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El. knyga: Statistical Methods in Biology: Design and Analysis of Experiments and Regression

(Rothamsted Research, UK), (School of Forest Resources & Conservation, University of Florida, USA), (Horticultural Research Institute, University of Warwick, UK), (Rothamsted Research, UK)
  • Formatas: 602 pages
  • Išleidimo metai: 22-Aug-2014
  • Leidėjas: Chapman & Hall/CRC
  • Kalba: eng
  • ISBN-13: 9781439898055
  • Formatas: 602 pages
  • Išleidimo metai: 22-Aug-2014
  • Leidėjas: Chapman & Hall/CRC
  • Kalba: eng
  • ISBN-13: 9781439898055

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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.

Recenzijos

"This is absolutely a traditional statistics textbook, with a strong basis in classical approaches such as blocking, crossed, and nested designs. There is much the volume does well. It provides one of the most lucid descriptions of ANOVA that I have come across, and the strong emphasis on coupling experimental design with appropriately planned analysis (often described as important but rarely covered in detail in other statistical publications) make this a textbook that would be useful to those setting up controlled experiments, particularly in the field. Additionally, the provision of plenty of online material and exercises (at http://www.stats4biol.info) for use with GenStat, SAS, and R packages is a useful practical resource. [ T]o those who might be looking for a new statistics textbook to work through systematically, it does provide a good reference for anyone who wishes to dissect specific topics in more depth." Matthew R.E. Symonds in The Quarterly Review of Biology, June 2017

"This book is the first serious and successful attempt to teach the general principles underlying sound experimental design and analysis to an audience of students and researchers in biology. The book is written from a strongly applied perspective with lots of real-life examples, but enough mathematical details are given to allow the reader to tailor design and analysis principles to new problems. The leading principle for analysis of experimental data is the multi-stratum analysis of variance. This powerful principle is part of the Rothamsted tradition of applied statistics to which the authors belong. This book makes statistical highlights from that tradition accessible to life scientists without demanding excessive mathematical skills." Fred van Eeuwijk, Wageningen University and Research Centre

"This book is easy to read. I am very happy to recommend this book to both scientists as a reference, and to students in the area of agricultural and biological plant sciences as a textbook. It covers most aspects of planning experiments and the steps necessary for analyzing the resulting data, bringing the authors experience to the reader with real examples. It is obvious that the authors have taken great care in framing their conclusions and the possible interpretations of the results." Clarice G.B. Demétrio, Professor of Experimental Statistics, Escola Superior de Agricultura "Luiz de Queiroz," University of Sćo Paulo

"This book connects the underlying principles of design and statistics to good practice in data analysis. It also gives a solid account of the most commonly used and needed statistical methods in experimental biology. It explains concepts in clear, practical, and accessible ways, using real data to illustrate throughout. Mathematical notation is used when necessary but the explanations of key points are in common language. I would particularly recommend this book for research students. It provides a no-nonsense, gimmick-free account of the key statistical concepts and practices that will allow you to do valid and useful analyses and understand the results from statistical software." Richard Coe, Principal Scientist-Research Methods, World Agroforestry Centre (ICRAF) and Statistical Services Centre

"This book will be invaluable to plant scientists who want to develop their knowledge of statistics. Based on courses developed by the authors, the aim is to provide a deep understanding of the most commonly used experimental designs and their analysis, along with linear regression, and to emphasize the connections between these areas. A background in basic statistics, to the level of t-tests, would be helpful, though a revision chapter is provided. Additional chapters introduce linear mixed models and generalised linear models for counts and proportions. The authors extensive practical experience is apparent throughout, particularly in the many interesting examples that pervade the book. A companion website provides associated data and code in GenStat, R, and (soon) SAS. This in itself is a terrific resource, with 50 well-commented programs covering basic analyses and extensions. Each chapter has exercises; these are often challenging and solutions will be provided on the website. Most of the examples stem from Rothamsted, where all of the authors work or have worked, and the book has something of a Rothamsted feel to it, for example with a strong emphasis on multi-stratum ANOVA to incorporate blocking and other experimental structure even when this is not strictly essential; the benefits of this approach for clarifying more complex designs become apparent as the book progresses. Everything is here for the plant scientist to develop a really solid understanding of the subject and it is difficult to see how the authors could have done a better job of delivering the book that they set out to write." Martin Ridout, Professor of Applied Statistics, University of Kent

