Practical Statistics and Experimental Design

Presents readers with a user-friendly, non-technical introduction to statistics and the principles of plant and crop experimentation. Avoiding mathematical jargon, it explains how to plan and design an experiment, analyse results, interpret computer output and present findings. Using specific crop and plant case studies, this guide presents: * The reasoning behind each statistical method is explained before giving relevant, practical examples * Step-by-step calculations with examples linked to three computer packages (MINITAB, GENSTAT and SAS) * Exercises at the end of many chapters * Advice on presenting results and report writing Written by experienced lecturers, this text will be invaluable to undergraduate and postgraduate students studying plant sciences, including plant and crop physiology, biotechnology, plant pathology and agronomy, plus ecology and environmental science students and those wanting a refresher or reference book in statistics.

Alan G. Clewer and David H. Scarisbrick T. H. Huxley School of Environment, Earth Sciences and Engineering, Imperial College at Wye, Ashford, Kent, UK

Preface

xi

Basic Principles of Experimentation

1

(8)

Introduction

1

(1)

Field and glasshouse experiments

1

(2)

Choice of site

3

(1)

Soil testing

4

(1)

Satellite mapping

5

(1)

Sampling

6

(3)

Basic Statistical Calculations

9

(7)

Introduction

9

(1)

Measurements and type of variable

9

(1)

Samples and populations

10

(6)

Basic Data Summary

16

(8)

Introduction

16

(1)

Frequency distributions (discrete data)

16

(2)

Frequency distributions (continuous data)

18

(4)

Descriptive statistics

22

(2)

The Normal Distribution, the t-Distribution and Confidence Intervals

24

(14)

Introduction to the normal distribution

24

(1)

The standard normal distribution

25

(2)

Further use of the normal tables

27

(2)

Use of the percentage points table (Appendix 2)

29

(1)

The normal distribution in practice

29

(2)

Introduction to confidence intervals

31

(1)

Estimation of the population mean

31

(1)

The sampling distribution of the mean, μ

32

(1)

Confidence limits for μ when σ is known

32

(2)

Confidence limits for μ when σ is unknown---use of the t-distribution

34

(2)

Determination of sample size

36

(1)

Estimation of total crop yield

36

(2)

Introduction to Hypothesis Testing

38

(11)

The standard normal distribution and the t-distribution

38

(1)

The single sample t-test

39

(3)

The P-value

42

(1)

Type I and Type II errors

43

(1)

Choice of level of significance

44

(1)

The usefulness of a test

45

(1)

Estimation versus hypothesis testing

46

(1)

The paired samples t-test

46

(3)

Comparison of Two Independent Sample Means

49

(14)

Introduction

49

(2)

The Independent Samples t-test

51

(4)

Confidence intervals

55

(1)

The theory behind the t-test

55

(3)

The F-test

58

(1)

Unequal sample variances

59

(1)

Determination of sample size for a given precision

60

(3)

Linear Regression and Correlation

63

(24)

Basic principles of Simple Linear Regression (SLR)

63

(3)

Experimental versus observational studies

66

(1)

The correlation coefficient

67

(1)

The least squares regression line and its estimation

67

(4)

Calculation of residuals

71

(1)

The goodness of fit

72

(2)

Calculation of the correlation coefficient

74

(1)

Assumptions, hypothesis tests and confidence intervals for simple linear regression

75

(8)

Testing the significance of a correlation coefficient

83

(4)

Curve Fitting

87

(15)

Introduction

87

(1)

Polynomial fitting

87

(2)

Quadratic regression

89

(4)

Other types of curve

93

(7)

Multiple linear regression

100

(2)

The Completely Randomised Design

102

(30)

Introduction

102

(1)

Design construction

103

(2)

Preliminary analysis

105

(3)

The one-way analysis of variance model

108

(2)

Analysis of variance

110

(8)

After Anova

118

(5)

Reporting results

123

(1)

The completely randomised design---unequal replication

124

(4)

Determination of number of replicates per treatment

128

(4)

The Randomised Block Design

132

(17)

Introduction

132

(3)

The analysis ignoring blocks

135

(1)

The analysis including blocks

136

(1)

Using the computer

136

(1)

The effect of blocking

137

(1)

The randomised blocks model

138

(3)

Using a hand calculator to find the sums of squares

141

(1)

