The analysis of variance / Henry Scheffé.

Format:

Book

Author/Creator:

Scheffé, Henry, 1907-1977.

Contributor:

Hazel M. Hussong Fund.

Series:

Wiley publication in mathematical statistics

A Wiley publication in mathematical statistics

Language:

English

Subjects (All):

Analysis of variance.

Analysis of Variance.

Medical Subjects:

Analysis of Variance.

Physical Description:

xvi, 477 pages : illustrations ; 23 cm.

Edition:

Wiley classics library edition.

Place of Publication:

New York : Wiley-Interscience Publication, 1999.

Summary:

Originally published in 1959, this classic volume has had a major impact on generations of statisticians. Newly issued in the Wiley Classics Series, the book examines the basic theory of analysis of variance by considering several different mathematical models. Part I looks at the theory of fixed-effects models with independent observations of equal variance, while Part II begins to explore the analysis of variance in the case of other models.

Contents:

Part I. The Analysis of Variance in the Case of Models with Fixed Effects and Independent Observations of Equal Variance

Chapter 1 Point Estimation

1.2 Mathematical models 4

1.3 Least-squares estimates and normal equations 8

1.4 Estimable functions. The Gauss-Markoff theorem 13

1.5 Reduction of the case where the observations have known correlations and known ratios of variances 19

1.6 The canonical form of the underlying assumptions [Omega]. The mean square for error 21

Chapter 2 Construction of Confidence Ellipsoids and Tests in the General Case Under Normal Theory

2.1 Underlying assumptions [Omega] and distribution of point estimates under [Omega] 25

2.2 Notation for certain tabled distributions 27

2.3 Confidence ellipsoids and confidence intervals for estimable functions 28

2.4 Test of hypothesis H derived from confidence ellipsoid 31

2.5 Test derived from likelihood ratio. The statistic J 32

2.6 Canonical form of [Omega] and H. Distribution of J 37

2.7 Equivalence of the two tests 39

2.8 Charts and tables for the power of the F-test 41

2.9 Geometric interpretation of J. Orthogonality relations 42

2.10 Optimum properties of the F-test 46

Chapter 3 The One-Way Layout. Multiple Comparison

3.1 The one-way layout 55

3.2 An illustration of the theory of estimable functions 60

3.3 An example of power calculations 62

3.4 Contrasts. The S-method of judging all contrasts 66

3.5 The S-method of multiple comparison, general case 68

3.6 The T-method of multiple comparison 73

3.7 Comparison of the S- and T-methods. Other multiple-comparison methods 75

3.8 Comparison of variances 83

Chapter 4 The Complete Two, Three, and Higher-Way Layouts. Partitioning a Sum of Squares

4.1 The two-way layout. Interaction 90

4.2 The two-way layout with one observation per cell 98

4.3 The two-way layout with equal numbers of observations in the cells 106

4.4 The two-way layout with unequal numbers of observations in the cells 112

4.5 The three-way layout 119

4.6 Formal analysis of variance. Partition of the total sum of squares 124

4.7 Partitioning a sum of squares more generally 127

4.8 Interactions in the two-way layout with one observation per cell 129

Chapter 5 Some Incomplete Layouts: Latin Squares, Incomplete Blocks, and Nested Designs

5.1 Latin squares 147

5.2 Incomplete blocks 160

5.3 Nested designs 178

Chapter 6 The Analysis of Covariance

6.2 Deriving the formulas for an analysis of covariance from those for a corresponding analysis of variance 199

6.3 An example with one concomitant variable 207

6.4 An example with two concomitant variables 209

6.5 Linear regression on controlled variables subject to error 213

Part II. The Analysis of Variance in the Case of Other Models

Chapter 7 Random-Effects Models

7.2 The one-way layout 221

7.3 Allocation of measurements 236

7.4 The complete two-way layout 238

7.5 The complete three- and higher-way layouts 245

7.6 A nested design 248

Chapter 8 Mixed Models

8.1 A mixed model for the two-way layout 261

8.2 Mixed models for higher-way layouts 274

Chapter 9 Randomization Models

9.1 Randomized blocks: estimation 291

9.2 Latin squares: estimation 304

9.3 Permutation tests 313

Chapter 10 The Effects of Departures from the Underlying Assumptions

10.2 Some elementary calculations of the effects of departures 334

10.3 More on the effects of nonnormality 345

10.4 More on the effects of inequality of variance 351

10.5 More on the effects of statistical dependence 359

10.7 Transformations of the observations 364

I Vector algebra 371

II Matrix algebra 387

III Ellipsoids and their planes of support 406

IV Noncentral X[superscript 2], F, and t 412

V The multivariate normal distribution 416

VI Cochran's theorem 419

F-Tables 424

Studentized Range Tables 434

Pearson and Hartley Charts for the Power of the F-Test 438

Fox Charts for the Power of the F-Test 446.

Notes:

Includes bibliographical references (pages 457-465) and indexes.

Local Notes:

Acquired for the Penn Libraries with assistance from the Hazel M. Hussong Fund.

ISBN:

0471345059

0471758345

OCLC:

41565462

Online:

Publisher description

Table of Contents