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Contents Preface Chapter 1 Fundamentals Everything Varies Significance Good and Bad Hypotheses Null Hypotheses p Values Interpretation 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 Chapter 2 Dataframes Selecting Parts of a Dataframe: Subscripts Sorting Tidying Up Chapter 3 Central Tendency Chapter 4 Variance Degrees of Freedom Variance A Worked Example Variance and Sample Size Using Variance A Measure of Unreliability Confidence Intervals Bootstrap 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 Chapter 6 Two Samples Comparing Two Variances Comparing Two Means Student's t-test Wilcoxon Rank Sum Test Tests on Paired Samples The Sign Test Binomial Tests to Compare Two Proportions Chi-square Contingency Tables Fisher's Exact Test Correlation and Covariance Data Dredging Partial Correlation Correlation and the Variance of Differences between Variables Scale-dependent Correlations Kolmogorov-Smirnov Test Chapter 7 Statistical Modelling The Steps Involved in Model Simplification Caveats Order of Deletion Model Formulae in R Interactions between Explanatory Variables Multiple Error Terms The Intercept as Parameter 1 Update in Model Simplification Examples of R Model Formulae Model Formulae for Regression GLMs: Generalized Linear Models The Error Structure The Linear Predictor Fitted Values The Link Function Canonical Link Functions Proportion Data and Binomial Errors Count Data and Poisson Errors GAMs: Generalized Additive Models Model Criticism Summary of Statistical Models in R Model Checking Non-constant Variance: Heteroscedasticity Non-normality of Errors Influence Leverage Mis-specified Model Chapter 8 Regression Linear Regression Linear Regression in R Error Variance in Regression: SSY = SSR + SSF Measuring the Degree of Fit, r2 Model Checking Polynomial Regression Non-linear Regression Testing for Humped Relationships Generalized Additive Models (GAMs) Chapter 9 Analysis of Variance One-way Anova Shortcut Formulae 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 Variance Components Analysis (VCA) What is the Difference between Split-plot and Hierarchical Samples? Chapter 10 Analysis of Covariance Chapter 11 Multiple Regression A Simple Example A More Complex Example Chapter 12 Contrasts Contrast Coefficients An Example of Contrasts in R A Priori Contrasts Model Simplification by Step-wise Deletion Contrast Sums of Squares by Hand Comparison of the Three Kinds of Contrasts Aliasing Contrasts and the Parameters of Ancova Models Multiple Comparisons 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 Chapter 14 Proportion Data Analyses of Data on One and Two 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 Chapter 15 Death and Failure Data Survival Analysis with Censoring Chapter 16 Binary Response Variable Incidence Functions Ancova with a Binary Response Variable Appendix 1: Fundamentals of the R Language R as a Calculator Assigning Values to Variables Generating Repeats Generating Factor Levels Changing the Look of Graphics Reading Data from a File Vector Functions in R Subscripts: Obtaining Parts of Vectors Subscripts as Logical Variables Subscripts with Arrays Subscripts with Lists Writing Functions in R Sorting and Ordering Counting Elements within Arrays Tables of Summary Statistics Converting Continuous Variables into Categorical Variables using cut The split Function Trellis Plots The xyplot Function Three-dimensional (3-D) Plots Matrix Arithmetic Solving Systems of Linear Equations

Library of Congress Subject Headings for this publication:

Mathematical statistics -- Textbooks.

R (Computer program language).