Statistics: an introduction using R / Michael J. Crawley

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Preface.. Chapter 1 Fundamentals.. Everything Varies.. Significance.. Good and Bad Hypotheses.. Null Hypotheses.. 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 ns 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.. Non-constant Variance: Heteroscedasticity.. 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, r2.. Model Checking.. Transformation.. Polynomial Regression.. Non-Linear Regression.. Generalized Additive Models.. Influence.. 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.. Akaike?s Information Criterion (AIC as a Measure of the Fit of a Model.. 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