The Analysis of Variance

Name: The Analysis of Variance
Author: Henry Scheffé, Henry Scheffé
ISBN: 9780471345053

by Henry Scheffé, Henry Scheffé

item #72 in the Wiley Classics Library

Paperback

The Analysis of Variance

by Henry Scheffé, Henry Scheffé

item #72 in the Wiley Classics Library

Paperback

Overview

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.

FormatPaperback

LanguageEnglish

PublisherWiley & Sons, Incorporated, John

Publication DateMar. 5th, 1999

Pages477

ISBN-139780471345053

Dimensions5.98 x 8.98 x 1.19 inches

ISBN-100471345059

Shipping Weight1.60 lbs

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The Analysis of Variance in the Case of Models with Fixed Effects and Independent Observations of Equal Variance
Point Estimation
Introduction	p. 3
Mathematical models	p. 4
Least-squares estimates and normal equations	p. 8
Estimable functions. The Gauss-Markoff theorem	p. 13
Reduction of the case where the observations have known correlations and known ratios of variances	p. 19
The canonical form of the underlying assumptions [Omega]. The mean square for error	p. 21
Problems	p. 24
Construction of Confidence Ellipsoids and Tests in the General Case Under Normal Theory
Underlying assumptions [Omega] and distribution of point estimates under [Omega]	p. 25
Notation for certain tabled distributions	p. 27
Confidence ellipsoids and confidence intervals for estimable functions	p. 28
Test of hypothesis H derived from confidence ellipsoid	p. 31
Test derived from likelihood ratio. The statistic J	p. 32
Canonical form of [Omega] and H. Distribution of J	p. 37
Equivalence of the two tests	p. 39
Charts and tables for the power of the F-test	p. 41
Geometric interpretation of J. Orthogonality relations	p. 42
Optimum properties of the F-test	p. 46
Problems	p. 51
The One-Way Layout. Multiple Comparison
The one-way layout	p. 55
An illustration of the theory of estimable functions	p. 60
An example of power calculations	p. 62
Contrasts. The S-method of judging all contrasts	p. 66
The S-method of multiple comparison, general case	p. 68
The T-method of multiple comparison	p. 73
Comparison of the S- and T-methods. Other multiple-comparison methods	p. 75
Comparison of variances	p. 83
Problems	p. 87
The Complete Two, Three, and Higher-Way Layouts. Partitioning a Sum of Squares
The two-way layout. Interaction	p. 90
The two-way layout with one observation per cell	p. 98
The two-way layout with equal numbers of observations in the cells	p. 106
The two-way layout with unequal numbers of observations in the cells	p. 112
The three-way layout	p. 119
Formal analysis of variance. Partition of the total sum of squares	p. 124
Partitioning a sum of squares more generally	p. 127
Interactions in the two-way layout with one observation per cell	p. 129
Problems	p. 137
Some Incomplete Layouts: Latin Squares, Incomplete Blocks, and Nested Designs
Latin squares	p. 147
Incomplete blocks	p. 160
Nested designs	p. 178
Problems	p. 188
The Analysis of Covariance
Introduction	p. 192
Deriving the formulas for an analysis of covariance from those for a corresponding analysis of variance	p. 199
An example with one concomitant variable	p. 207
An example with two concomitant variables	p. 209
Linear regression on controlled variables subject to error	p. 213
Problems	p. 216
The Analysis of Variance in the Case of Other Models
Random-Effects Models
Introduction	p. 221
The one-way layout	p. 221
Allocation of measurements	p. 236
The complete two-way layout	p. 238
The complete three- and higher-way layouts	p. 245
A nested design	p. 248
Problems	p. 258
Mixed Models
A mixed model for the two-way layout	p. 261
Mixed models for higher-way layouts	p. 274
Problems	p. 289
Randomization Models
Randomized blocks: estimation	p. 291
Latin squares: estimation	p. 304
Permutation tests	p. 313
Problems	p. 329
The Effects of Departures from the Underlying Assumptions
Introduction	p. 331
Some elementary calculations of the effects of departures	p. 334
More on the effects of nonnormality	p. 345
More on the effects of inequality of variance	p. 351
More on the effects of statistical dependence	p. 359
Conclusions	p. 360
Transformations of the observations	p. 364
Problems	p. 368
Appendices
Vector algebra	p. 371
Problems	p. 385
Matrix algebra	p. 387
Problems	p. 401
Ellipsoids and their planes of support	p. 406
Problems	p. 410
Noncentral X[superscript 2], F, and t	p. 412
Problems	p. 415
The multivariate normal distribution	p. 416
Problems	p. 418
Cochran's theorem	p. 419
Problems	p. 423
F-Tables	p. 424
Studentized Range Tables	p. 434
Pearson and Hartley Charts for the Power of the F-Test	p. 438
Fox Charts for the Power of the F-Test	p. 446
Author Index and Bibliography	p. 457
Subject Index	p. 467
Table of Contents provided by Syndetics. All Rights Reserved.

