TY  - BOOK
AU  - Gomez, K. A. 
AU  - Gomez, A. A.
TI  - Statistical procedures for agricultural research
U1  - e-book (NRM) 
PY  - 2012///
CY  - Hyderabad
PB  - John Wiley & Sons
KW  - 1. Agriculture-Research-Statistical methods. 2. Rice-Research-Statistical methods 3. Field experiments-Statistical methods. 1. Gomez, Arturo A. II. Gomez. Kwanchai A. Statistical procedures for agricultural research with emphasis on rice. III. Title
N1  - Includes bibliographical references and index
N2  - Contents
CHAPTER 1 ELEMENTS OF EXPERIMENTATION
1.1
Estimate of Error, 2
1.1.1
Replication, 3
1.1.2
Randomization, 3
1.2
Control of Error, 4
1.2.1
Blocking, 4
1.2.2
Proper Plot Technique, 4
1.2.3
Data Analysis, 5
1.3
Proper Interpretation of Results, 5
CHAPTER 2 SINGLE-FACTOR EXPERIMENTS 7
2.1
Completely Randomized Design, 8
2.1.1
Randomization and Layout, 8
2.1.2
Analysis of Variance, 13
2.2
Randomized Complete Block Design, 20
2.2.1
Blocking Technique, 20
2.2.2
Randomization and Layout, 22
2.2.3
Analysis of Variance, 25
2.2.4
Block Efficiency, 29
2.3
Latin Square Design, 30
2.3.1
Randomization and Layout, 31
2.3.2
Analysis of Variance, 33
2.3.3
Efficiencies of Row-and Column-Blockings, 37
2.4
Lattice Design, 39
2.4.1
Balanced Lattice, 41
2.4.2
Partially Balanced Lattice, 52
2.5
Group Balanced Block Design, 75
2.5.1
Randomization and Layout, 76
2.5.2
Analysis of Variance, 76
CHAPTER 3 TWO-FACTOR EXPERIMENTS 84
3.1
Interaction Between Two Factors, 84
3.2
Factorial Experiment, 89
3.3
Complete Blo,:k Design, 91
3.4
Split-Plot Design, 97
3.4.1
Randomization and Layout, 99
3.4.2
Analysis of Variance, 101
xi
4A
\'*\
xii Contenis
3.5
Strip-Plot Design, 108
3.5.1
Randomization and Layout, 108
3.5.2
Analysis of Variance, 109
3.6
Group Balanced Block in Split-Plot Design, 116
3.6.1
Randomization and Layout, 116
3.6.2
Analysis of Variance, 118
CHAPTER 4 THREE-OR-MORE-FACTOR EXPERIMENTS 130
4.1
Interaction Between Three or More Factors, 130
4.2
Alternative Designs, 133
4.2.1
Single-Factor Experimental Designs, 133
4.2.2
Two-Factor Experimental Designs, 134
4.2.3
Three-or-More-Factor Experimental Designs, 138
4.2.4
Fractional Factorial Designs, 139
4.3
Split-Split-Plot Designs, 139
4.3.1
Randomization and Layout, 140
4.3.2
Analysis of Variance, 141
4.4
Strip-Split-Plot Design, 14
4.4.1
Randomization and Layout, 154
4.4.2
Analysis of Variance, 157
4.5
Fractional Factorial Design, 167
4.5.1
Randomization and Layout, 169
4.5.2
Analysis of Variance, 170
CHAPTER 5 COMPARISON BETWEEN TREATMENT MEANS 187
5.1
Pair Comparison, 188
5.1.1
Least Significant Difference Test, 188
5.1.2
Duncan's Multip,, Range Test, 207
5.2
Group Comparison, 215
5.2.1
Between-Group Comparison, 217
5.2.2
Within-Group Comparison, 222
5.2.3
Trend Comparison, 225
5.2.4
Factorial Comparison, 233
CHAPTER 6 ANALYSIS OF MULTIOBSERVATION DATA 241
6.1
Data from Plot Sampling, 241
6.1.1
RCB Design, 243
6.1.2
Split-Plot Design, 247
6.2
Measurement Over Time, 256
6.2.1
RCB Design, 258
6.2.2