Preface xv
Authors xix
1 Introduction 1(12)
1.1 Different Types of Scientific Study
1(2)
1.2 Relating Sample Results to More General Populations
3(1)
1.3 Constructing Models to Represent Reality
4(3)
1.4 Using Linear Models
7(1)
1.5 Estimating the Parameters of Linear Models
8(1)
1.6 Summarizing the Importance of Model Terms
9(2)
1.7 The Scope of This Book
11(2)
2 A Review of Basic Statistics 13(30)
2.1 Summary Statistics and Notation for Sample Data
13(3)
2.2 Statistical Distributions for Populations
16(12)
2.2.1 Discrete Data
17(5)
2.2.2 Continuous Data
22(2)
2.2.3 The Normal Distribution
24(2)
2.2.4 Distributions Derived from Functions of Normal Random Variables
26(2)
2.3 From Sample Data to Conclusions about the Population
28(2)
2.3.1 Estimating Population Parameters Using Summary Statistics
28(1)
2.3.2 Asking Questions about the Data: Hypothesis Testing
29(1)
2.4 Simple Tests for Population Means
30(6)
2.4.1 Assessing the Mean Response: The One-Sample t-Test
30(2)
2.4.2 Comparing Mean Responses: The Two-Sample t-Test
32(4)
2.5 Assessing the Association between Variables
36(3)
2.6 Presenting Numerical Results
39(2)
Exercises
41(2)
3 Principles for Designing Experiments 43(26)
3.1 Key Principles
43(9)
3.1.1 Replication
46(2)
3.1.2 Randomization
48(3)
3.1.3 Blocking
51(1)
3.2 Forms of Experimental Structure
52(5)
3.3 Common Forms of Design for Experiments
57(5)
3.3.1 The Completely Randomized Design
57(1)
3.3.2 The Randomized Complete Block Design
58(1)
3.3.3 The Latin Square Design
59(1)
3.3.4 The Split-Plot Design
60(1)
3.3.5 The Balanced Incomplete Block Design
61(1)
3.3.6 Generating a Randomized Design
62(1)
Exercises
62(7)
4 Models for a Single Factor 69(24)
4.1 Defining the Model
69(4)
4.2 Estimating the Model Parameters
73(1)
4.3 Summarizing the Importance of Model Terms
74(10)
4.3.1 Calculating Sums of Squares
76(4)
4.3.2 Calculating Degrees of Freedom and Mean Squares
80(1)
4.3.3 Calculating Variance Ratios as Test Statistics
81(1)
4.3.4 The Summary ANOVA Table
82(2)
4.4 Evaluating the Response to Treatments
84(4)
4.4.1 Prediction of Treatment Means
84(1)
4.4.2 Comparison of Treatment Means
85(3)
4.5 Alternative Forms of the Model
88(2)
Exercises
90(3)
5 Checking Model Assumptions 93(20)
5.1 Estimating Deviations
93(3)
5.1.1 Simple Residuals
94(1)
5.1.2 Standardized Residuals
95(1)
5.2 Using Graphical Tools to Diagnose Problems
96(8)
5.2.1 Assessing Homogeneity of Variances
96(2)
5.2.2 Assessing Independence
98(3)
5.2.3 Assessing Normality
101(1)
5.2.4 Using Permutation Tests Where Assumptions Fail
102(1)
5.2.5 The Impact of Sample Size
103(1)
5.3 Using Formal Tests to Diagnose Problems
104(4)
5.4 Identifying Inconsistent Observations
108(2)
Exercises
110(3)
6 Transformations of the Response 113(16)
6.1 Why Do We Need to Transform the Response?
113(1)
6.2 Some Useful Transformations
114(8)
6.2.1 Logarithms
114(5)
6.2.2 Square Roots
119(1)
6.2.3 Logits
120(1)
6.2.4 Other Transformations
121(1)
6.3 Interpreting the Results after Transformation
122(1)
6.4 Interpretation for Log-Transformed Responses
123(3)
6.5 Other Approaches
126(1)
Exercises
127(2)
7 Models with a Simple Blocking Structure 129(20)
7.1 Defining the Model
130(2)
7.2 Estimating the Model Parameters
132(2)
7.3 Summarizing the Importance of Model Terms
134(6)
7.4 Evaluating the Response to Treatments
140(1)
7.5 Incorporating Strata: The Multi-Stratum Analysis of Variance
141(5)
Exercises
146(3)
8 Extracting Information about Treatments 149(60)
