Statistics

Binomial Test 98 Binomial Tests to Compare Two Proportions 100 Chi-Squared Contingency Tables 100 Fisher's Exact Test 105 Correlation and Covariance 108 Correlation and the Variance of Differences between Variables 110 Scale-Dependent Correlations 112 Reference 113 Further Reading 113 Chapter 7 Regression 114 Linear Regression 116 Linear Regression in R 117 Calculations Involved in Linear Regression 122 Partitioning Sums of Squares in Regression: SSY = SSR + SSE 125 Measuring the Degree of Fit, r2 133 Model Checking 134 Transformation 135 Polynomial Regression 140 Non-Linear Regression 142 Generalized Additive Models 146 Influence 148 Further Reading 149 Chapter 8 Analysis of Variance 150 One-Way ANOVA 150 Shortcut Formulas 157 Effect Sizes 159 Plots for Interpreting One-Way ANOVA 162 Factorial Experiments 168 Pseudoreplication: Nested Designs and Split Plots 173 Split-Plot Experiments 174 Random Effects and Nested Designs 176 Fixed or Random Effects? 177 Removing the Pseudoreplication 178 Analysis of Longitudinal Data 178 Derived Variable Analysis 179 Dealing with Pseudoreplication 179 Variance Components Analysis (VCA) 183 References 184 Further Reading 184 Chapter 9 Analysis of Covariance 185 Further Reading 192 Chapter 10 Multiple Regression 193 The Steps Involved in Model Simplification 195 Caveats 196 Order of Deletion 196 Carrying Out a Multiple Regression 197 A Trickier Example 203 Further Reading 211 Chapter 11 Contrasts 212 Contrast Coefficients 213 An Example of Contrasts in R 214 A Priori Contrasts 215 Treatment Contrasts 216 Model Simplification by Stepwise Deletion 218 Contrast Sums of Squares by Hand 222 The Three Kinds of Contrasts Compared 224 Reference 225 Further Reading 225 Chapter 12 Other Response Variables 226 Introduction to Generalized Linear Models 228 The Error Structure 229 The Linear Predictor 229 Fitted Values 230 A General Measure of Variability 230 The Link Function 231 Canonical Link Functions 232 Akaike's Information Criterion (AIC) as a Measure of the Fit of a Model 233 Further Reading 233 Chapter 13 Count Data 234 A Regression with Poisson Errors 234 Analysis of Deviance with Count Data 237 The Danger of Contingency Tables 244 Analysis of Covariance with Count Data 247 Frequency Distributions 250 Further Reading 255 Chapter 14 Proportion Data 256 Analyses of Data on One and Two Proportions 257 Averages of Proportions 257 Count Data on Proportions 257 Odds 259 Overdispersion and Hypothesis Testing 260 Applications 261 Logistic Regression with Binomial Errors 261 Proportion Data with Categorical Explanatory Variables 264 Analysis of Covariance with Binomial Data 269 Further Reading 272 Chapter 15 Binary Response Variable 273 Incidence Functions 275 ANCOVA with a Binary Response Variable 279 Further Reading 284 Chapter 16 Death and Failure Data 285 Survival Analysis with Censoring 287 Further Reading 290 Appendix Essentials of the R Language 291 R as a Calculator 291 Built-in Functions 292 Numbers with Exponents 294 Modulo and Integer Quotients 294 Assignment 295 Rounding 295 Infinity and Things that Are Not a Number (NaN) 296 Missing Values (NA) 297 Operators 298 Creating a Vector 298 Named Elements within Vectors 299 Vector Functions 299 Summary Information from Vectors by Groups 300 Subscripts and Indices 301 Working with Vectors and Logical Subscripts 301 Addresses within Vectors 304 Trimming Vectors Using Negative Subscripts 304 Logical Arithmetic 305 Repeats 305 Generate Factor Levels 306 Generating Regular Sequences of Numbers 306 Matrices 307 Character Strings 309 Writing Functions in R 310 Arithmetic Mean of a Single Sample 310 Median of a Single Sample 310 Loops and Repeats 311 The ifelse Function 312 Evaluating Functions with apply 312 Testing for Equality 313 Testing and Coercing in R 314 Dates and Times in R 315 Calculations with Dates and Times 319 Understanding the Structure of an R Object Using str 320 Reference 322 Further Reading 322 Index 323