TABLE OF CONTENTS Page PREFACE - Gylling Data Management Inc

TABLE OF CONTENTS

Page

PREFACE ……………………………………………………………………. 2

TABLE OF CONTENTS ……………………………………………………. 3

1- INTRODUCTION

1.1. General introduction ……………………………………………. 6
1.2. Purpose ……………………………………………………………. 6
1.3. How to read this statistical guideline ……………………………. 6

2- SETTING THE TRIAL OBJECTIVES

2.1. Glossary ……………………………………………………………. 7
7
2.2. Defining the number of factors …………………………. 8
8
2.3. Description of a level within a factor …………………………. 9

2.4. Pesticide evaluations ………………………………………..…... 10
10
2.5. Seed variety evaluations ……………………………………. 11

2.6. Experimental conditions

2.6.1. Soil Heterogeneity ……………………………………….

2.6.2. Practical constraints …………………………………….

2.6.3. Local control …………………………………………….

3- SETTING UP THE COMPLETE BLOCK EXPERIMENTAL DESIGN

3.1. Selection an Experimental Design type ……………………. 12

3.2. Characteristics of the Experimental Designs 13
13
3.2.1. Fully Randomised ……………………………………. 13
14
3.2.2. Random Complete Block [RCB] …….……………………. 16
16
3.2.3. Latin Square …………………………………………….
17
3.2.4. Factorial Design ……………………………………..…… 17
18
3.2.5. Split-Plot …………………………………………………..
19
3.2.6. Criss-Cross or Strip-Plot …………………………………….
20
3.3. Number of Replications / Number of Blocks
21
3.3.1. Blocking ……………………………………………………. 21
25
3.3.2. Prerequisites …………………………………………….
25
3.3.3. Estimation of the number of replicates. ……………. 25
26
3.3.4. Number of treatments and replicates in relation
27
to “degrees of freedom” …………………………………. 27

3.3.5. Minimum required replicates by type of Experimental

Design …………………………………………………….

3.4. Randomization and allocation of the plots.

3.4.1. Purpose …………………………………………………….

3.4.2. Guidelines ………………………………………………….

3.5. Layout of the plots in relation to crop. ………………..……..

3.6. Untreated Plots.

3.6.1. Purpose ……………………………………………………..

3.6.2. Types of control arrangements …………………………

3.6.3. Selection of the type of untreated control arrangement

3.7. Trial Series

3.7.1. Single trial versus Trial Series ………………………….

3.7.2. Planning trial series …………………………………….

4- INCOMPLETE BLOCK DESIGNS.

4.1. Preliminary and definitions.

4.1.1. Resolvable incomplete block designs ………………. 28
28
4.1.2. Lattice Designs. ……………………………………… 29

4.2. Selection of a Lattice Experimental Design ……………….. 30
30
4.3. Characteristics of the Lattice Designs 31
31
4.3.1. Glossary …………………………………………………….. 32
33
4.3.2. Square Lattice ……………………………………………..
33
4.3.3. Rectangular Lattice …………………………………….. 34

4.3.4. Alpha Lattice ……………………………………… …….. 34
35
4.3.5. Lattice Square (row-column) ………………………….. 35
36
4.4. Number of Replications / Number of Blocks ………………. 38

4.4.1. Number of treatments and replications in relation 39
40
to "degrees of freedom" ………………………………… 41
42
4.4.2. Minimum required replications by type of Lattice design 43

4.5. Randomization and allocation of plots 45

4.5.1. Purpose ………………………………………………….. 45
46
4.5.2. Guidelines ………………………………………………….. 50
51
4.6. Construction of Lattice Designs …………………………… 51
55
4.7. Construction of Lattice Designs with ARM …………….…. 60
63
4.7.1. Efficiency Factor …………………………………….….. 66

5- ASSESSING THE TRIAL RESULTS 67
67
5.1. Reliability of the Trial …………………………………………... 69
69
5.2. "BOX-WHISKER" Graph …………………………………………
71
5.3. Nature of the variables …………………………………… 73
77
5.4. Transformation of variables: How to select …….………. 78

5.5. Missing data ………………………………………………….

6- STATISTICAL ANALYSIS

6.1. Choice of the method of analysis ……………………………
6.2. Analysis of Variance [AOV]

6.2.1. Principles ………………………………………………..…
6.2.2. Assumptions Underlying the Analysis of Variance …..
6.2.3. AOV Violations assumptions detection in ARM ………

6.2.3.1. Corrections ARM Action codes …………………….
6.2.4. Analysis of Variance results [Outputs] ………………...
6.2.5. Analysis of Variance for other types of Designs …….
6.3. ARM Factorial AOV Table reports ………………………………
6.4. Lattice Designs AOV analysis ……………………………………
6.4.1. Efficiency Gain ………………………………………………

7- MULTIPLE COMPARISONS

7.1. Decision errors …………………………………………………..
7.2. Selection of Multiple Comparison test …………………….
7.3. Setting the significance level of a test …………………….
7.4. Examples. ………………………………………………………….

8- ADVANCED ARM TOPICS
8.1. Dose Response Analysis ………………………………………...
8.1.1. Dose-Response Analysis process with an ARM example .
8.2. Area Under Disease Pressure Curve (AUDPC) …………
8.2.1 Measuring Plant Disease – AUDPC with an ARM Example

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8.3. Control Correction Transformations …………….. ………………. 81
8.3.1. Henderson-Tilton Transformation ………………………….. 82
8.3.2. Abbott’s Transformation …………………………………... 82
8.3.3. Schneider-Orelli Transformation …………………………… 83
8.3.4. Control Corrections with ARM ……………………………... 84

APPENDIX

A1. - LAYOUT OF THE PLOTS IN RELATION TO THE EXPERIMENTAL CROP 86

A2. - COMPARISONS INVOLVING TWO SAMPLE MEANS 93
[TWO TREATMENTS] 93
94
A2.1. Independent samples comparisons - t-Test ……………. 95
A2.2. Paired samples comparisons - Paired t-Test …………….
A2.3. Examples…………………………………………………………….
A2.4. Paired versus independent comparisons ………………….

A3. - NONPARAMETRIC STATISTICS.

“DISTRIBUTION FREE” TESTS

A3.1. Principles ……………………………………………………. 95
96
A3.2. Choice of a test according the nature of variables ……. 96

A3.3. Chi-Squared Test – χ²-Test ………………………………… 98
98
A3.4. Most frequently encountered tests 98
98
A3.4.1. Fisher’s Exact Test …………………………………… 98
99
A3.4.2. Sign Test …………………………………………………. 99
100
A3.4.3. Wilcoxon Signed-Rank Test ………………………….

A3.4.4. Kruskal-Wallis k-Samples Test …………………………….

A3.4.5. Friedman Test ………………………………………….

A3.4.6. Cochran Q Test …………………………………………

A3.4.7. Mac Nemar Test ……………………………………….

A3.4.8. Median Test …………………………………………….

References - Bibliography ……………………………………………. 101

INDEX ……………………………………………………………….…… 103

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