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Summary:

"Written in simple language with relevant examples, this illustrative introductory book presents best practices in experimental design and simple data analysis. Taking a practical and intuitive approach, it 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"-- [Provided by publisher]
"This book provides an introductory, practical and illustrative guide to design of experiments and data analysis in the biological and agricultural plant sciences. It is aimed both at research scientists and at students (from final year undergraduate level through taught masters to PhD students) who either need to design their own experiments and perform their own analyses or can consult with a professional applied statistician, and want to have a clear understanding of the methods that they are using. The material is based on courses developed at two British research institutes (Rothamsted Research and Horticulture Research International (HRI)--then Warwick HRI, and now the School of Life Science, University of Warwick) to train research scientists and post-graduate students in these key areas of statistics. Our overall approach is intended to be practical and intuitive rather than overly theoretical, with mathematical formulae presented only to formalise the methods where appropriate and necessary. Our intention is to present statistical ideas in the context of the biological and agricultural sciences to which they are being applied, drawing on relevant examples from our own experiences as consultant applied statisticians at research institutes, to encourage best practice in design and data analysis. The first two chapters of this book provide introductory, review and background material. In Chapter 1, we introduce types of data and statistical models, together with an overview of the basic statistical concepts and terminology used throughout"-- [Provided by publisher]

Table of Contents:

• Machine generated contents note: 1.1. Different Types of Scientific Study
• 1.2. Relating Sample Results to More General Populations
• 1.3. Constructing Models to Represent Reality
• 1.4. Using Linear Models
• 1.5. Estimating the Parameters of Linear Models
• 1.6. Summarizing the Importance of Model Terms
• 1.7. Scope of This Book
• 2.1. Summary Statistics and Notation for Sample Data
• 2.2. Statistical Distributions for Populations
• 2.2.1. Discrete Data
• 2.2.2. Continuous Data
• 2.2.3. Normal Distribution
• 2.2.4. Distributions Derived from Functions of Normal Random Variables
• 2.3. From Sample Data to Conclusions about the Population
• 2.3.1. Estimating Population Parameters Using Summary Statistics
• 2.3.2. Asking Questions about the Data: Hypothesis Testing
• 2.4. Simple Tests for Population Means
• 2.4.1. Assessing the Mean Response: The One-Sample t-Test
• 2.4.2. Comparing Mean Responses: The Two-Sample t-Test
• 2.5. Assessing the Association between Variables