8.1 From Scientific Questions to the Treatment Structure
150(2)
8.2 A Crossed Treatment Structure with Two Factors
152(12)
8.2.1 Models for a Crossed Treatment Structure with Two Factors
153(2)
8.2.2 Estimating the Model Parameters
155(3)
8.2.3 Assessing the Importance of Individual Model Terms
158(2)
8.2.4 Evaluating the Response to Treatments: Predictions from the Fitted Model
160(2)
8.2.5 The Advantages of Factorial Structure
162(1)
8.2.6 Understanding Different Parameterizations
163(1)
8.3 Crossed Treatment Structures with Three or More Factors
164(9)
8.3.1 Assessing the Importance of Individual Model Terms
166(5)
8.3.2 Evaluating the Response to Treatments: Predictions from the Fitted Model
171(2)
8.4 Models for Nested Treatment Structures
173(6)
8.5 Adding Controls or Standards to a Set of Treatments
179(3)
8.6 Investigating Specific Treatment Comparisons
182(8)
8.7 Modelling Patterns for Quantitative Treatments
190(5)
8.8 Making Treatment Comparisons from Predicted Means
195(11)
8.8.1 The Bonferroni Correction
196(1)
8.8.2 The False Discovery Rate
197(1)
8.8.3 All Pairwise Comparisons
198(3)
8.8.3.1 The LSD and Fisher's Protected LSD
198(1)
8.8.3.2 Multiple Range Tests
199(1)
8.8.3.3 Tukey's Simultaneous Confidence Intervals
200(1)
8.8.4 Comparison of Treatments against a Control
201(1)
8.8.5 Evaluation of a Set of Pre-Planned Comparisons
201(4)
8.8.6 Summary of Issues
205(1)
Exercises
206(3)
9 Models with More Complex Blocking Structure 209(32)
9.1 The Latin Square Design
209(11)
9.1.1 Defining the Model
211(1)
9.1.2 Estimating the Model Parameters
211(1)
9.1.3 Assessing the Importance of Individual Model Terms
212(3)
9.1.4 Evaluating the Response to Treatments: Predictions from the Fitted Model
215(2)
9.1.5 Constraints and Extensions of the Latin Square Design
217(3)
9.2 The Split-Plot Design
220(12)
9.2.1 Defining the Model
222(1)
9.2.2 Assessing the Importance of Individual Model Terms
223(2)
9.2.3 Evaluating the Response to Treatments: Predictions from the Fitted Model
225(3)
9.2.4 Drawbacks and Variations of the Split-Plot Design
228(4)
9.3 The Balanced Incomplete Block Design
232(6)
9.3.1 Defining the Model
235(1)
9.3.2 Assessing the Importance of Individual Model Terms
236(1)
9.3.3 Drawbacks and Variations of the Balanced Incomplete Block Design
237(1)
Exercises
238(3)
10 Replication and Power 241(16)
10.1 Simple Methods for Determining Replication
242(3)
10.1.1 Calculations Based on the LSD
242(1)
10.1.2 Calculations Based on the Coefficient of Variation
243(1)
10.1.3 Unequal Replication and Models with Blocking
244(1)
10.2 Estimating the Background Variation
245(1)
10.3 Assessing the Power of a Design
245(4)
10.4 Constructing a Design for a Particular Experiment
249(4)
10.5 A Different Hypothesis: Testing for Equivalence
253(3)
Exercise
256(1)
11 Dealing with Non-Orthogonality 257(30)
11.1 The Benefits of Orthogonality
257(2)
11.2 Fitting Models with Non-Orthogonal Terms
259(13)
11.2.1 Parameterizing Models for Two Non-Orthogonal Factors
259(6)
11.2.2 Assessing the Importance of Non-Orthogonal Terms: The Sequential ANOVA Table
265(4)
11.2.3 Calculating the Impact of Model Terms
269(1)
11.2.4 Selecting the Best Model
270(1)
11.2.5 Evaluating the Response to Treatments: Predictions from the Fitted Model
270(2)
11.3 Designs with Planned Non-Orthogonality
272(2)
11.3.1 Fractional Factorial Designs
273(1)
11.3.2 Factorial Designs with Confounding
274(1)
11.4 The Consequences of Missing Data
274(3)
11.5 Incorporating the Effects of Unplanned Factors
