Written in simple language with relevant examples, Statistical Methods in Biology: Design and Analysis of Experiments and Regression is a practical and illustrative guide to the design of experiments and data analysis in the biological and agricultural sciences. The book presents statistical ideas in the context of biological and agricultural sciences to which they are being applied, drawing on relevant examples from the authors’ experience.
Taking a practical and intuitive approach, the book only uses mathematical formulae to formalize the methods where necessary and appropriate. The text features extended discussions of examples that include real data sets arising from research. The authors analyze data in detail to illustrate the use of basic formulae for simple examples while using the GenStat® statistical package for more complex examples. Each chapter offers instructions on how to obtain the example analyses in GenStat and R.
By the time you reach the end of the book (and online material) you will have gained:
A clear appreciation of the importance of a statistical approach to the design of your experiments,
A sound understanding of the statistical methods used to analyse data obtained from designed experiments and of the regression approaches used to construct simple models to describe the observed response as a function of explanatory variables,
Sufficient knowledge of how to use one or more statistical packages to analyse data using the approaches described, and most importantly,
An appreciation of how to interpret the results of these statistical analyses in the context of the biological or agricultural science within which you are working.
The book concludes with a guide to practical design and data analysis. It gives you the understanding to better interact with consultant statisticians and to identify statistical approaches to add value to your scientific research.