• 2.6. Presenting Numerical Results
• Exercises
• 3.1. Key Principles
• 3.1.1. Replication
• 3.1.2. Randomization
• 3.1.3. Blocking
• 3.2. Forms of Experimental Structure
• 3.3. Common Forms of Design for Experiments
• 3.3.1. Completely Randomized Design
• 3.3.2. Randomized Complete Block Design
• 3.3.3. Latin Square Design
• 3.3.4. Split-Plot Design
• 3.3.5. Balanced Incomplete Block Design
• 3.3.6. Generating a Randomized Design
• Exercises
• 4.1. Defining the Model
• 4.2. Estimating the Model Parameters
• 4.3. Summarizing the Importance of Model Terms
• 4.3.1. Calculating Sums of Squares
• 4.3.2. Calculating Degrees of Freedom and Mean Squares
• 4.3.3. Calculating Variance Ratios as Test Statistics
• 4.3.4. Summary ANOVA Table
• 4.4. Evaluating the Response to Treatments
• 4.4.1. Prediction of Treatment Means
• 4.4.2. Comparison of Treatment Means
• 4.5. Alternative Forms of the Model
• Exercises
• 5.1. Estimating Deviations
• 5.1.1. Simple Residuals
• 5.1.2. Standardized Residuals
• 5.2. Using Graphical Tools to Diagnose Problems
• 5.2.1. Assessing Homogeneity of Variances
• 5.2.2. Assessing Independence
• 5.2.3. Assessing Normality
• 5.2.4. Using Permutation Tests Where Assumptions Fail
• 5.2.5. Impact of Sample Size
• 5.3. Using Formal Tests to Diagnose Problems
• 5.4. Identifying Inconsistent Observations
• Exercises
• 6.1. Why Do We Need to Transform the Response?
• 6.2. Some Useful Transformations
• 6.2.1. Logarithms
• 6.2.2. Square Roots
• 6.2.3. Logits
• 6.2.4. Other Transformations
• 6.3. Interpreting the Results after Transformation
• 6.4. Interpretation for Log-Transformed Responses
• 6.5. Other Approaches
• Exercises
• 7.1. Defining the Model
• 7.2. Estimating the Model Parameters
• 7.3. Summarizing the Importance of Model Terms
• 7.4. Evaluating the Response to Treatments
• 7.5. Incorporating Strata: The Multi-Stratum Analysis of Variance
• Exercises
• 8.1. From Scientific Questions to the Treatment Structure
• 8.2. Crossed Treatment Structure with Two Factors
• 8.2.1. Models for a Crossed Treatment Structure with Two Factors
• 8.2.2. Estimating the Model Parameters
• 8.2.3. Assessing the Importance of Individual Model Terms
• 8.2.4. Evaluating the Response to Treatments: Predictions from the Fitted Model
• 8.2.5. Advantages of Factorial Structure
• 8.2.6. Understanding Different Parameterizations
• 8.3. Crossed Treatment Structures with Three or More Factors
• 8.3.1. Assessing the Importance of Individual Model Terms
• 8.3.2. Evaluating the Response to Treatments: Predictions from the Fitted Model
• 8.4. Models for Nested Treatment Structures
• 8.5. Adding Controls or Standards to a Set of Treatments
• 8.6. Investigating Specific Treatment Comparisons
• 8.7. Modelling Patterns for Quantitative Treatments
• 8.8. Making Treatment Comparisons from Predicted Means
• 8.8.1. Bonferroni Correction
• 8.8.2. False Discovery Rate
• 8.8.3. All Pairwise Comparisons
• 8.8.3.1. LSD and Fisher's Protected LSD
• 8.8.3.2. Multiple Range Tests
• 8.8.3.3. Tukey's Simultaneous Confidence Intervals
• 8.8.4. Comparison of Treatments against a Control
• 8.8.5. Evaluation of a Set of Pre-Planned Comparisons
• 8.8.6. Summary of Issues
• Exercises
• 9.1. Latin Square Design
• 9.1.1. Defining the Model
• 9.1.2. Estimating the Model Parameters
• 9.1.3. Assessing the Importance of Individual Model Terms
• 9.1.4. Evaluating the Response to Treatments: Predictions from the Fitted Model
• 9.1.5. Constraints and Extensions of the Latin Square Design
• 9.2. Split-Plot Design
• 9.2.1. Defining the Model
• 9.2.2. Assessing the Importance of Individual Model Terms
• 9.2.3. Evaluating the Response to Treatments: Predictions from the Fitted Model
• 9.2.4. Drawbacks and Variations of the Split-Plot Design
• 9.3. Balanced Incomplete Block Design
• 9.3.1. Defining the Model
• 9.3.2. Assessing the Importance of Individual Model Terms
• 9.3.3. Drawbacks and Variations of the Balanced Incomplete Block Design
• Exercises
• 10.1. Simple Methods for Determining Replication
• 10.1.1. Calculations Based on the LSD
• 10.1.2. Calculations Based on the Coefficient of Variation
• 10.1.3. Unequal Replication and Models with Blocking
• 10.2. Estimating the Background Variation
• 10.3. Assessing the Power of a Design
• 10.4. Constructing a Design for a Particular Experiment
• 10.5. Different Hypothesis: Testing for Equivalence
• Exercise
• 11.1. Benefits of Orthogonality
• 11.2. Fitting Models with Non-Orthogonal Terms
• 11.2.1. Parameterizing Models for Two Non-Orthogonal Factors
• 11.2.2. Assessing the Importance of Non-Orthogonal Terms: The Sequential ANOVA Table
• 11.2.3. Calculating the Impact of Model Terms
• 11.2.4. Selecting the Best Model
• 11.2.5. Evaluating the Response to Treatments: Predictions from the Fitted Model
• 11.3. Designs with Planned Non-Orthogonality
• 11.3.1. Fractional Factorial Designs
• 11.3.2. Factorial Designs with Confounding
• 11.4. Consequences of Missing Data
• 11.5. Incorporating the Effects of Unplanned Factors
• 11.6. Analysis Approaches for Non-Orthogonal Designs
• 11.6.1. Simple Approach: The Intra-Block Analysis
• Exercises
• 12.1. Defining the Model
• 12.2. Estimating the Model Parameters
• 12.3. Assessing the Importance of the Model
• 12.4. Properties of the Model Parameters
• 12.5. Using the Fitted Model to Predict Responses
• 12.6. Summarizing the Fit of the Model
• 12.7. Consequences of Uncertainty in the Explanatory Variate
• 12.8. Using Replication to Test Goodness of Fit
• 12.9. Variations on the Model
• 12.9.1. Centering and Scaling the Explanatory Variate