Split-Plot Design, 262
6.3
Measurement Over Time with Plot Sampling, 266
CHAPTER 7 PROBLEM DATA 272
7.1
Missing Data, 272
7.1.1
Common Causes of Missing Data, 272
7.1.2
Missing Data Formula Technique, 276
Contents xii
7.2
Data tfrst Violate Some Assumptions of the Analysis of Variance, 294
7.2.1
Common Violations in Agricultural Experiments, 295
7.2.2
Remedial Measures for Handling Variance Heterogeneity, 297
CHAPTER 8 ANALYSIS OF DATA FROM A SERIES OF EXPERIMENTS 316
8.1
Preliminary Evaluation Experiment, 317
8.1.1
Analysis Over Seasons, 317
8.1.2
Analysis Over Years, 328
8.2
Technology Adaptation Experiment: Analysis Over Sites, 332
8.2.1
Variety Trial in Randomized Complete Blov-k Design, 335
8.2.2
Fertilizer Trial in Split-Plot Design, 339
8.3
Long-Term Experiments, 350
8.4
Response Prediction Experiment, 355
CHAPTER 9 REGRESSION AND CORRELATION ANALYSIS 357
9.1
Linear Relationship, 359
9.1.1
Simple Linear Regress)n and Correlation, 361
9.1.2
Multiple Linear Regression and Correlation, 382
9.2
Nonlinear Relationship, 388
9.2.1
Simple Nonlinear Regression, 388
9.2.2
Multiple Nonlinear Regression, 395
9.3
Searching for the Best Regression, 397
9.3.1
The Scatter Diagram Technique, 398
9.3.2
The Analysis of Variance Technique, 401
9.3.3
The Test of Significance Technique, 405
9.3
A Stepwise Regression Technique, 411
9.4
Common Misuses of Correlation and Regression Analysis in
Agricultural Research, 416
9.4.1
Improper Match Between Data and Objective, 417
9.4.2
Broad Generalization of Regression and Correlation Analysis
Results, 420
9.4.3
Use of Data from Individual Replications, 421
9.4.4
Misinterpretation of the Simple Linear Regression and
Correlation Analysis, 422
CHAPTER 10 COVARIANCE3 ANALYSIS 424
10.1
Uses of Covariance Analysis in Agricultural Research, 424
10.1.1
Error Control and Adjustment of Treatment Means, 425
10.1.2
Estimation of Missing Data, 429
10.1.3
Interpretation of Experimental Results, 429
10.2
Computational Procedures, 430
10.2.1
Error Control, 431
10.2.2
Estimation of Missing Data, 454
CHAPTER 11 CHI-SQUARE TEST 458
11.1
Analysis of Attribute Data, 458
11.1.1
Test for a Fixed-Ratio Hypothesis. 459
Xiv Contents
11.1.2
Test for Independence in a Contingenc) Table, 462
11.1.3
Test for Homogeneity of Ratio, 464
11.2
Test for Homogeneity of Variance, 467
11.2.1
Equal Degree of Freedom, 467
11.2.2
Unequal Degrees of Freedom, 469
11.3
Test for Goodness of Fit, 471
CHAPTER 12 SOIL JIEEIOGENEItrY 478
12.1
Choosing a Good Experimental Site, 478
12.1.1
Slopes, 478
12.1.2
Areas Used for Experiments in Previous Croppings, 478
12.1.3
Graded Areas, 479
12.1.4
Presence of Large Trees, Poles, and Structures, 479
12.1.5
Unproductive Site, 479
12.2
Measuring Soil Heterogeneity, 479
12.2.1
Uniformity Trials, 479
12.2.2
Data from Field Experiments, 494
12.3
Coping with Soil Heterogeneity, 500
12.3.1
Plot Size and Shape, 500
12.3.2
Block Size and Shape. 503
12.3.3
Number of Replications, 503
CHAPTER 13 COMPETITION EFFECTS 505
