1 INTRODUCTION 1
1．1 The Contribution of Statistics to Experimentation 1
1．2 Initial Steps in the Planning of Experiments 9
References 14
2 METHODS FOR INCREASING THE ACCURACY OF EXPERIMENTS 15
2．1 Introduction 15
2．2 Number of Replications 17
2．3 Other Methods for Increasing Accuracy 31
2．4 The Grouping of Experimental Units 41
References 43
3 NOTES ON THE STATISTICAL ANALYSIS OF THE RESULTS 45
3．1 Introduction 45
3．2 The General Method of Analysis 45
3．3 Accuracy in Computations 58
3．4 Subdivision of the Sum of Squares for Treatments 61
3．5 Calculation of Standard Errors for Comparisons among Treatment Means 70
3．6 Subdivision of the Sum of Squares for Error 77
3．7 Missing Date 80
3．8 The Analysis o f Covaiance 82
3．9 Effects of Errors in the Assumptions Underlying the Analysis of Variance 91
References 92
4 COMPLETELY RANDOMIZED,RANDOMIZED BLOCK,AND LATIN SQUARE DESIGNS 95
4．1 Completely Randomized Designs 95
4．2 Single Grouping:Randomized Blocks 95
4．3 Double Grouping:Latin Squares 117
4．4 Cross-over Designs 127
4．5 Triple Grouping:Graeco-latin Squares 132
4．6a Designs for Estimating Residual Effects When Treatments Are Applied in Sequence 133
References 142
Plans 145
5 FACTORIAL EXPERIMENTS 148
5．1 Description 148
5．2 Calculation of Main Effects and Interactions 153
5．3 Designs for Factorial Experiments 175
References 181
6 CONFOUNDING 183
6．1 The Principle of Confounding 183
6．2 The Use of Confounded Designs 212
6．3 Notes on the Plans and Statistical Analysis 219
References 232
Plans 234
6A FACTORIAL EXPERIMENTS IN FRACTIONAL REPLICATION 244
6A．1 Construction and Properties of Fractionally Replicated Designs 244
6A．2 The Use of Fractional Factorial Designs in Practice 259
6A．3 Designs with Factors at More Than Two Levels 270
References 275
Plans 276
7 FACTORIAL EXPERIMENTS WITH MAIN EFFECTS CONFOUNDED:SPLITPLOT DESIGNS 293
7．1 The Simple Split-plot Design 293
7．2 Repeated Subdivision 304
7．3 Some Variants of the Split-plot Design 305
References 315
8 FACTORIAL EXPERIMENTS CONFOUNDEN IN QUASI-LATIN SQUARES 317
8．1 Introduction 317
8．2 Randomization of Quasi-latin Squares 317
8．3 Notes on the Plans and Statistical Analysis 318
8．4 Other Quasi-latin Squares 322
8．5 Estimation of the Efficiency of Quasi-latin Squares 323
8．6 Treatments Applied to Complete Rows of a Latin Square 324
8．7 Treatments Applied to Complete Rows and Columns of a Latin Square 327
References 327
Plans 328
8A SOME METHODS FOR THE STUDY OF RESPONSE SURFACES 335
8A．1 First Order Designs 335
8A．2 Second Order Designs 342
8A．3 Methods for Determining the Optimum Combination of Factor Levels 354
8A．4 The Single-factor Method 356
8A．5 The Method of Steepest Ascent 357
8A．6 Summary Comments 365
References 369
Plans 370
9 INCOMPLETE BLOCK DESIGNS 376
9．1 Balanced Designs 376
9．2 Partially Balanced Designs 378
9．3 Basis of the Statistical Analysis 380
9．4 Comparison of Incomplete Block and Randomized Block Designs 385
9．5 Comparisons with Other Designs 387
9．6 Choice of Incomplete Block Design 388
References 394
10 LATTICE DESIGNS 396
10．1 Balanced Lattices 396
10．2 Partially Balanced Lattices 403
10．3 Rectangular Lattices 415
10．4 Cubic Lattices 422
References 426
Plans 428
11 BALANCED AND PARTIALLY BALANCED INCOMPLETE BLOCK DESIGNS 439
11．1 Balanced Incomplete Blocks 439
11．1a Balanced Incomplete Blocks in Taste and Preference Testing 440
11．2 Comparisons with Other Designs 441
11．3 Arrangement of Experimental Material 442
11．4 Randomization 442
11．5 Statistical Analysis 443
11．6a Partially Balanced Incomplete Block Designs 453
11．7a Chain Block Designs 463
References 468
Plans 469
12 LATTICE SQUARES 483
12．1 Description 483
12．2 Statistical Analysis 485
References 497
Plans 497
13 INCOMPLETE LATIN SQUARES 507
13．1 Description 507
13．2 Statistical Analysis 508
13．3 Other Designs for Small Numbers of Treatments 513
13．4a Partially Balanced Designs 518
References 519
Plans 520
14 ANALYSIS OF THE RESULTS OF A SERIES OF EXPERIMENTS 545
14．1 Initial Steps in the Analysis 545
14．2 Criticisms of the Preliminary Analysis 550
14．3 Experiments of Unequal Size 555
14．4 A Test of the Treatments × Places Interactions 561
14．5 Repetitions in Both Space and Time 565
References 567
15 RANDOM PERMUTATIONS OF 9 AND 16 NUMBERS 569
15．1 Use of the Random Permutations 569
15．2 Construction of the Random Permutations 569
15．3 Randomization of More than 16 Numbers 571
15．4 Tests of Randomness 571
References 576
15．5 Tables of Random Permutations 577
Permutations of 9 577
Permutations of 16 583
SELECTED BIBLIOGRAPHY 597
LIST OF AUTHOR REFERENCES 599
INDEX 603
TABLES OF t AND F 613