277(3)
11.6 Analysis Approaches for Non-Orthogonal Designs
280(4)
11.6.1 A Simple Approach: The Intra-Block Analysis
281(3)
Exercises
284(3)
12 Models for a Single Variate: Simple Linear Regression 287(38)
12.1 Defining the Model
288(4)
12.2 Estimating the Model Parameters
292(4)
12.3 Assessing the Importance of the Model
296(3)
12.4 Properties of the Model Parameters
299(2)
12.5 Using the Fitted Model to Predict Responses
301(4)
12.6 Summarizing the Fit of the Model
305(1)
12.7 Consequences of Uncertainty in the Explanatory Variate
306(2)
12.8 Using Replication to Test Goodness of Fit
308(5)
12.9 Variations on the Model
313(8)
12.9.1 Centering and Scaling the Explanatory Variate
313(1)
12.9.2 Regression through the Origin
314(6)
12.9.3 Calibration
320(1)
Exercises
321(4)
13 Checking Model Fit 325(20)
13.1 Checking the Form of the Model
325(3)
13.2 More Ways of Estimating Deviations
328(2)
13.3 Using Graphical Tools to Check Assumptions
330(2)
13.4 Looking for Influential Observations
332(6)
13.4.1 Measuring Potential Influence: Leverage
333(2)
13.4.2 The Relationship between Residuals and Leverages
335(1)
13.4.3 Measuring the Actual Influence of Individual Observations
336(2)
13.5 Assessing the Predictive Ability of a Model: Cross-Validation
338(4)
Exercises
342(3)
14 Models for Several Variates: Multiple Linear Regression 345(36)
14.1 Visualizing Relationships between Variates
345(2)
14.2 Defining the Model
347(3)
14.3 Estimating the Model Parameters
350(2)
14.4 Assessing the Importance of Individual Explanatory Variates
352(6)
14.4.1 Adding Terms into the Model: Sequential ANOVA and Incremental Sums of Squares
353(3)
14.4.2 The Impact of Removing Model Terms: Marginal Sums of Squares
356(2)
14.5 Properties of the Model Parameters and Predicting Responses
358(1)
14.6 Investigating Model Misspecification
359(2)
14.7 Dealing with Correlation among Explanatory Variates
361(4)
14.8 Summarizing the Fit of the Model
365(1)
14.9 Selecting the Best Model
366(12)
14.9.1 Strategies for Sequential Variable Selection
369(7)
14.9.2 Problems with Procedures for the Selection of Subsets of Variables
376(1)
14.9.3 Using Cross-Validation as a Tool for Model Selection
377(1)
14.9.4 Some Final Remarks on Procedures for Selecting Models
378(1)
Exercises
378(3)
15 Models for Variates and Factors 381(46)
15.1 Incorporating Groups into the Simple Linear Regression Model
382(17)
15.1.1 An Overview of Possible Models
383(5)
15.1.2 Defining and Choosing between the Models
388(8)
15.1.2.1 Single Line Model
388(1)
15.1.2.2 Parallel Lines Model
388(2)
15.1.2.3 Separate Lines Model
390(1)
15.1.2.4 Choosing between the Models: The Sequential ANOVA Table
391(5)
15.1.3 An Alternative Sequence of Models
396(2)
15.1.4 Constraining the Intercepts
398(1)
15.2 Incorporating Groups into the Multiple Linear Regression Model
399(7)
15.3 Regression in Designed Experiments
406(3)
15.4 Analysis of Covariance: A Special Case of Regression with Groups
409(5)
15.5 Complex Models with Factors and Variates
414(3)
15.5.1 Selecting the Predictive Model
414(3)
15.5.2 Evaluating the Response: Predictions from the Fitted Model
417(1)
15.6 The Connection between Factors and Variates
417(6)
15.6.1 Rewriting the Model in Matrix Notation
421(2)
Exercises
423(4)
16 Incorporating Structure: Linear Mixed Models 427(24)
16.1 Incorporating Structure
427(1)
16.2 An Introduction to Linear Mixed Models
428(2)
16.3 Selecting the Best Fixed Model
430(2)
16.4 Interpreting the Random Model
432(3)