• 12.9.2. Regression through the Origin
• 12.9.3. Calibration
• Exercises
• 13.1. Checking the Form of the Model
• 13.2. More Ways of Estimating Deviations
• 13.3. Using Graphical Tools to Check Assumptions
• 13.4. Looking for Influential Observations
• 13.4.1. Measuring Potential Influence: Leverage
• 13.4.2. Relationship between Residuals and Leverages
• 13.4.3. Measuring the Actual Influence of Individual Observations
• 13.5. Assessing the Predictive Ability of a Model: Cross-Validation
• Exercises
• 14.1. Visualizing Relationships between Variates
• 14.2. Defining the Model
• 14.3. Estimating the Model Parameters
• 14.4. Assessing the Importance of Individual Explanatory Variates
• 14.4.1. Adding Terms into the Model: Sequential ANOVA and Incremental Sums of Squares
• 14.4.2. Impact of Removing Model Terms: Marginal Sums of Squares
• 14.5. Properties of the Model Parameters and Predicting Responses
• 14.6. Investigating Model Misspecification
• 14.7. Dealing with Correlation among Explanatory Variates
• 14.8. Summarizing the Fit of the Model
• 14.9. Selecting the Best Model
• 14.9.1. Strategies for Sequential Variable Selection
• 14.9.2. Problems with Procedures for the Selection of Subsets of Variables
• 14.9.3. Using Cross-Validation as a Tool for Model Selection
• 14.9.4. Some Final Remarks on Procedures for Selecting Models
• Exercises
• 15.1. Incorporating Groups into the Simple Linear Regression Model
• 15.1.1. Overview of Possible Models
• 15.1.2. Defining and Choosing between the Models
• 15.1.2.1. Single Line Model
• 15.1.2.2. Parallel Lines Model
• 15.1.2.3. Separate Lines Model
• 15.1.2.4. Choosing between the Models: The Sequential ANOVA Table
• 15.1.3. Alternative Sequence of Models
• 15.1.4. Constraining the Intercepts
• 15.2. Incorporating Groups into the Multiple Linear Regression Model
• 15.3. Regression in Designed Experiments
• 15.4. Analysis of Covariance: A Special Case of Regression with Groups
• 15.5. Complex Models with Factors and Variates
• 15.5.1. Selecting the Predictive Model
• 15.5.2. Evaluating the Response: Predictions from the Fitted Model
• 15.6. Connection between Factors and Variates
• 15.6.1. Rewriting the Model in Matrix Notation
• Exercises
• 16.1. Incorporating Structure
• 16.2. Introduction to Linear Mixed Models
• 16.3. Selecting the Best Fixed Model
• 16.4. Interpreting the Random Model
• 16.4.1. Connection between the Linear Mixed Model and Multi-Stratum ANOVA
• 16.5. What about Random Effects?
• 16.6. Predicting Responses
• 16.7. Checking Model Fit
• 16.8. Example
• 16.9. Some Pitfalls and Dangers
• Contents note continued: 16.10. Extending the Model
• Exercises
• 17.1. Fitting Curved Functions by Transformation
• 17.1.1. Simple Transformations of an Explanatory Variate
• 17.1.2. Polynomial Models
• 17.1.3. Trigonometric Models for Periodic Patterns
• 17.2. Curved Surfaces as Functions of Two or More Variates
• 17.3. Fitting Models Including Non-Linear Parameters
• Exercises
• 18.1. Introduction to Generalized Linear Models
• 18.2. Analysis of Proportions Based on Counts: Binomial Responses
• 18.2.1. Understanding and Defining the Model
• 18.2.2. Assessing the Importance of the Model and Individual Terms: The Analysis of Deviance
• 18.2.2.1. Interpreting the ANODEV with No Over-Dispersion
• 18.2.2.2. Interpreting the ANODEV with Over-Dispersion
• 18.2.2.3. Sequential ANODEV Table
• 18.2.3. Checking the Model Fit and Assumptions
• 18.2.4. Properties of the Model Parameters
• 18.2.5. Evaluating the Response to Explanatory Variables: Prediction
• 18.2.6. Aggregating Binomial Responses
• 18.2.7. Special Case of Binary Data
• 18.2.8. Other Issues with Binomial Responses
• 18.3. Analysis of Count Data: Poisson Responses
• 18.3.1. Understanding and Defining the Model
• 18.3.2. Analysis of the Model
• 18.3.3. Analysing Poisson Responses with Several Explanatory Variables
• 18.3.4. Other Issues with Poisson Responses
• 18.4. Other Types of GLM and Extensions
• Exercises
• 19.1. Designing Real Studies
• 19.1.1. Aims, Objectives and Choice of Explanatory Structure
• 19.1.2. Resources, Experimental Units and Constraints
• 19.1.3. Matching the Treatments to the Resources
• 19.1.4. Designs for Series of Studies and for Studies with Multiple Phases
• 19.1.5. Design Case Studies
• 19.2. Choosing the Best Analysis Approach
• 19.2.1. Analysis of Designed Experiments
• 19.2.2. Analysis of Observational Studies
• 19.2.3. Different Types of Data
• 19.3. Presentation of Statistics in Reports, Theses and Papers
• 19.3.1. Statistical Information in the Materials and Methods
• 19.3.2. Presentation of Results
• 19.4. And Finally.

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Author/Creator:

Welham, S. J. (Suzanne Jane) , author

Languages:

English

Language Notes:

Item content: English

Main Work:

Statistical methods in biology: design and analysis of experiments and regression [by Welham, S.J.]

Subjects:

Biometry

Regression analysis

Experimental design

General Notes:

"A Chapman & Hall book."
Includes bibliographical references (pages 545-549) and index.
Description based on print version record.

Physical Description:

1 online resource.

Call Numbers:

QH323.5 .W45 2015eb

ISBNs:

1439898057 (electronic bk.)
9781439898055 (electronic bk.)
9781439808788 (hardback, acid-free paper) [Invalid]
1439808783 (hardback, acid-free paper) [Invalid]

Other Standard Numbers:

[Unknown Type]: 40024068694

OCLC Numbers:

923511649

Other Control Numbers:

EBC1644962 (source: MiAaPQ)
[Unknown Type]: ybp12368313