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1 INTRODUCTION1

1．1 The Contribution of Statistics to Experimentation1

1．2 Initial Steps in the Planning of Experiments9

References14

2 METHODS FOR INCREASING THE ACCURACY OF EXPERIMENTS15

2．1 Introduction15

2．2 Number of Replications17

2．3 Other Methods for Increasing Accuracy31

2．4 The Grouping of Experimental Units41

References43

3 NOTES ON THE STATISTICAL ANALYSIS OF THE RESULTS45

3．1 Introduction45

3．2 The General Method of Analysis45

3．3 Accuracy in Computations58

3．4 Subdivision of the Sum of Squares for Treatments61

3．5 Calculation of Standard Errors for Comparisons among Treatment Means70

3．6 Subdivision of the Sum of Squares for Error77

3．7 Missing Date80

3．8 The Analysis o f Covaiance82

3．9 Effects of Errors in the Assumptions Underlying the Analysis of Variance91

References92

4 COMPLETELY RANDOMIZED,RANDOMIZED BLOCK,AND LATIN SQUARE DESIGNS95

4．1 Completely Randomized Designs95

4．2 Single Grouping:Randomized Blocks95

4．3 Double Grouping:Latin Squares117

4．4 Cross-over Designs127

4．5 Triple Grouping:Graeco-latin Squares132

4．6a Designs for Estimating Residual Effects When Treatments Are Applied in Sequence133

References142

Plans145

5 FACTORIAL EXPERIMENTS148

5．1 Description148

5．2 Calculation of Main Effects and Interactions153

5．3 Designs for Factorial Experiments175

References181

6 CONFOUNDING183

6．1 The Principle of Confounding183

6．2 The Use of Confounded Designs212

6．3 Notes on the Plans and Statistical Analysis219

References232

Plans234

6A FACTORIAL EXPERIMENTS IN FRACTIONAL REPLICATION244

6A．1 Construction and Properties of Fractionally Replicated Designs244

6A．2 The Use of Fractional Factorial Designs in Practice259

6A．3 Designs with Factors at More Than Two Levels270

References275

Plans276

7 FACTORIAL EXPERIMENTS WITH MAIN EFFECTS CONFOUNDED:SPLITPLOT DESIGNS293

7．1 The Simple Split-plot Design293

7．2 Repeated Subdivision304

7．3 Some Variants of the Split-plot Design305

References315

8 FACTORIAL EXPERIMENTS CONFOUNDEN IN QUASI-LATIN SQUARES317

8．1 Introduction317

8．2 Randomization of Quasi-latin Squares317

8．3 Notes on the Plans and Statistical Analysis318

8．4 Other Quasi-latin Squares322

8．5 Estimation of the Efficiency of Quasi-latin Squares323

8．6 Treatments Applied to Complete Rows of a Latin Square324

8．7 Treatments Applied to Complete Rows and Columns of a Latin Square327

References327

Plans328

8A SOME METHODS FOR THE STUDY OF RESPONSE SURFACES335

8A．1 First Order Designs335

8A．2 Second Order Designs342

8A．3 Methods for Determining the Optimum Combination of Factor Levels354

8A．4 The Single-factor Method356

8A．5 The Method of Steepest Ascent357

8A．6 Summary Comments365

References369

Plans370

9 INCOMPLETE BLOCK DESIGNS376

9．1 Balanced Designs376

9．2 Partially Balanced Designs378

9．3 Basis of the Statistical Analysis380

9．4 Comparison of Incomplete Block and Randomized Block Designs385

9．5 Comparisons with Other Designs387

9．6 Choice of Incomplete Block Design388

References394

10 LATTICE DESIGNS396

10．1 Balanced Lattices396

10．2 Partially Balanced Lattices403

10．3 Rectangular Lattices415

10．4 Cubic Lattices422

References426

Plans428

11 BALANCED AND PARTIALLY BALANCED INCOMPLETE BLOCK DESIGNS439

11．1 Balanced Incomplete Blocks439

11．1a Balanced Incomplete Blocks in Taste and Preference Testing440

11．2 Comparisons with Other Designs441

11．3 Arrangement of Experimental Material442

11．4 Randomization442

11．5 Statistical Analysis443

11．6a Partially Balanced Incomplete Block Designs453

11．7a Chain Block Designs463

References468

Plans469

12 LATTICE SQUARES483

12．1 Description483

12．2 Statistical Analysis485

References497

Plans497

13 INCOMPLETE LATIN SQUARES507

13．1 Description507

13．2 Statistical Analysis508

13．3 Other Designs for Small Numbers of Treatments513

13．4a Partially Balanced Designs518

References519

Plans520

14 ANALYSIS OF THE RESULTS OF A SERIES OF EXPERIMENTS545

14．1 Initial Steps in the Analysis545

14．2 Criticisms of the Preliminary Analysis550

14．3 Experiments of Unequal Size555

14．4 A Test of the Treatments × Places Interactions561

14．5 Repetitions in Both Space and Time565

References567

15 RANDOM PERMUTATIONS OF 9 AND 16 NUMBERS569

15．1 Use of the Random Permutations569

15．2 Construction of the Random Permutations569

15．3 Randomization of More than 16 Numbers571

15．4 Tests of Randomness571

References576

15．5 Tables of Random Permutations577

Permutations of 9577

Permutations of 16583

SELECTED BIBLIOGRAPHY597

LIST OF AUTHOR REFERENCES599

INDEX603

TABLES OF t AND F613