Preface xv

Authors xix

1. Introduction 1

1.1 Different Types of Scientic Study 1

1.2 Relating Sample Results to More General Populations 3

1.3 Constructing Models to Represent Reality 4

1.4 Using Linear Models 7

1.5 Estimating the Parameters of Linear Models 8

1.6 Summarizing the Importance of Model Terms 9

1.7 The Scope of This Book 11

2. A Review of Basic Statistics 13

2.1 Summary Statistics and Notation for Sample Data 13

2.2 Statistical Distributions for Populations 16

      2.2.1 Discrete Data 17

      2.2.2 Continuous Data 22

      2.2.3 The Normal Distribution 24

      2.2.4 Distributions Derived from Functions of Normal Random Variables 26

2.3 From Sample Data to Conclusions about the Population 28

      2.3.1 Estimating Population Parameters Using Summary Statistics 28

      2.3.2 Asking Questions about the Data: Hypothesis Testing 29

2.4 Simple Tests for Population Means 30

      2.4.1 Assessing the Mean Response: The One-Sample t-Test 30

      2.4.2 Comparing Mean Responses: The Two-Sample t-Test 32

2.5 Assessing the Association between Variables 36

2.6 Presenting Numerical Results 39

Exercises 41

3. Principles for Designing Experiments 43

3.1 Key Principles 43

      3.1.1 Replication 46

      3.1.2 Randomization 48

      3.1.3 Blocking 51

3.2 Forms of Experimental Structure 52

3.3 Common Forms of Design for Experiments 57

      3.3.1 The Completely Randomized Design 57

      3.3.2 The Randomized Complete Block Design 58

      3.3.3 The Latin Square Design 59

      3.3.4 The Split-Plot Design 60

      3.3.5 The Balanced Incomplete Block Design 61

      3.3.6 Generating a Randomized Design 62

Exercises 62

4. Models for a Single Factor 69

4.1 Dening the Model 69

4.2 Estimating the Model Parameters 73

4.3 Summarizing the Importance of Model Terms 74

      4.3.1 Calculating Sums of Squares 76

      4.3.2 Calculating Degrees of Freedom and Mean Squares 80

      4.3.3 Calculating Variance Ratios as Test Statistics 81

      4.3.4 The Summary ANOVA Table 82

4.4 Evaluating the Response to Treatments 84

      4.4.1 Prediction of Treatment Means 84

      4.4.2 Comparison of Treatment Means 85

4.5 Alternative Forms of the Model 88

Exercises 90

5. Checking Model Assumptions 93

5.1 Estimating Deviations 93

      5.1.1 Simple Residuals 94

      5.1.2 Standardized Residuals 95

5.2 Using Graphical Tools to Diagnose Problems 96

      5.2.1 Assessing Homogeneity of Variances 96

      5.2.2 Assessing Independence 98

      5.2.3 Assessing Normality 101

      5.2.4 Using Permutation Tests Where Assumptions Fail 102

      5.2.5 The Impact of Sample Size 103

5.3 Using Formal Tests to Diagnose Problems 104

5.4 Identifying Inconsistent Observations 108

Exercises 110

6. Transformations of the Response 113

6.1 Why Do We Need to Transform the Response? 113

6.2 Some Useful Transformations 114

      6.2.1 Logarithms 114

      6.2.2 Square Roots 119

      6.2.3 Logits 120

      6.2.4 Other Transformations 121

6.3 Interpreting the Results after Transformation 122

6.4 Interpretation for Log-Transformed Responses 123

6.5 Other Approaches 126

Exercises 127

7. Models with a Simple Blocking Structure 129

7.1 Dening the Model 130

7.2 Estimating the Model Parameters 132

7.3 Summarizing the Importance of Model Terms 134

7.4 Evaluating the Response to Treatments 140

7.5 Incorporating Strata: The Multi-Stratum Analysis of Variance 141

Exercises 146

8. Extracting Information about Treatments 149

8.1 From Scientic Questions to the Treatment Structure 150

8.2 A Crossed Treatment Structure with Two Factors 152

      8.2.1 Models for a Crossed Treatment Structure with Two Factors 153

      8.2.2 Estimating the Model Parameters 155

      8.2.3 Assessing the Importance of Individual Model Terms 158

      8.2.4 Evaluating the Response to Treatments: Predictions from the Fitted Model 160

      8.2.5 The Advantages of Factorial Structure 162

      8.2.6 Understanding Different Parameterizations 163

8.3 Crossed Treatment Structures with Three or More Factors 164

      8.3.1 Assessing the Importance of Individual Model Terms 166

      8.3.2 Evaluating the Response to Treatments: Predictions from the Fitted Model 171

8.4 Models for Nested Treatment Structures 173

8.5 Adding Controls or Standards to a Set of Treatments 179

8.6 Investigating Specic Treatment Comparisons 182

8.7 Modelling Patterns for Quantitative Treatments 190

