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A useful book for all experimental scientists and statisticians. Analysis of Two-way Layouts is the only book that presents a comprehensive treatment of two-way tables of measurement. The reader will be able to determine the structure of a set of data and this will provide more insight than the usual analyses with analysis of variance and covariance and tests of significance. This book determines how to analyze data in an objective way without relying upon preconceived models. To the extent that the models are used, they are based on a prior detailed examination of the data.

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CONTENTS
Preface = ⅸ
Introduction = xiii
1. Statistics of the Straight Line
  1.1 The Classical Case = 1
  1.2 Computations for the Classical Case = 2
  1.3 An Example of Classical Linear Regression = 4
  1.4 Weighted Straight Line Fitting = 4
  1.5 An Example of Weighted Linear Regression = 7
  1.6 Errors in Both Variables = 8
  1.7 An Example of Regression with Errors in Both Variables = 9
  1.8 The Importance of Choosing the Correct Model = 10
  References = 11
2. Structures of Two-Way Tables
  2.1 Introduction and Terminology = 12
  2.2 Structure = 13
  2.3 The Row-Linear Structure = 15
  2.4 The Column-Linear Structure = 17
  References = 17
3. Functional Expressions of Structure
  3.1 Additive Structures = 18
  3.2 Multiplicative Structures = 19
  3.3 Row-Linear Structure = 19
  3.4 Effects of Coding = 20
  3.5 Interrelationships Between Structures = 21
  3.6 Canonical Form of the Row-Linear Structure = 22
4. The Row-Linear and Concurrent Structures
  4.1 The Concurrent Structure = 24
  4.2 Characterization of a Row-Linear Structure : An Example = 25
  4.3 A Test for Concurrence = 28
  4.4 Point of Concurrence = 29
  4.5 Return to the Example = 30
  4.6 The Interdependence of and = 32
5. Graphical Representation of the Row-Linear Structure
  5.1 Introduction = 35
  5.2 The h Graph and the h' Graph = 35
  5.3 A Numerical Example = 36
  5.4 An Important Property of h and h' = 38
  5.5 Return to the Example = 39
  5.6 Discussion of an Artificial Example = 39
  Reference = 40
6. Some Analysis of Variance
  6.1 Introduction = 41
  6.2 A General Principle = 41
  6.3 Further Discussion of Table 5.1 = 42
  6.4 Further Discussion of Table 5.4 = 43
  References = 44
7. A General Representation of Two-Way Arrays
  7.1 Introduction = 45
  7.2 A Single Multiplicative Term = 45
  7.3 Algorithm for finding θ, ui and vj = 47
  7.4 The Complete Singular Value Decomposition = 48
  7.5 Approximations Made Possible by Singular Value Decomposition = 49
  7.6 The Biplot = 49
  7.7 Additive and Multiplicative Terms = 51
  References = 53
8. A Systematic Approach to the Analysis of Two-Way Arrays
  8.1 Introduction = 54
  8.2 Statistical Procedures = 54
  8.3 Further Discussion of Table 5.4 = 58
  Reference = 58
9. Two-Way Analysis with Replication Within Cells
  9.1 Introduction = 59
  9.2 Analysis of Replicated Two-Way Arrays = 59
  9.3 The k Statistic = 62
  Reference = 64
10. Interlaboratory Testing
  10.1 Introduction = 65
  10.2 Proficiency Studies = 65
  10.3 An Example of Proficiency Testing = 65
  10.4 Youden's Split-Level Analysis = 67
  10.5 An Alternative Analysis to Youden's Model = 69
  10.6 Analysis of the Example = 69
  10.7 The Study of a Test Method = 74
  10.8 The Determination of Beta-Carotene in Serum = 75
  References = 79
11. Missing Values
  11.1 Introduction = 80
  11.2 Theoretical Considerations = 80
  11.3 A Numerical Example = 81
  References = 84
12. Curve Fitting
  12.1 Introduction = 85
  12.2 The Box-Cox Tranformation = 86
  12.3 Procedure for Fitting the Quadratic Four Parameter Curve = 86
  12.4 First Numerical Example = 87
  12.5 A Second Example = 88
  12.6 Conclusion = 89
  References = 90
  Appendix : Fitting a Quadratic Function = 91
13. Two-Way Tables with Quantitative Labels
  13.1 Introduction = 93
  13.2 The Density of Aqueous Solutions of Alcohol = 94
  13.3 Conclusions = 99
  Reference = 99
14. Applications to Real Data Sets
  14.1 Introduction = 100
  14.2 Total Solids in Wet Brewers' Yeast = 101
  14.3 Absorption of Gamma Rays by Aluminum = 104
  14.4 Two Further Examples = 108
  14.5 Potassium and Chlorine in Serum = 114
  References = 120
15. One-Way Tables and the h Statistic
  15.1 Introduction = 121
  15.2 One-Way Tables = 121
  15.3 Iterative Weighting for One-Way Tables = 125
  References = 126
16. How Useful Are Models?
  16.1 Introduction = 127
  16.2 Data Reduction = 127
  16.3 Prediction = 128
  16.4 Linear Structures = 128
  16.5 Minimal Assumptions Analysis = 129
  16.6 Analysis of Variance = 129
  16.7 Graphical Results = 130
  16.8 Models and Logic = 131
  16.9 The Brightness of Shrink-wrapped Paper = 131
  16.10 Conclusions = 135
  Reference = 136