Experimental design, ANOVA, and regression:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Harper & Row
1987
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes index. - Bibliography: p. 497-500 |
| Physical Description: | XII, 508 S. |
| ISBN: | 0060414790 |
Staff View
MARC
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| adam_text |
Experimental Design,
ANOVA, and
Regression
Richard A _Damon, Jr
University of Massachusetts at Amherst
Walter R Harvey
The Ohio State University
HARPER amp; ROW, PUBLISHERS, New York
Cambridge, Philadelphia, San Francisco, Washington,
London, Mexico City, Sao Paulo, Singapore, Sydney
Contents
Preface xi
CHAPTER 1 REVIEW OF STATISTICAL CONCEPTS
AND DEFINITIONS 1
1 1 Introduction 1
1 2 Objectives 1
1 3 Common Definitions 2
1 4 Mathematical Models, Sigma, and Dot Notation
1 5 Descriptive Statistics and Parameters 5
151 Mean 5
152 Variance 6
755 Standard Deviation 1
154 Standard Error of the Mean 8
755 Confidence Interval 9
756 Coefficient of Variation 10
CHAPTER 2 ONE-WAY CLASSIFICATION OF DATA 12
2 1 Introduction 12 ,
2 2 Analysis of Variance (ANOVA) 12
2 3 One-Way Classification: Equal Numbers 14
2 4 One-Way Classification: Unequal Numbers 18
25t Test: Equal Numbers 21
26t Test: Unequal Numbers 23
Vi CONTENT!
27't Test: Unequal Variances 23
2 8 Nested Classification: Balanced Design 24
2 9 Nested Classification: Unbalanced Design 28
2 10 The Method of Least Squares 31
2 10 1 Introduction to Least-Squares Analysis 31
2 10 2 One-Way Classification: Equal or Unequal Numbers 31
CHAPTER 3 MULTIWAY CLASSIFICATION OF DATA 38
3 1 Introduction 38
3 2 Two-Way Classification: Single Observation per Subclass 44
3 3 Paired t Test 46
3 4 Two-Way Classification: Multiple Observations per Subclass 49
3 5 Interaction 52
3 6 Setting Up the Analysis of Variance Table in the Balanced Design 55
361 Notation 55
362 Determining the Possible Lines in the Analysis of Variance Table 5
363 Determining Degrees of Freedom 56
364 Computation of Sums of Squares in the Balanced Design 57
365 Rules for Computing a Mean Square 57
3 7 Combination of Main and Nested Classifications 58
3 8 Cross-Classified Equivalents of Nested Classifications 62
3 9 Fixed and Random Classifications 63
3 10 Fixed, Random, and Mixed Models 64
3 11 Expectations of Mean Squares: Balanced Design 64
5 77 7 Method of Calculation 64
3 11 2 Examples of the Calculation of the Expectations of Mean Squares 6
3 12 Two-Way Classification Using Dummy Variables 70
3 13 Assumptions Underlying the Analysis of Variance 75
3 14 Homogeneity of Variances 77
3 15 Tukey's Test for Nonadditivity 81
3 16 Transformations 84
3 16 1 Logarithmic Transformation 85
3 16 2 Arcsin Transformation 86
5 76 5 Square Root Transformation 88
3 17 Three-Way Classification: Single Observation per Subclass 90
3 18 Three-Way Classification: Multiple Observations per Subclass 92
3 19 Estimation and Use of Variance Components 95
3 19 1 Examples of Analyses Under Random Models 97
3 19 2 Analyses Under Mixed Models: Balanced Designs 103
3 20 Fixed Model Analysis: Disproportionate Subclass Frequencies 112
3 20 1 Two- Way Classification: No Interaction 114
3 20 2 Two-Way Classification: With Interaction 121
3 20 3 Multiway Classification 126
3 21 Mixed Model Analyses: Disproportionate Subclass Frequencies 129
5 27 7 Two- Way Classification: No Interaction 130
5 27 2 Two-Way Classification: With Interaction 140
CONTENTS Vii
CHAPTER 4 MEAN SEPARATION PROCEDURES 152
4 1 Introduction 152
4 2 Single Degree of Freedom Components or Comparisons:
Equal Numbers 15 3
4 3 Linear Functions and Comparisons 154
4 4 Orthogonality of Comparisons 155
4 5 Multiple Degree of Freedom Components 157
4 6 Standard Errors for Linear Functions of Treatment Means 159
4 7 Pairwise Comparisons of Treatment Means 164
471 Least Significant Difference 164
472 Duncan's New Multiple-Range Test 165
473 Student-Newman-Keuls (SNK) Test 169