8.8 Making Treatment Comparisons from Predicted Means 195

      8.8.1 The Bonferroni Correction 196

      8.8.2 The False Discovery Rate 197

      8.8.3 All Pairwise Comparisons 198

      8.8.3.1 The LSD and Fisher’s Protected LSD 198

      8.8.3.2 Multiple Range Tests 199

      8.8.3.3 Tukey’s Simultaneous Condence Intervals 200

      8.8.4 Comparison of Treatments against a Control 201

      8.8.5 Evaluation of a Set of Pre-Planned Comparisons 201

      8.8.6 Summary of Issues 205

Exercises 206

9. Models with More Complex Blocking Structure 209

9.1 The Latin Square Design 209

      9.1.1 Dening the Model 211

      9.1.2 Estimating the Model Parameters 211

      9.1.3 Assessing the Importance of Individual Model Terms 212

      9.1.4 Evaluating the Response to Treatments: Predictions from the Fitted Model 215

      9.1.5 Constraints and Extensions of the Latin Square Design 217

9.2 The Split-Plot Design 220

      9.2.1 Dening the Model 222

      9.2.2 Assessing the Importance of Individual Model Terms 223

      9.2.3 Evaluating the Response to Treatments: Predictions from the Fitted Model 225

      9.2.4 Drawbacks and Variations of the Split-Plot Design 228

9.3 The Balanced Incomplete Block Design 232

      9.3.1 Dening the Model 235

      9.3.2 Assessing the Importance of Individual Model Terms 236

      9.3.3 Drawbacks and Variations of the Balanced Incomplete Block Design 237

Exercises 238

10. Replication and Power 241

10.1 Simple Methods for Determining Replication 242

      10.1.1 Calculations Based on the LSD 242

      10.1.2 Calculations Based on the Coefcient of Variation 243

      10.1.3 Unequal Replication and Models with Blocking 244

10.2 Estimating the Background Variation 245

10.3 Assessing the Power of a Design 245

10.4 Constructing a Design for a Particular Experiment 249

10.5 A Different Hypothesis: Testing for Equivalence 253

Exercise 256

11. Dealing with Non-Orthogonality 257

11.1 The Benets of Orthogonality 257

11.2 Fitting Models with Non-Orthogonal Terms 259

      11.2.1 Parameterizing Models for Two Non-Orthogonal Factors 259

      11.2.2 Assessing the Importance of Non-Orthogonal Terms: The Sequential ANOVATable 265

      11.2.3 Calculating the Impact of Model Terms 269

      11.2.4 Selecting the Best Model 270

      11.2.5 Evaluating the Response to Treatments: Predictions from the Fitted Model 270

11.3 Designs with Planned Non-Orthogonality 272

      11.3.1 Fractional Factorial Designs 273

      11.3.2 Factorial Designs with Confounding 274

11.4 The Consequences of Missing Data 274

11.5 Incorporating the Effects of Unplanned Factors 277

11.6 Analysis Approaches for Non-Orthogonal Designs 280

      11.6.1 A Simple Approach: The Intra-Block Analysis 281

      Exercises 284

12. Models for a Single Variate: Simple Linear Regression 287

12.1 Dening the Model 288

12.2 Estimating the Model Parameters 292

12.3 Assessing the Importance of the Model 296

12.4 Properties of the Model Parameters 299

12.5 Using the Fitted Model to Predict Responses 301

12.6 Summarizing the Fit of the Model 305

12.7 Consequences of Uncertainty in the Explanatory Variate 306

12.8 Using Replication to Test Goodness of Fit 308

12.9 Variations on the Model 313

      12.9.1 Centering and Scaling the Explanatory Variate 313

      12.9.2 Regression through the Origin 314

      12.9.3 Calibration 320

Exercises 321

13. Checking Model Fit 325

13.1 Checking the Form of the Model 325

13.2 More Ways of Estimating Deviations 328

13.3 Using Graphical Tools to Check Assumptions 330

13.4 Looking for Inuential Observations 332

      13.4.1 Measuring Potential Inuence: Leverage 333

      13.4.2 The Relationship between Residuals and Leverages 335

      13.4.3 Measuring the Actual Inuence of Individual Observations 336

13.5 Assessing the Predictive Ability of a Model: Cross-Validation 338

Exercises 342

14. Models for Several Variates: Multiple Linear Regression 345

14.1 Visualizing Relationships between Variates 345

14.2 Dening the Model 347

14.3 Estimating the Model Parameters 350

14.4 Assessing the Importance of Individual Explanatory Variates 352

      14.4.1 Adding Terms into the Model: Sequential ANOVA and IncrementalSumsofSquares 353

      14.4.2 The Impact of Removing Model Terms: Marginal Sums of Squares 356

14.5 Properties of the Model Parameters and Predicting Responses 358

14.6 Investigating Model Misspecication 359

14.7 Dealing with Correlation among Explanatory Variates 361

