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Statistics: An Introduction Using R, 2nd Edition

Book Description

"...I know of no better book of its kind..." (Journal of the Royal Statistical Society, Vol 169 (1), January 2006)

A revised and updated edition of this bestselling introductory textbook to statistical analysis using the leading free software package R

This new edition of a bestselling title offers a concise introduction to a broad array of statistical methods, at a level that is elementary enough to appeal to a wide range of disciplines. Step-by-step instructions help the non-statistician to fully understand the methodology. The book covers the full range of statistical techniques likely to be needed to analyse the data from research projects, including elementary material like t--tests and chi--squared tests, intermediate methods like regression and analysis of variance, and more advanced techniques like generalized linear modelling.

Includes numerous worked examples and exercises within each chapter.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Preface
  5. Chapter 1: Fundamentals
    1. Everything Varies
    2. Significance
    3. Good and Bad Hypotheses
    4. Null Hypotheses
    5. p Values
    6. Interpretation
    7. Model Choice
    8. Statistical Modelling
    9. Maximum Likelihood
    10. Experimental Design
    11. The Principle of Parsimony (Occam's Razor)
    12. Observation, Theory and Experiment
    13. Controls
    14. Replication: It's the ns that Justify the Means
    15. How Many Replicates?
    16. Power
    17. Randomization
    18. Strong Inference
    19. Weak Inference
    20. How Long to Go On?
    21. Pseudoreplication
    22. Initial Conditions
    23. Orthogonal Designs and Non-Orthogonal Observational Data
    24. Aliasing
    25. Multiple Comparisons
    26. Summary of Statistical Models in R
    27. Organizing Your Work
    28. Housekeeping within R
    29. References
    30. Further Reading
  6. Chapter 2: Dataframes
    1. Selecting Parts of a Dataframe: Subscripts
    2. Sorting
    3. Summarizing the Content of Dataframes
    4. Summarizing by Explanatory Variables
    5. First Things First: Get to Know Your Data
    6. Relationships
    7. Looking for Interactions between Continuous Variables
    8. Graphics to Help with Multiple Regression
    9. Interactions Involving Categorical Variables
    10. Further Reading
  7. Chapter 3: Central Tendency
    1. Further Reading
  8. Chapter 4: Variance
    1. Degrees of Freedom
    2. Variance
    3. Variance: A Worked Example
    4. Variance and Sample Size
    5. Using Variance
    6. A Measure of Unreliability
    7. Confidence Intervals
    8. Bootstrap
    9. Non-constant Variance: Heteroscedasticity
    10. Further Reading
  9. Chapter 5: Single Samples
    1. Data Summary in the One-Sample Case
    2. The Normal Distribution
    3. Calculations Using z of the Normal Distribution
    4. Plots for Testing Normality of Single Samples
    5. Inference in the One-Sample Case
    6. Bootstrap in Hypothesis Testing with Single Samples
    7. Student's t Distribution
    8. Higher-Order Moments of a Distribution
    9. Skew
    10. Kurtosis
    11. Reference
    12. Further Reading
  10. Chapter 6: Two Samples
    1. Comparing Two Variances
    2. Comparing Two Means
    3. Student's t Test
    4. Wilcoxon Rank-Sum Test
    5. Tests on Paired Samples
    6. The Binomial Test
    7. Binomial Tests to Compare Two Proportions
    8. Chi-Squared Contingency Tables
    9. Fisher's Exact Test
    10. Correlation and Covariance
    11. Correlation and the Variance of Differences between Variables
    12. Scale-Dependent Correlations
    13. Reference
    14. Further Reading
  11. Chapter 7: Regression
    1. Linear Regression
    2. Linear Regression in R
    3. Calculations Involved in Linear Regression
    4. Partitioning Sums of Squares in Regression: SSY = SSR + SSE
