Experimental Designs

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Edition: 2nd
Format: Paperback
Pub. Date: 1992-08-04
Publisher(s): Wiley
List Price: $248.81

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Summary

The past six years have seen a substantial increase in the attention paid by research workers to the principles of experimental design. The Second Edition of brings this handbook up to date, while retaining the basic framework that made it so popular. Describes the most useful of the designs that have been developed with accompanying plans and an account of the experimental situations for which each design is most suitable. Examples come from diverse fields of research, with an emphasis on biology and agriculture, two of the authors' specialties. New chapters have been added: one discusses the fractional replication of experiments. A second is concerned with experiments of the factorial type that present new methods and designs in which the factors represent quantitative variables measured on a continuous scale. Other new material includes an introductory account of experimental strategies for finding the levels at which the factors must be set in order to obtain maximum response and coverage of new incomplete block designs.

Author Biography

William Gemmell Cochran was a prominent statistician. He was born in Scotland but spent most of his life in the United States. Cochran studied mathematics at the University of Glasgow and the University of Cambridge. He worked at Rothamsted Experimental Station from 1934 to 1939, when he moved to the United States.

Gertrude Mary Cox was an American statistician and founder of the department of Experimental Statistics at North Carolina State University.

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

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