Statistical Methods in Biology Design and Analysis of Experiments and Regression 1st Edition by SJ Welham, SA Gezan, SJ Clark, A Mead ISBN 9781439808788 1439808783

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ISBN 10: 1439808783
ISBN 13: 9781439808788
Author: SJ Welham, SA Gezan, SJ Clark, A Mead

Statistical Methods in Biology Design and Analysis of Experiments and Regression 1st Edition Table of contents:

1 Introduction

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 The Scope of This Book

2 A Review of Basic Statistics

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 The 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 Principles for Designing Experiments

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 The Completely Randomized Design

3.3.2 The Randomized Complete Block Design

3.3.3 The Latin Square Design

3.3.4 The Split-Plot Design

3.3.5 The Balanced Incomplete Block Design

3.3.6 Generating a Randomized Design

Exercises

4 Models for a Single Factor

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 The 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 Checking Model Assumptions

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 The Impact of Sample Size

5.3 Using Formal Tests to Diagnose Problems

5.4 Identifying Inconsistent Observations

Exercises

6 Transformations of the Response

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 Models with a Simple Blocking Structure

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 Extracting Information about Treatments

8.1 From Scientific Questions to the Treatment Structure

8.2 A 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 The 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 The Bonferroni Correction

8.8.2 The False Discovery Rate

8.8.3 All Pairwise Comparisons

8.8.3.1 The 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 Models with More Complex Blocking Structure

9.1 The 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 The 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 The 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 Replication and Power

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 A Different Hypothesis: Testing for Equivalence

Exercise

11 Dealing with Non-Orthogonality

11.1 The 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 The Consequences of Missing Data

11.5 Incorporating the Effects of unplanned Factors

11.6 Analysis Approaches for Non-Orthogonal Designs

11.6.1 A Simple Approach: The Intra-Block Analysis

Exercises

12 Models for a Single Variate: Simple Linear Regression

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 Checking Model Fit

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 The 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 Models for Several Variates: Multiple Linear Regression

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 The 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 Models for Variates and Factors

15.1 Incorporating Groups into the Simple Linear Regression Model

15.1.1 An 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 An 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 The Connection between Factors and Variates

15.6.1 Rewriting the Model in Matrix Notation

Exercises

16 Incorporating Structure: Linear Mixed Models

16.1 Incorporating Structure

16.2 An Introduction to Linear Mixed Models

16.3 Selecting the Best Fixed Model

16.4 Interpreting the Random Model

16.4.1 The 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 An Example

16.9 Some Pitfalls and Dangers

16.10 Extending the Model

Exercises

17 Models for Curved Relationships

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 Models for Non-Normal Responses: Generalized Linear Models

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 The 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 The 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 Practical Design and Data Analysis for Real Studies

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

Case Study 19.2: Multi-Phase Experiments – Gene Expression Microarrays for Plant Response to Pathogens

Case Study 19.3: Designing a Sampling Scheme to Detect Variation within a Population

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…

References

Appendix A: Data Tables

Appendix B: Quantiles of Statistical Distributions

Appendix C: Statistical and Mathematical Results

C.1 Derivation of Least Squares Estimates for a Model with a Single Factor

C.2 Partitioning the Total Sum of Squares for a Model with a Single Factor

C.3 Derivation of Least Squares Estimates for a Model with a Single Variate

C.4 Variances and Standard Errors of Linear Combinations of Random Variables

C.5 Matrix Addition and Multiplication

Index

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Tags: SJ Welham, SA Gezan, SJ Clark, A Mead, Statistical Methods, Biology Design, Experiments, Regression