    5. Measuring the Degree of Fit, r2
    6. Model Checking
    7. Transformation
    8. Polynomial Regression
    9. Non-Linear Regression
    10. Generalized Additive Models
    11. Influence
    12. Further Reading
  12. Chapter 8: Analysis of Variance
    1. One-Way ANOVA
    2. Shortcut Formulas
    3. Effect Sizes
    4. Plots for Interpreting One-Way ANOVA
    5. Factorial Experiments
    6. Pseudoreplication: Nested Designs and Split Plots
    7. Split-Plot Experiments
    8. Random Effects and Nested Designs
    9. Fixed or Random Effects?
    10. Removing the Pseudoreplication
    11. Analysis of Longitudinal Data
    12. Derived Variable Analysis
    13. Dealing with Pseudoreplication
    14. Variance Components Analysis (VCA)
    15. References
    16. Further Reading
  13. Chapter 9: Analysis of Covariance
    1. Further Reading
  14. Chapter 10: Multiple Regression
    1. The Steps Involved in Model Simplification
    2. Caveats
    3. Order of Deletion
    4. Carrying Out a Multiple Regression
    5. A Trickier Example
    6. Further Reading
  15. Chapter 11: Contrasts
    1. Contrast Coefficients
    2. An Example of Contrasts in R
    3. A Priori Contrasts
    4. Treatment Contrasts
    5. Model Simplification by Stepwise Deletion
    6. Contrast Sums of Squares by Hand
    7. The Three Kinds of Contrasts Compared
    8. Reference
    9. Further Reading
  16. Chapter 12: Other Response Variables
    1. Introduction to Generalized Linear Models
    2. The Error Structure
    3. The Linear Predictor
    4. Fitted Values
    5. A General Measure of Variability
    6. The Link Function
    7. Canonical Link Functions
    8. Akaike's Information Criterion (AIC) as a Measure of the Fit of a Model
    9. Further Reading
  17. Chapter 13: Count Data
    1. A Regression with Poisson Errors
    2. Analysis of Deviance with Count Data
    3. The Danger of Contingency Tables
    4. Analysis of Covariance with Count Data
    5. Frequency Distributions
    6. Further Reading
  18. Chapter 14: Proportion Data
    1. Analyses of Data on One and Two Proportions
    2. Averages of Proportions
    3. Count Data on Proportions
    4. Odds
    5. Overdispersion and Hypothesis Testing
    6. Applications
    7. Logistic Regression with Binomial Errors
    8. Proportion Data with Categorical Explanatory Variables
    9. Analysis of Covariance with Binomial Data
    10. Further Reading
  19. Chapter 15: Binary Response Variable
    1. Incidence Functions
    2. ANCOVA with a Binary Response Variable
    3. Further Reading
  20. Chapter 16: Death and Failure Data
    1. Survival Analysis with Censoring
    2. Further Reading
  21. Appendix: Essentials of the R Language
    1. R as a Calculator
    2. Built-in Functions
    3. Numbers with Exponents
    4. Modulo and Integer Quotients
    5. Assignment
    6. Rounding
    7. Infinity and Things that Are Not a Number (NaN)
    8. Missing Values (NA)
    9. Operators
    10. Creating a Vector
    11. Named Elements within Vectors
    12. Vector Functions
    13. Summary Information from Vectors by Groups
    14. Subscripts and Indices
    15. Working with Vectors and Logical Subscripts
    16. Addresses within Vectors
    17. Trimming Vectors Using Negative Subscripts
    18. Logical Arithmetic
    19. Repeats
    20. Generate Factor Levels
    21. Generating Regular Sequences of Numbers
    22. Matrices
    23. Character Strings
    24. Writing Functions in R
    25. Arithmetic Mean of a Single Sample
    26. Median of a Single Sample
    27. Loops and Repeats
    28. The ifelse Function
    29. Evaluating Functions with apply
    30. Testing for Equality
    31. Testing and Coercing in R
    32. Dates and Times in R
    33. Calculations with Dates and Times
    34. Understanding the Structure of an R Object Using str
    35. Reference
    36. Further Reading
  22. Index
  23. End User License Agreement