14.8 Summarizing the Fit of the Model 365

14.9 Selecting the Best Model 366

      14.9.1 Strategies for Sequential Variable Selection 369

      14.9.2 Problems with Procedures for the Selection of Subsets of Variables 376

      14.9.3 Using Cross-Validation as a Tool for Model Selection 377

      14.9.4 Some Final Remarks on Procedures for Selecting Models 378

Exercises 378

15. Models for Variates and Factors 381

15.1 Incorporating Groups into the Simple Linear Regression Model 382

      15.1.1 An Overview of Possible Models 383

      15.1.2 Dening and Choosing between the Models 388

      15.1.2.1 Single Line Model 388

      15.1.2.2 Parallel Lines Model 388

      15.1.2.3 Separate Lines Model 390

      15.1.2.4 Choosing between the Models: The Sequential ANOVATable 391

      15.1.3 An Alternative Sequence of Models 396

      15.1.4 Constraining the Intercepts 398

15.2 Incorporating Groups into the Multiple Linear Regression Model 399

15.3 Regression in Designed Experiments 406

15.4 Analysis of Covariance: A Special Case of Regression with Groups 409

15.5 Complex Models with Factors and Variates 414

      15.5.1 Selecting the Predictive Model 414

      15.5.2 Evaluating the Response: Predictions from the Fitted Model 417

15.6 The Connection between Factors and Variates 417

      15.6.1 Rewriting the Model in Matrix Notation 421

Exercises 423

16. Incorporating Structure: Linear Mixed Models 427

16.1 Incorporating Structure 427

16.2 An Introduction to Linear Mixed Models 428

16.3 Selecting the Best Fixed Model 430

16.4 Interpreting the Random Model 432

      16.4.1 The Connection between the Linear Mixed Model and Multi-Stratum ANOVA 434

16.5 What about Random Effects? 435

16.6 Predicting Responses 436

16.7 Checking Model Fit 437

16.8 An Example 438

16.9 Some Pitfalls and Dangers 444

16.10 Extending the Model 445

Exercises 447

17. Models for Curved Relationships 451

17.1 Fitting Curved Functions by Transformation 451

      17.1.1 Simple Transformations of an Explanatory Variate 451

      17.1.2 Polynomial Models 456

      17.1.3 Trigonometric Models for Periodic Patterns 460

17.2 Curved Surfaces as Functions of Two or More Variates 463

17.3 Fitting Models Including Non-Linear Parameters 472

Exercises 476

18. Models for Non-Normal Responses: Generalized Linear Models 479

18.1 Introduction to Generalized Linear Models 480

18.2 Analysis of Proportions Based on Counts: Binomial Responses 481

      18.2.1 Understanding and Dening the Model 483

      18.2.2 Assessing the Importance of the Model and Individual Terms: TheAnalysisofDeviance 487

      18.2.2.1 Interpreting the ANODEV with No Over-Dispersion 489

      18.2.2.2 Interpreting the ANODEV with Over-Dispersion 490

      18.2.2.3 The Sequential ANODEV Table 493

      18.2.3 Checking the Model Fit and Assumptions 494

      18.2.4 Properties of the Model Parameters 496

      18.2.5 Evaluating the Response to Explanatory Variables: Prediction 498

      18.2.6 Aggregating Binomial Responses 500

      18.2.7 The Special Case of Binary Data 501

      18.2.8 Other Issues with Binomial Responses 501

18.3 Analysis of Count Data: Poisson Responses 502

      18.3.1 Understanding and Dening the Model 503

      18.3.2 Analysis of the Model 506

      18.3.3 Analysing Poisson Responses with Several Explanatory Variables 509

      18.3.4 Other Issues with Poisson Responses 512

18.4 Other Types of GLM and Extensions 512

Exercises 513

19. Practical Design and Data Analysis for Real Studies 517

19.1 Designing Real Studies 518

      19.1.1 Aims, Objectives and Choice of Explanatory Structure 518

      19.1.2 Resources, Experimental Units and Constraints 519

      19.1.3 Matching the Treatments to the Resources 520

      19.1.4 Designs for Series of Studies and for Studies with Multiple Phases 521

      19.1.5 Design Case Studies 523

19.2 Choosing the Best Analysis Approach 535

      19.2.1 Analysis of Designed Experiments 536

      19.2.2 Analysis of Observational Studies 537

      19.2.3 Different Types of Data 538

19.3 Presentation of Statistics in Reports, Theses and Papers 538

      19.3.1 Statistical Information in the Materials and Methods 539

      19.3.2 Presentation of Results 540

19.4 And Finally 543

References 545

Appendix A: Data Tables 551

Appendix B: Quantiles of Statistical Distributions 559

Appendix C: Statistical and Mathematical Results 563

Index 569

中科院文献情报中心