Experimental designs / 2nd ed.

Table Of Contents:

Introduction 1(14)

The Contribution of Statistics to Experimentation 1(8)

Initial Steps in the Planning of Experiments 9(6)

References 14(1)

Methods for Increasing the Accuracy of Experiments 15(30)

Introduction 15(2)

Number of Replications 17(14)

Other Methods for Increasing Accuracy 31(10)

The Grouping of Experimental Units 41(4)

References 43(2)

Notes on the Statistical Analysis of the Results 45(50)

Introduction 45(1)

The General Method of Analysis 45(13)

Accuracy in Computations 58(3)

Subdivision of the Sum of Squares for Treatments 61(9)

Calculation of Standard Errors for Comparisons among Treatment Means 70(7)

Subdivision of the Sum of Squares for Error 77(3)

Missing Data 80(2)

The Analysis of Covariance 82(9)

Effects of Errors in the Assumptions Underlying the Analysis of Variance 91(4)

References 92(3)

Completely Randomized, Randomized Block, and Latin Square Designs 95(53)

Completely Randomized Designs 95(11)

Single Grouping: Randomized Blocks 106(11)

Double Grouping: Latin Squares 117(10)

Cross-over Designs 127(5)

Triple Grouping: Graeco-latin Squares 132(1)

Designs for Estimating Residual Effects When Treatments Are Applied in Sequence 133(15)

References 142(3)

Plans 145(3)

Factorial Experiments 148(35)

Description 148(5)

Calculation of Main Effects and Interactions 153(22)

Designs for Factorial Experiments 175(8)

References 181(2)

Confounding 183(61)

The Principle of Confounding 183(29)

The Use of Confounded Designs 212(7)

Notes on the Plans and Statistical Analysis 219(25)

References 232(2)

Plans 234(10)

Factorial Experiments in Fractional Replication 244(49)

Construction and Properties of Fractionally Replicated Designs 244(15)

The Use of Fractional Factorial Designs in Practice 259(11)

Designs with Factors at More Than Two Levels 270(23)

References 275(1)

Plans 276(17)

Factorial Experiments with Main Effects Confounded: Split-plot Designs 293(24)

The Simple Split-plot Design 293(11)

Repeated Subdivision 304(1)

Some Variants of the Split-plot Design 305(12)

References 315(2)

Factorial Experiments Confounded in Quasi-Latin Squares 317(18)

Introduction 317(1)

Randomization of Quasi-latin Squares 317(1)

Notes on the Plans and Statistical Analysis 318(4)

Other Quasi-latin Squares 322(1)

Estimation of the Efficiency of Quasi-latin Squares 323(1)

Treatments Applied to Complete Rows of a Latin Square 324(3)

Treatments Applied to Complete Rows and Columns of a Latin Square 327(8)

References 327(1)

Plans 328(7)

Some Methods for the Study of Response Surfaces 335(41)

First Order Designs 335(7)

Second Order Designs 342(12)

Methods for Determining the Optimum Combination of Factor Levels 354(2)

The Single-factor Method 356(1)

The Method of Steepest Ascent 357(8)

Summary Comments 365(11)

References 369(1)

Plans 370(6)

Incomplete Block Designs 376(20)

Balanced Designs 376(2)

Partially Balanced Designs 378(2)

Basis of the Statistical Analysis 380(5)

Comparison of Incomplete Block and Randomized Block Designs 385(2)

Comparisons with Other Designs 387(1)

Choice of Incomplete Block Design 388(8)

References 394(2)

Lattice Designs 396(43)

Balanced Lattices 396(7)

Partially Balanced Lattices 403(12)

Rectangular Lattices 415(7)

Cubic Lattices 422(17)

References 426(2)

Plans 428(11)

Balanced and Partially Balanced Incomplete Block Designs 439(44)

Balanced Incomplete Blocks 439(1)

Balanced Incomplete Blocks in Taste and Preference Testing 440(1)

Comparisons with Other Designs 441(1)

Arrangement of Experimental Material 442(1)

Randomization 442(1)

Statistical Analysis 443(10)

Partially Balanced Incomplete Block Designs 453(10)

Chain Block Designs 463(20)

References 468(1)

Plans 469(14)

Lattice Squares 483(24)

Description 483(2)

Statistical Analysis 485(22)

References 497(1)

Plans 497(10)

Incomplete Latin Squares 507(38)

Description 507(1)

Statistical Analysis 508(5)

Other Designs for Small Numbers of Treatments 513(5)

Partially Balanced Designs 518(27)

References 519(1)

Plans 520(25)

Analysis of the Results of a Series of Experiments 545(24)

Initial Steps in the Analysis 545(5)

Criticisms of the Preliminary Analysis 550(5)

Experiments of Unequal Size 555(6)

A Test of the Treatments X Places Interactions 561(4)

Repetitions in Both Space and Time 565(4)

References 567(2)

Random Permutations of 9 and 16 Numbers 569(28)

Use of the Random Permutations 569(1)

Construction of the Random Permutations 569(2)

Randomization of More than 16 Numbers 571(1)

Tests of Randomness 571(6)

References 576(1)

Tables of Random Permutations 577(20)

Permutations of 9 577(6)

Permutations of 16 583(14)
Selected Bibliography 597(2)
List of Author References 599(4)
Index 603(10)
Tables of t and F 613