Statistics: An Introduction Using R

A revised and updated edition of this bestselling introduction to statistical analysis using the leading free software package R In recent years R has become one of the most popular, powerful and flexible statistical software packages available. It enables users to apply a wide variety of statistical methods, ranging from simple regression to generalized linear modelling, and has been widely adopted by life scientists and social scientists. This new edition 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 such as t tests and chi–squared tests, intermediate methods such as regression and analysis of variance, and more advanced techniques such as generalized linear modelling. Numerous worked examples and exercises are included within each chapter. Comprehensively revised to include more detailed introductory material on working with R Updated to be compatible with the current R Version 3 Complete coverage of all the essential statistical methods Focus on linear models (regression, analysis of variance and analysis of covariance) and generalized linear models (for count data, proportion data and age–at–death data) Now includes more detail on experimental design Accompanied by a website featuring worked examples, data sets, exercises and solutions www.imperial.ac.uk/bio/research/crawley/statistics Statistics: An introduction using R is primarily aimed at undergraduate students in medicine, engineering, economics and biology – but will also appeal to postgraduates in these areas who wish to switch to using R.  

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