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Overview

Product Details

FormatPaperback

LanguageEnglish

PublisherWiley & Sons, Incorporated, John

Publication DateMar. 5th, 1999

Pages477

ISBN-139780471345053

Dimensions5.98 x 8.98 x 1.19 inches

ISBN-100471345059

Shipping Weight1.60 lbs

The Analysis of Variance in the Case of Models with Fixed Effects and Independent Observations of Equal Variance
Point Estimation
Introduction	p. 3
Mathematical models	p. 4
Least-squares estimates and normal equations	p. 8
Estimable functions. The Gauss-Markoff theorem	p. 13
Reduction of the case where the observations have known correlations and known ratios of variances	p. 19
The canonical form of the underlying assumptions [Omega]. The mean square for error	p. 21
Problems	p. 24
Construction of Confidence Ellipsoids and Tests in the General Case Under Normal Theory
Underlying assumptions [Omega] and distribution of point estimates under [Omega]	p. 25
Notation for certain tabled distributions	p. 27
Confidence ellipsoids and confidence intervals for estimable functions	p. 28
Test of hypothesis H derived from confidence ellipsoid	p. 31
Test derived from likelihood ratio. The statistic J	p. 32
Canonical form of [Omega] and H. Distribution of J	p. 37
Equivalence of the two tests	p. 39
Charts and tables for the power of the F-test	p. 41
Geometric interpretation of J. Orthogonality relations	p. 42
Optimum properties of the F-test	p. 46
Problems	p. 51
The One-Way Layout. Multiple Comparison
The one-way layout	p. 55
An illustration of the theory of estimable functions	p. 60
An example of power calculations	p. 62
Contrasts. The S-method of judging all contrasts	p. 66
The S-method of multiple comparison, general case	p. 68
The T-method of multiple comparison	p. 73
Comparison of the S- and T-methods. Other multiple-comparison methods	p. 75
Comparison of variances	p. 83
Problems	p. 87
The Complete Two, Three, and Higher-Way Layouts. Partitioning a Sum of Squares
The two-way layout. Interaction	p. 90
The two-way layout with one observation per cell	p. 98
The two-way layout with equal numbers of observations in the cells	p. 106
The two-way layout with unequal numbers of observations in the cells	p. 112
The three-way layout	p. 119
Formal analysis of variance. Partition of the total sum of squares	p. 124
Partitioning a sum of squares more generally	p. 127
Interactions in the two-way layout with one observation per cell	p. 129
Problems	p. 137
Some Incomplete Layouts: Latin Squares, Incomplete Blocks, and Nested Designs
Latin squares	p. 147
Incomplete blocks	p. 160
Nested designs	p. 178
Problems	p. 188
The Analysis of Covariance
Introduction	p. 192
Deriving the formulas for an analysis of covariance from those for a corresponding analysis of variance	p. 199
An example with one concomitant variable	p. 207
An example with two concomitant variables	p. 209
Linear regression on controlled variables subject to error	p. 213
Problems	p. 216
The Analysis of Variance in the Case of Other Models
Random-Effects Models
Introduction	p. 221
The one-way layout	p. 221
Allocation of measurements	p. 236
The complete two-way layout	p. 238
The complete three- and higher-way layouts	p. 245
A nested design	p. 248
Problems	p. 258
Mixed Models
A mixed model for the two-way layout	p. 261
Mixed models for higher-way layouts	p. 274
Problems	p. 289
Randomization Models
Randomized blocks: estimation	p. 291
Latin squares: estimation	p. 304
Permutation tests	p. 313
Problems	p. 329
The Effects of Departures from the Underlying Assumptions
Introduction	p. 331
Some elementary calculations of the effects of departures	p. 334
More on the effects of nonnormality	p. 345
More on the effects of inequality of variance	p. 351
More on the effects of statistical dependence	p. 359
Conclusions	p. 360
Transformations of the observations	p. 364
Problems	p. 368
Appendices
Vector algebra	p. 371
Problems	p. 385
Matrix algebra	p. 387
Problems	p. 401
Ellipsoids and their planes of support	p. 406
Problems	p. 410
Noncentral X[superscript 2], F, and t	p. 412
Problems	p. 415
The multivariate normal distribution	p. 416
Problems	p. 418
Cochran's theorem	p. 419
Problems	p. 423
F-Tables	p. 424
Studentized Range Tables	p. 434
Pearson and Hartley Charts for the Power of the F-Test	p. 438
Fox Charts for the Power of the F-Test	p. 446
Author Index and Bibliography	p. 457
Subject Index	p. 467
Table of Contents provided by Syndetics. All Rights Reserved.

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