Comparison of treatment means

142

(2)

Reporting the results

144

(1)

Deciding how many blocks to use

144

(2)

Plot sampling

146

(3)

The Latin Square Design

149

(10)

Introduction

149

(2)

Randomisation

151

(2)

Interpretation of computer output

153

(2)

The Latin square model

155

(1)

Using your calculator

156

(3)

Factorial Experiments

159

(23)

Introduction

159

(1)

Advantages of factorial experiments

160

(3)

Main effects and interactions

163

(2)

Varieties as factors

165

(1)

Analysis of a randomised blocks factorial experiment with two factors

166

(10)

General advice on presentation

176

(1)

Experiments with more than two factors

177

(2)

Confounding

179

(1)

Fractional replication

180

(2)

Comparison of Treatment Means

182

(31)

Introduction

182

(1)

Treatments with no structure

182

(9)

Treatments with structure (factorial structure)

191

(4)

Treatments with structure (levels of a quantitative factor)

195

(7)

Treatments with structure (contrasts)

202

(11)

Checking the Assumptions and Transformation of Data

213

(13)

The assumptions

213

(6)

Transformations

219

(7)

Missing Values and Incomplete Blocks

226

(12)

Introduction

226

(1)

Missing values in a completely randomised design

226

(3)

Missing values in a randomised block design

229

(5)

Other types of experiment

234

(1)

Incomplete block designs

234

(4)

Split Plot Designs

238

(18)

Introduction

238

(1)

Uses of this design

238

(2)

The skeleton analysis of variance tables

240

(2)

An example with interpretation of computer output

242

(8)

The growth cabinet problem

250

(2)

Other types of split plot experiment

252

(1)

Repeated measures

252

(4)

Comparison of Regression Lines and Analysis of Covariance

256

(16)

Introduction

256

(1)

Comparison of two regression lines

256

(4)

Analysis of covariance

260

(1)

Analysis of covariance applied to a completely randomised design

260

(5)

Comparing several regression lines

265

(5)

Conclusion

270

(2)

Analysis of Counts

272

(21)

Introduction

272

(1)

The binomial distribution

272

(3)

Confidence intervals for a proportion

275

(2)

Hypothesis test of a proportion

277

(2)

Comparing two proportions

279

(1)

The chi-square goodness of fit test

280

(4)

r x c contingency tables

284

(2)

2 x c contingency tables: comparison of several proportions

286

(1)

2 x 2 contingency tables: comparison of two proportions

287

(2)

Association of plant species

289

(1)

Heterogeneity chi-square

290

(3)

Some Non-parametric Methods

293

(14)

Introduction

293

(1)

The Sign test

294

(2)

The Wilcoxon single-sample test

296

(1)

The Wilcoxon matched pairs test

297

(2)

The Mann-Whitney U test

299

(3)

The Kruskal-Wallis test

302

(2)

Friedman's test

304

(3)

Appendix 1: The normal distribution function

307

(1)

Appendix 2: Percentage points of the normal distribution

308

(1)

Appendix 3: Percentage points of the t-distribution

309

(1)

Appendix 4a: 5 per cent points of the F-distribution

310

(2)

Appendix 4b: 2.5 per cent points of the F-distribution

312

(2)

Appendix 4c: 1 per cent points of the F-distribution

314

(2)

Appendix 4d: 0.1 per cent points of the F-distribution

316

(2)

Appendix 5: Percentage points of the sample correlation coefficient (r) when the population correlation coefficient is 0 and n is the number of X, Y pairs

318

(1)

Appendix 6: 5 per cent points of the Studentised range, for use in Tukey and SNK tests

319

(2)

Appendix 7: Percentage points of the chi-square distribution

321

(1)

Appendix 8: Probabilities of S or fewer successes in the binomial distribution with n `trials' and p=0.5

322

(1)

Appendix 9: Critical values of T in the Wilcoxon signed rank or matched pairs test

323

(1)

Appendix 10: Critical values of U in the Mann-Whitney test

324

(3)

References

327

(1)

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Practical Statistics and Experimental Design for Plant and Crop Science

Summary

Author Biography

Table of Contents

Supplemental Materials

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Practical Statistics and Experimental Design for Plant and Crop Science

Summary

Author Biography

Table of Contents

Supplemental Materials

Digital License