474 Tukey 's w Procedure 170
475 Scheffe's Test 170
476 Dunnett 's Procedure: Testing Treatment Means Against
a Control 171
4 8 Trend Analysis 172
4 9 Selection of Procedure to Be Used 173
4 10 Comparison of Least-Squares Means: Disproportionate
Subclass Frequencies 173
4 10 1 Linear Comparisons: t Test 174
4 10 2 Approximate Mean Separation Procedures 179
CHAPTER 5 REGRESSION AND CORRELATION ANALYSES 185
5 1 Introduction 185
5 2 Linear Regression 185
527 Test of Significance of Linear Regression 188
522 Confidence Interval for the Regression Coefficient 191
523 Standard Error and Confidence Interval for a Subpopulation Mean
and Confidence Band About the Regression Line 192
524 Standard Error and Confidence Interval for a Predicted Value and
Confidence Band for Predicted Values 193
525 Test of Significance Between Two Linear Regression Lines or
Coefficients 194
526 Test of Significance Between Two Intercepts or Adjusted Means 195
527 Test of Significance Among Several Regression Lines 197
528 Test of Significance Among Several Intercepts or Adjusted Means 199
5 3 Correlation Coefficient 199
557 Test of Significance of the Correlation Coefficient 201
532 Confidence Interval for the Correlation Coefficient 203
533 Test of Significance Between Two Correlation Coefficients 204
534 Test of Significance for Homogeneity of Correlation Coefficients 205
5 4 Coefficient of Determination 206
5 5 Quadratic Regression 206
557 Method of Calculation 207
552 Test for the Significance of Quadratic Regression 209
Viii CONTENTS
5 6 Cubic Regression 211
567 Method of Calculation 211
562 Test for the Significance of Cubic Regression 213
5 7 Linear Regression Through Treatment Means 214
577 Method of Calculation 214
572 Test for the Significance of Linear Regression Through
Treatment Means 215
5 8 Curvilinear Regression Through Treatment Means 217
581 Method of Calculation 217
582 Test for the Significance of Curvilinear Regression Through Treatment
Means 219
5 9 Orthogonal Polynomial Coefficients 222
597 Prediction Equations Using Orthogonal Polynomial Coefficients 225
592 Conversion from Orthogonal Polynomial Prediction Equation to
Nonorthogonal Prediction Equation 226
593 Orthogonal Polynomial Coefficients with Unequal Intervals 228
594 Orthogonal Polynomial Coefficients with Unequal Numbers in the
• One-Way Classification 229
5 10 Multiple Regression 233
5 70 7 Tests of Significance in Multiple Regression 236
5 70 2 Tests of Significance for Partial Regression Coefficients 238
5 70 5 Tests of Significance Among Partial Regression Coefficients 240
5 11 Elimination of One or More Independent Variables 240
5 12 Interaction of Independent Variables in Multiple Regression 241
5 13 Partial and Multiple Correlation 244
5 14 Relationship of Regression Analysis to the Analysis of Variance 247
5 14 1 Prediction Using the Analysis of Variance 247
5 14 2 Prediction Using Nonorthogonal Polynomial Coefficients as
Dummy Variables 248
5 14 3 Prediction Using Orthogonal Polynomial Coefficients as
Dummy Variables 252
5 15 Decision on Final Multiple Regression Model 255
5 16 Discriminant Function 256
5 17 Curve Fitting to Least-Squares Means: Disproportionate Subclass
Frequencies and Unequal Intervals 261
5 17 1 Fitting the Linear Regression 262
5772 General Polynomial Fitting 263
5 77 5 Illustration of Computing Procedures 264
5 18 General Surface Fitting Procedures 267
CHAPTER 6 EXPERIMENTAL DESIGNS 280
6 1 Introduction 280
6 2 Completely Randomized Design 281
6 3 Randomized Block Design 282
6 4 Gain in Efficiency: Randomized Block Versus Completely
Randomized Design 284
ENTS IX
6 5 Missing Values in the Randomized Block Design 285
6 6 Latin Square Design 288
6 7 Orthogonal Latin Squares 292
6 8 Randomization in the Latin Square 298
6 9 Gain in Efficiency: Latin Square Versus Randomized Block 299
6 10 Missing Values in the Latin Square 300
6 11 Graeco-Latin Square 301
