71

(8)

A Sausage Example

72

(1)

An Incorrect Analysis of the Sausage Data

72

(2)

Testing for Sausage Type*Judge Interaction

74

(1)

Comparing Sausage Means

75

(4)

A Three-Way Treatment Structure with No Replications

79

(13)

An Example

80

(2)

Testing for Expert*Treatment Interaction

82

(1)

Analyzing Treatments for Interaction

82

(2)

Treatment Contracts

84

(8)

Factorial Treatment Structures

92

(17)

Notation

93

(1)

Main Effects and Interaction Effects

94

(3)

Estimating σ2 in 2n Factorial Experiments

97

(1)

Analyzing 2n Factorial Experiments for Significant Treatment Effects

98

(4)

Completing the Analysis

102

(7)

Blocking 2n Factorial Treatment Structures

109

(21)

A 23 Experiments in Two Blocks of Size 4

110

(1)

2n Factorial Experiments in Two Blocks of Size 2n-1

111

(2)

Analyzing 2n Factorial Experiments Conducted in Two Blocks of Size 2n-1

113

(1)

Confounding 2n Factorial Experiments in More Than Two Blocks

114

(5)

Analyzing Confounded 2n Factorial Experiments When Experimental Units Have Been Grouped into More Than Two Blocks

119

(1)

An Example

120

(10)

Fractional Replications of 2n Factorial Treatment Structures

130

(17)

A One-Half Replicate of a 23 Factorial Experiment

131

(3)

A One-Half Replicate of a 25 Factorial Experiment

134

(1)

The Analysis of Fractional Factorial Experiments

135

(4)

Smaller Fractions of 2n Factorial Experiments

139

(5)

3n Factorial Experiments

144

(3)

Polynomial Model Approximations

147

(7)

A Cautionary Note

148

(2)

Choosing a Degree

150

(1)

An Example

150

(4)

Quadratic Response Surface Models

154

(15)

Analyzing a Quadratic Response Surface Model

155

(1)

An Example

156

(13)

Appendices

169

(25)

References

194

(3)

Index

197

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

FREE SHIPPING

Amazon no longer offers textbook rentals. We do!

Analysis of Messy Data, Volume II: Nonreplicated Experiments

Summary

Table of Contents

Supplemental Materials