| Preface |
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vii | |
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Chapter 1 Introduction and Preliminary Results |
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1 | (12) |
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1.1 Introduction: Elementary Statistical Notions |
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1 | (1) |
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1.2 Sampling Distributions |
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2 | (2) |
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4 | (3) |
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1.4 Methods of Estimation |
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7 | (1) |
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8 | (1) |
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1.6 Linear Functions of Normally Distributed Variables |
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9 | (1) |
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10 | (3) |
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Chapter 2 Theory of Linear Estimation |
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13 | (40) |
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2.1 Basic Assumptions and Definition of Least Squares |
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13 | (8) |
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2.2 Linear Functions with Zero Expectation |
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21 | (2) |
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23 | (4) |
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27 | (4) |
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2.5 Observational Equations with Linear Restrictions On The Parameters |
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31 | (22) |
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Chapter 3 Analysis of Variance |
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53 | (76) |
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3.1 Fundamental Principles |
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54 | (6) |
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3.2 Partitioning of Sums of Squares and Degrees of Freedom |
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60 | (5) |
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65 | (1) |
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3.4 Assumptions Underlying the Analysis of Variance |
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65 | (3) |
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3.5 Analysis of Variance in the Case of Regression |
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68 | (3) |
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3.6 One--Way Classification |
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71 | (6) |
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3.7 Two--Way Classification with a Single Observation per Cell |
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77 | (7) |
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3.8 Testing of Individual Hypotheses |
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84 | (2) |
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86 | (1) |
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3.10 Two-Way Classification with Multiple but Equal Number of Observations in Cells |
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86 | (7) |
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3.11 Two-Way Classification with Multiple and Unequal Number of Observations in Cells |
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93 | (6) |
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3.12 Matrix Methods (when there is no interaction) |
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99 | (5) |
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3.13 Case of Proportional Frequencies |
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104 | (3) |
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3.14 Three-Way Classification |
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107 | (6) |
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3.15 Randomized Block Design (RBD) |
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113 | (5) |
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3.16 Judging the Relative Merits of Treatment |
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118 | (1) |
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3.17 Confidence Limits for Treatment Differences |
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118 | (1) |
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119 | (1) |
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120 | (4) |
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3.20 Judging the Relative Merits of Treatments |
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124 | (1) |
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125 | (3) |
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3.22 Hyper -- Graeco Latin Square |
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128 | (1) |
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Chapter 4 Analysis of Covariance (ANCOVA) |
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129 | (12) |
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4.1 One-Way Classification with a Single Concomitant Variable |
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129 | (5) |
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4.2 Two-Way Classification with One Observation per Cell and a Single Concomitant Variable |
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134 | (4) |
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4.3 Some Examples of ANCOVA |
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138 | (3) |
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Chapter 5 Missing and Mixed Plots |
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141 | (16) |
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5.1 Two-Way Classification with One Cell Missing |
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141 | (3) |
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5.2 Two-Way Classification with Two Missing Plots |
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144 | (1) |
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5.3 K-Missing Plots: Yates' Method |
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145 | (1) |
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5.4 Bartlett's Method: Use of Concomitant Variables |
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146 | (2) |
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148 | (3) |
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151 | (6) |
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Chapter 6 Balanced Incomplete Block Designs |
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157 | (34) |
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157 | (2) |
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6.2 Symmetrical Balanced Incomplete Blocks |
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159 | (2) |
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6.3 Resolvable Balanced Incomplete Blocks |
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161 | (3) |
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6.4 Affine Resolvable Balanced Incomplete Blocks |
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164 | (1) |
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165 | (1) |
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6.6 Analysis of BIBD Experiment |
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166 | (16) |
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182 | (3) |
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6.8 Principle of Connectedness |
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185 | (6) |
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Chapter 7 Factorial Designs |
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191 | (52) |
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191 | (13) |
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204 | (5) |
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7.3 Confounding in Factorial Designs |
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209 | (3) |
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7.4 23 Factorial Experiment |
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212 | (17) |
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7.5 Fractional Replications |
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229 | (2) |
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7.6 Confounding in Latin Squares |
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231 | (2) |
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233 | (10) |
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Chapter 8 Elements of Modern Algebra |
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243 | (22) |
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243 | (9) |
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252 | (1) |
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253 | (9) |
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8.4 Cyclotomic Polynomial |
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262 | (3) |
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Chapter 9 Construction of Designs |
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265 | (30) |
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9.1 Orthogonal Latin Squares |
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265 | (9) |
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9.2 Construction of BIBD's |
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274 | (6) |
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9.3 Geometric Method (Finite Projective Geometry) |
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280 | (3) |
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9.4 Finite Euclidean Geometry |
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283 | (12) |
| Index |
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295 | |