6 12 Changeover Design to Measure Residual Effects 303
6 13 Crossover Design 308
6 14 Other Designs 313
6 15 Factorial Experiments 314
CHAPTER 7 SPLIT-PLOT DESIGNS 317
7 1 Introduction 317
7 2 Completely Randomized Split-Plot Design 322
7 3 Factorial Split-Plot Design 331
7 4 Randomized Block, Factorial Split-Plot Design 337
7 5 Randomized Block, Split-Plot Design: Multiple Observations 342
7 6 Latin Square Split-Plot Design 348
7 7 Crossover Split-Plot Design 354
7 8 Crossover Split-Split-Plot Design 360
7 9 Analysis of Data from Split-Plot Designs: Disproportionate
Subclass Frequencies' 362
797 Completely Randomized Split-Plot Design 364
792 Completely Randomized Split-Plot Design: Multiple Observations 368
793 Randomized Block, Split-Plot Design 376
CHAPTER 8 ANALYSIS OF COVARIANCE 389
8 1 Introduction 389
8 2 One-Way Classification: Analysis of Covariance 390
8 3 Covariance with Curvilinear Regression 395
8 4 One-Way Classification: Split-Plot Design 398
8 5 One-Way Classification: Split-Plot Design and Single Covariate
per Whole Plot 403
8 6 Covariance with Latin Square and Crossover Designs 406
8 7 Multiple Covariance 407 •,
8 8 Covariance Analysis with Disproportionate Subclass Frequencies 411
8 9 Individual Class and/or Subclass Regressions 416
t
CHAPTER 9 MATRIX ALGEBRA 423
9 1 Introduction 423
9 2 Definition 423
9 3 Order 424
9 4 Coefficient Matrix 424
CONTENTS
9 5 Vector 424
9 6 Addition of Matrices 424
9 7 Subtraction of Matrices 424
9 8 Scalar Multiplication 425
9 9 Multiplication 425
9 10 Element by Element Multiplication 426
9 11 Transpose of a Matrix 426
9 12 Trace 426
9 13 Symmetric Matrix 426
9 14 Identity Matrix 427
9 15 Matrix Inversion 427
9 16 Solution of Equations 432
9 17 Necessity for Restrictions or Constraints 434
9 18 Inversion of Special Matrices 435
9 19 Inversion by Partitioning 436
Appendix 441
Solutions 471
References 497
Index 501
o |
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| spelling | Damon, Richard A. Verfasser aut Experimental design, ANOVA, and regression Richard A. Damon, Jr., Walter R. Harvey New York [u.a.] Harper & Row 1987 XII, 508 S. txt rdacontent n rdamedia nc rdacarrier Includes index. - Bibliography: p. 497-500 Biometry Versuchsplan (DE-588)4480816-1 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Varianzanalyse (DE-588)4187413-4 gnd rswk-swf Versuchsplanung (DE-588)4078859-3 gnd rswk-swf Versuchsplanung (DE-588)4078859-3 s DE-604 Versuchsplan (DE-588)4480816-1 s Varianzanalyse (DE-588)4187413-4 s Regressionsanalyse (DE-588)4129903-6 s Harvey, Walter Robert Sonstige oth HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010315071&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Damon, Richard A. Experimental design, ANOVA, and regression Biometry Versuchsplan (DE-588)4480816-1 gnd Regressionsanalyse (DE-588)4129903-6 gnd Varianzanalyse (DE-588)4187413-4 gnd Versuchsplanung (DE-588)4078859-3 gnd |
| subject_GND | (DE-588)4480816-1 (DE-588)4129903-6 (DE-588)4187413-4 (DE-588)4078859-3 |
| title | Experimental design, ANOVA, and regression |
| title_auth | Experimental design, ANOVA, and regression |
| title_exact_search | Experimental design, ANOVA, and regression |
| title_full | Experimental design, ANOVA, and regression Richard A. Damon, Jr., Walter R. Harvey |
| title_fullStr | Experimental design, ANOVA, and regression Richard A. Damon, Jr., Walter R. Harvey |
| title_full_unstemmed | Experimental design, ANOVA, and regression Richard A. Damon, Jr., Walter R. Harvey |
| title_short | Experimental design, ANOVA, and regression |
| title_sort | experimental design anova and regression |
| topic | Biometry Versuchsplan (DE-588)4480816-1 gnd Regressionsanalyse (DE-588)4129903-6 gnd Varianzanalyse (DE-588)4187413-4 gnd Versuchsplanung (DE-588)4078859-3 gnd |
| topic_facet | Biometry Versuchsplan Regressionsanalyse Varianzanalyse Versuchsplanung |
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