16.4.1 The Connection between the Linear Mixed Model and Multi-Stratum ANOVA
434(1)
16.5 What about Random Effects?
435(1)
16.6 Predicting Responses
436(1)
16.7 Checking Model Fit
437(1)
16.8 An Example
438(6)
16.9 Some Pitfalls and Dangers
444(1)
16.10 Extending the Model
445(2)
Exercises
447(4)
17 Models for Curved Relationships 451(28)
17.1 Fitting Curved Functions by Transformation
451(12)
17.1.1 Simple Transformations of an Explanatory Variate
451(5)
17.1.2 Polynomial Models
456(4)
17.1.3 Trigonometric Models for Periodic Patterns
460(3)
17.2 Curved Surfaces as Functions of Two or More Variates
463(9)
17.3 Fitting Models Including Non-Linear Parameters
472(4)
Exercises
476(3)
18 Models for Non-Normal Responses: Generalized Linear Models 479(38)
18.1 Introduction to Generalized Linear Models
480(1)
18.2 Analysis of Proportions Based on Counts: Binomial Responses
481(21)
18.2.1 Understanding and Defining the Model
483(4)
18.2.2 Assessing the Importance of the Model and Individual Terms: The Analysis of Deviance
487(7)
18.2.2.1 Interpreting the ANODEV with No Over-Dispersion
489(1)
18.2.2.2 Interpreting the ANODEV with Over-Dispersion
490(3)
18.2.2.3 The Sequential ANODEV Table
493(1)
18.2.3 Checking the Model Fit and Assumptions
494(2)
18.2.4 Properties of the Model Parameters
496(2)
18.2.5 Evaluating the Response to Explanatory Variables: Prediction
498(2)
18.2.6 Aggregating Binomial Responses
500(1)
18.2.7 The Special Case of Binary Data
501(1)
18.2.8 Other Issues with Binomial Responses
501(1)
18.3 Analysis of Count Data: Poisson Responses
502(10)
18.3.1 Understanding and Defining the Model
503(3)
18.3.2 Analysis of the Model
506(3)
18.3.3 Analysing Poisson Responses with Several Explanatory Variables
509(3)
18.3.4 Other Issues with Poisson Responses
512(1)
18.4 Other Types of GLM and Extensions
512(1)
Exercises
513(4)
19 Practical Design and Data Analysis for Real Studies 517(28)
19.1 Designing Real Studies
518(17)
19.1.1 Aims, Objectives and Choice of Explanatory Structure
518(1)
19.1.2 Resources, Experimental Units and Constraints
519(1)
19.1.3 Matching the Treatments to the Resources
520(1)
19.1.4 Designs for Series of Studies and for Studies with Multiple Phases
521(2)
19.1.5 Design Case Studies
523(12)
19.2 Choosing the Best Analysis Approach
535(3)
19.2.1 Analysis of Designed Experiments
536(1)
19.2.2 Analysis of Observational Studies
537(1)
19.2.3 Different Types of Data
538(1)
19.3 Presentation of Statistics in Reports, Theses and Papers
538(5)
19.3.1 Statistical Information in the Materials and Methods
539(1)
19.3.2 Presentation of Results
540(3)
19.4 And Finally
543(2)
References 545(6)
Appendix A: Data Tables 551(8)
Appendix B: Quantiles of Statistical Distributions 559(4)
Appendix C: Statistical and Mathematical Results 563(6)
Index 569
Suzanne Jane Welham obtained an MSc in statistical sciences from University College London in 1987 and worked as an applied statistician at Rothamsted Research from 1987 to 2000, collaborating with scientists and developing statistical software. She pursued a PhD from 2000 to 2003 at the London School of Hygiene and Tropical Medicine and then returned to Rothamsted, during which time she coauthored the in-house statistics courses that motivated the writing of this book. She is a coauthor of about 60 published papers and currently works for VSN International Ltd on the development of statistical software for analysis of linear mixed models and presents training courses on their use in R and GenStat.

