Table Of Content6 (IZ-?
STATISTICAL PROCEDURES
FOR AGRICULTURAL RESEARCH
Second Edition
KWANCHAI A. GOMEZ
Head, Department of Statistics
The International Rice Resoarch Institute
Los Banos, Laguna, Philippines
ARTURO A. GOMEZ
Professor of Agronomy
University of the Philippines at Los Baflos
College, Laguna, Philippines
AN INTERNATIONAL RICE RESEARCH INSTITUTE BOOK
A Wiley-intersclence Publication
JOHN WILEY & SONS,
New York Chichester Brisbane Toronto Singapore
. . . .
I
First edition published in the Philippines in 1976 by the
International Rice Research Institute.
Copyright 0 1984 by John Wiley & Sons, Inc.
All rights reserved. Published simultaneously in Canada.
Reproduction or translation of any part of this work
beyond that permitted by Section 107 or 108 of the
1976 United States Copyright Act without the permission
of the copyright owner is unlawful. Requests for
permission or further information should be addressed to
the Permissions Department, John Wiley & Sons, Inc.
Librar of Congress Cataloging in Publication Data.:
,
Gomez, Kwanchai A.
Statistical procedures for agricultural research.
"An International Rice Research Institute book."
"A Wiley-Interscience publication."
Previously published as: Statistical procedures for
agricultural research with emphasis on rice/K. A. Gomez,
A. A. Gomez.
Includes index
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 agri
cultural research with emphasis on rice. III. Title.
$540.$7G65 1983 630'.72 83-14556
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
C/) I
To ourson, Victor
Preface
There is universal acceptance of statistics as an essential tool for all types of
research. That acceptance and ever-proliferating areas of research specializa
tion have led to corresponding increases in the number and diversity of
available statistical procedures. In agricultural research, for example, there are
different statistical techniques for crop and animal research, for laboratory and
field experiments, for genevic and physiological research, and so on. Although
this diversit" indicates the aailability of appropriate statistical techniques for
most research problems, il.also indicates the difficulty of matching the best
technique to a specific expe, 2ment. Obviously, this difficulty increases as more
procedures develop.
Choosing the correct st'tistical procedure for a given experiment must be
bas;ed on expertise in statistics and in the subject matter of the experiment.
Thorough knowledge of only one of the two is not enough. Such a choice,
therefore, should be made by:
A,.subject matter specialist with some training in experimental stat,istics
SA,statistician with some background and experience in the subject matter of
ihe experiment
* The joint effort and cooperation of a statistician and a subject matter
specialist
For most agricultural research institutions in the developing countries, the
presence of trained statisticians is a luxury. Of the already small number of
such statisticians, only a small fraction have the interest and experience i
agricultural research necessary for effective consultation. Thus, we feel the best
alternative is to give agricultural researchers a statistical background so that
they can correctly choose the statistical technique most appropriate for their
experiment. The major objective of this book is to provide the developing
couutry researcher that background.
For research institutions in the developed countries, the shortage of trained
statisticians may not be as acute as in the developing countries. Nevertheless,
the subject matter specialist must be able to communicate with the consulting
statistician. Thus, for the developed-country researcher, this volume should
help forge a closer researcher-statistician relationship.
, k
viii Preface
We have tried to create a book that any subject matter specialist can use.
First, we chose only the simpler and more commonly used statistical proce
dures in agricultural research, with special emphasis on field experiments with
crops. In fact, our examples are mostly concerned with rice, the most im
portant crop in Asia and the crop most familiar to us. Our examples, however,
have applicability to a wide range of annual crops. In addition, we have used a
minimum of mathematical and statistical theories and jargon and a maximum
of actual examples.
This is a second edition of an International Rice Research Institute publica
tion with a similar title and we made extensive revisions to ail but three of the
original chapters. We added four new chapters. The primary emphases of the
working chapters are as follows:
Chapters 2 to 4 cover the most commonly used experimental designs for
single-factor, two-factor, and three-or-more-factor experiments. For each de
sign, the corresponding randomization and analysis of variance procedures are
described in detail.
Chapter 5 gives the procedures for comparing specific treatment means:
LSD and DMRT for pair comparison, and single and multiple d.f. contrast
methods for group comparison.
Chapters 6 to 8 detail the modifications of the procedures described in
Chapters 2 to 4 necessary to handle the following special cases:
" Experiments with more than one observation per experimental unit
* Experiments with missing values or in which data violate one or more
assumptions of the analysis of variance
" Experiments that are repeated over time or site
Chapters 9 to 11 give the three most commonly used statistical techniques
for data analysis in agricultural research besides the analysis of variance. These
techniques are regression and correlation, covariance, and chi-square. We also
include a detailed discussion of the common misuses of the regression and
correlation analysis.
Chapters 12 to 14 cover the most important problems commonly encoun
tered in conducting field experiments and the corresponding techniques for
coping with them. The problems are:
* Soil heterogeneity
" Competition effects
" Mechanical errors
Chapter 15 describes the principles and procedures for developing an
appropriate sampling plan for a replicated field experiment.
Chapter 16 gives the problems and procedures for research in farmers'
fields. In the developing countries where farm yields are much lower than
Preface ix
experiment-station yields, the appropriate environment for comparing new and
existing technologies is the actual farmers' fields and not the favorable environ
ment of the experiment stations. This poses a major challenge to existing
statistical procedures and substantial adjustments are required.
Chapter 17 covers the serious pitfalls and provides guidelines for the
presentation of research results. Most of these guidelines were generated from
actual experience.
We are grateful to the International Rice Research Institute (IRRI) and the
University of the Philippines at Los Bafios (UPLB) for granting us the study
leaves needed to work on this edition; and the Food Research Institute,
Stanford University, and the College of Natural Resources, University of
California at Berkeley, for being our hosts during our leaves.
Most of the examples were obtained from scientists at IRRI. We are
grateful to them for the use of their data.
We thank the research staff of IRRI's Department of Statistics for their
valuable assistance in searching and processing the suitable examples; and the
secretarial staff for their excellent typing and patience in proofreading the
manuscript. We are grateful to Walter G. Rockwood who suggested modifica
tions to make this book more readable.
We appreciate permission from the Literary Executor of the late Sir Ronald
A. Fisher, F.R.S., Dr. Frank Yates, F '.S., and Longman Group Ltd., London
to reprint Table III, "Distribution of Probability," from their book Statistical
Tables for Biological, Agricultural and Medical Research (6th edition, 1974).
KWANCHAI A. GOMEZ
ARTURO A. GOMEZ
Los Blaw, Philippines
Seifember 1983
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