13.1
Types of Competition Effect, 505
13.1.1
Nonplanted Borders, 505
13.1.2
Varietal Competition, 506
13.1.3
Fertilizer Competition, 506
13.1.4
Missing Hills, 506
13.2
Measuring Competition Effects, 506
13.2.1
Experiments to Measure Competition Effects, 507
13.2.2
Experiments Set Up for Other Purposes, 515
13.2.3
Uniformity Trials or Prod,. ction Plots, 519
13.3
Control of Competition Effects, 520
13.3.1
Removal of Border Plants, 520
13.3.2
Grouping of Homogeneous Treatments, 521
13.3.3
Stand Correction, 521
CHAPTER 14 MECHANICAL ERRORS 523
14.1
Furrowing for Row Spacing, 523
14.2
Selection of Seedlings, 525
14.3
Thinning, 525
14.4
Transplanting, 527
14.5
Fertilizer Application, 528
14.6
Seed Mixtures and Off-Type Plants, 528
14.7
Plot Layout and Labeling, 529
14.8
Measurement Errors, 530
14.9
Transcription of Data, 531
Contents xv
CHAPTER 15 SAMPLING IN EXPERIMENTAL PLOTS 532
15.1
Components of a Plot Sampling Technique, 533
15.1.1
Sampling Unit, 533
15.1.2
Sample Size, 534
15.1.3
Sampling Design, 536
15.1.4
Supplementary Techniques, 543
15.2
Developing an Appropriate Plot Sampling Technique, 546
15.2.1
Data from Previous Experiments, 547
15.2.2
Additional Data from On-Going Experiments, 550
15.2.3
Specifically Planned Sampling Studies, 557
CHAPTER 16 EXPERIMENTS IN FARMERS' FIELDS 562
16.1
Farmer's Ficid as the Test Site, 563
16.2
Technology-Generatior Experiments, 564
16.2.1
Selection of Test Site, 564
16.2.2
Experimental Design and Field Layout, 565
16.2.3
Data Collection, 566
16.2.4
Data Analysis, 567
16.3
Technology-Verification Experiments, 571
16.3.1
Selection of Test Farms, 572
16.3.2
Experimental Design, 572
16.3.3
Field-Plot Technique, 574
16.3.4
Data Collection, 577
16.3.5
Data Analysis, 577
CHAPTER 17 PRESENTATION OF RESEARCH RESULTS 591
17.1
Single-Factor Experiment, 594
17.1.1
Discrete Treatments, 594
17.1.2
Quantitative Treatments: Line Graph, 601
17.2
Factorial Experiment, 605
17.2.1
Tabular Form, 605
17.2.2
Bar Chart, 611
17.2.3
Line Graph, 614
17.3
More-Than-One Set of Data, 618
17.3.1
Measurement Over Time, 620
17.3.2
Multicharacter Data, 623
APPENDIXES 629
A.
Table of Random Numbers, 630
B.
Cumulative Normal Frequency Distribution, 632
C.
Distribution of t Probability, 633
D.
Percentage Points of the Chi-Square Distribution, 634
E.
Points for the Distribution of F, 635
F.
Significant Studentized Ranges for 5%and 1%Level New
Multiple-Range Test, 639
I
xvi Contents
G. Orthogonal Polynomial Coeffcients for Comparison between Three to
Six Equally Spaced Treatments, 641
H. Simple Linear Correlation Coefficients, r, at the 5%and 1%Levels of
Significance, 641
I. Table of Corresponding Values of r and z, 642
J. The Arcsin Percentage Transformation, 643
K. Selected Latin Squares, 646
L. Basic Plans for Balanced and Partially Balanced Lattice Designs, 647
M. Selected Plans of I Fractional Factorial Design for 25, 26, and 27
Factorial Experiments, 652
INDEX 657
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