Salvador Alejandro Gezan, PhD, is an assistant professor at the School of Forest Resources and Conservation at the University of Florida since 2011. Salvador obtained his bachelors from the Universidad of Chile in forestry and his PhD from the University of Florida in statistics-genetics. He then worked as an applied statistician at Rothamsted Research, collaborating on the production and development of the in-house courses that formed the basis for this book. Currently, he teaches courses in linear and mixed model effects, quantitative genetics and forest mensuration. He carries out research and consulting in statistical application to biological sciences with emphasis on genetic improvement of plants and animals. Salvador is a long-time user of SAS, which he combines with GenStat, R and MATLAB as required.

Suzanne Jane Clark has worked at Rothamsted Research as an applied statistician since 1981. She primarily collaborates with ecologists and entomologists at Rothamsted, providing and implementing advice on statistical issues ranging from planning and design of experiments through to data analysis and presentation of results, and has coauthored over 130 scientific papers. Suzanne coauthored and presents several of the in-house statistics courses for scientists and research students, which inspired the writing of this book. An experienced and long-term GenStat user, Suzanne has also written several procedures for the GenStat Procedure Library and uses GenStat daily for the analyses of biological data using a wide range of statistical techniques, including those covered in this book.

Andrew Mead obtained a BSc in statistics at the University of Bath and an MSc in biometry at the University of Reading, where he spent over 16 years working as a consultant and research biometrician at the Institute of Horticultural Research and Horticulture Research International at Wellesbourne, Warwickshire, UK. During this time, he developed and taught a series of statistics training courses for staff and students at the institute, producing some of the material on which this book is based. For 10 years from 2004 he worked as a research biometrician and teaching fellow at the University of Warwick, developing and leading the teaching of statistics for both postgraduate and undergraduate students across a range of life sciences. In 2014 he was appointed as Head of Applied Statistics at Rothamsted Research. Throughout his career he has had a strong association with the International Biometric Society, serving as International President and Vice President from 2007 to 2010 inclusive, having been the first recipient of the Award for Outstanding Contribution to the Development of the International Biometric Society in 2006, serving as a Regional Secretary of the British and Irish Region from 2000 to 2007 and on the International Council from 2002 to 2010. He is a (co)author of over 80 papers, and coauthor of Statistical Principles for the Design of Experiments: Applications to Real Experiments published in 2012.