Preface xv
R quick reference card xix
General key to statistical methods xxvii
1 Introduction to R 1
1.1 Why R? 1
1.2 Installing R 2
1.3 The R environment 3
1.4 Object names 4
1.5 Expressions, Assignment and Arithmetic 5
1.6 R Sessions and workspaces 6
1.7 Getting help 8
1.8 Functions 9
1.9 Precedence 10
1.10 Vectors - variables 11
1.11 Matrices, lists and data frames 16
1.12 Object information and conversion 18
1.13 Indexing vectors, matrices and lists 20
1.14 Pattern matching and replacement (character search and replace) 24
1.15 Data manipulation 26
1.16 Functions that perform other functions repeatedly 28
1.17 Programming in R 30
1.18 An introduction to the R graphical environment 35
1.19 Packages 42
1.20 Working with scripts 45
1.21 Citing R in publications 46
1.22 Further reading 47
2 Datasets 48
2.1 Constructing data frames 48
2.2 Reviewingadataframe-fix() 49
2.3 Importing (reading) data 50
2.4 Exporting (writing) data 52
2.5 Saving and loading of R objects 53
2.6 Data frame vectors 54
2.7 Manipulating data sets 56
2.8 Dummy data sets - generating random data 62
3 Introductory Statistical Principles 65
3.1 Distributions 66
3.2 Scale transformations 68
3.3 Measures of location 69
3.4 Measures of dispersion and variability 70
3.5 Measures of the precision of estimates - standard errors and confidence intervals 71
3.6 Degrees of freedom 73
3.7 Methods of estimation 73
3.8 Outliers 75
3.9 Further reading 75
4 Sampling and Experimental Design with R 76
4.1 Random sampling 76
4.2 Experimental design 83
5 Graphical Data Presentation 85
5.1 The plot() function 86
5.2 Graphical Parameters 89
5.3 Enhancing and customizing plots with low-level plotting functions 99
5.4 Interactive graphics 113
5.5 Exporting graphics 114
5.6 Working with multiple graphical devices 115
5.7 High-level plotting functions for univariate (single variable) data 116
5.8 Presenting relationships 120
5.9 Presenting grouped data 125
5.10 Presenting categorical data 128
5.11 Trellis graphics 129
5.12 Further reading 133
6 Simple Hypothesis Testing - One and Two Population Tests 134
6.1 Hypothesis testing 134
6.2 One- and two-tailed tests 136
6.3 t-tests 136
6.4 Assumptions 137
6.5 Statistical decision and power 137
6.6 Robust tests 139
6.7 Further reading 139
6.8 Key for simple hypothesis testing 140
6.9 Worked examples of real biological data sets 142
7 Introduction to Linear Models 151
7.1 Linear models 152
7.2 Linear models in R 154
7.3 Estimating linear model parameters 156
7.4 Comments about the importance of understanding the structure and parameterization of linear models 164
8 Correlation and Simple Linear Regression 167
8.1 Correlation 168
8.2 Simple linear regression 170
8.3 Smoothers and local regression 178
8.4 Correlation and regression in R 178
8.5 Further reading 179
8.6 Key for correlation and regression 180
8.7 Worked examples of real biological data sets 184
9 Multiple and Curvilinear Regression 208
9.1 Multiple linear regression 208
9.2 Linear models 209
9.3 Null hypotheses 209
9.4 Assumptions 210
9.5 Curvilinear models 211
9.6 Robust regression 214
9.7 Model selection 214
9.8 Regression trees 218
9.9 Further reading 219
9.10 Key and analysis sequence for multiple and complex regression 219
9.11 Worked examples of real biological data sets 224
10 Single Factor Classification (ANOVA) 254
10.1 Null hypotheses 255
10.2 Linear model 255
10.3 Analysis of variance 256
10.4 Assumptions 258
10.5 Robust classification (ANOVA) 259
10.6 Tests of trends and means comparisons 259
10.7 Power and sample size determination 261
10.8 ANOVA in R 261
10.9 Further reading 262
10.10 Key for single factor classification (ANOVA) 262
10.11 Worked examples of real biological data sets 265
11 Nested ANOVA 283
11.1 Linear models 284
11.2 Null hypotheses 285
11.3 Analysis of variance 286
11.4 Variance components 286
11.5 Assumptions 289
11.6 Pooling denominator terms 289
11.7 Unbalanced nested designs 290
11.8 Linear mixed effects models 290
11.9 Robust alternatives 292
11.10 Power and optimisation of resource allocation 292
11.11 Nested ANOVA in R 293
11.12 Further reading 294
11.13 Key for nested ANOVA 294
11.14 Worked examples of real biological data sets 298
12 Factorial ANOVA 313
12.1 Linear models 314
12.2 Null hypotheses 314
12.3 Analysis of variance 317
12.4 Assumptions 321
12.5 Planned and unplanned comparisons 321
12.6 Unbalanced designs 322
12.7 Robust factorial ANOVA 325
12.8 Power and sample sizes 327
12.9 Factorial ANOVA in R 327
12.10 Further reading 327
12.11 Key for factorial ANOVA 328
12.12 Worked examples of real biological data sets 334
13 Unreplicated Factorial Designs - Randomized Block and Simple Repeated Measures 360
13.1 Linear models 363
13.2 Null hypotheses 363
13.3 Analysis of variance 364
13.4 Assumptions 365
13.5 Specific comparisons 370
13.6 Unbalanced un-replicated factorial designs 370
13.7 Robust alternatives 371
13.8 Power and blocking efficiency 371
13.9 Unreplicated factorial ANOVA in R 371
13.10 Further reading 371
13.11 Key for randomized block and simple repeated measures ANOVA 372
13.12 Worked examples of real biological data sets 376
14 Partly Nested Designs: Split Plot and Complex Repeated Measures 399
14.1 Null hypotheses 400
14.2 Linear models 402
14.3 Analysis of variance 403
14.4 Assumptions 403
14.5 Other issues 408
14.6 Further reading 408
14.7 Key for partly nested ANOVA 409
14.8 Worked examples of real biological data sets 413
15 Analysis of Covariance (ANCOVA) 448
15.1 Null hypotheses 450
15.2 Linear models 450
15.3 Analysis of variance 451
15.4 Assumptions 452
15.5 Robust ANCOVA 455
15.6 Specific comparisons 455
15.7 Further reading 455
15.8 Key for ANCOVA 455
15.9 Worked examples of real biological data sets 457
16 Simple Frequency Analysis 466
16.1 The chi-square statistic 467
16.2 Goodness of fit tests 469
16.3 Contingency tables 469
16.4 G-tests 472
16.5 Small sample sizes 473
16.6 Alternatives 474
16.7 Power analysis 474
16.8 Simple frequency analysis in R 475
16.9 Further reading 475
16.10 Key for Analysing frequencies 475
16.11 Worked examples of real biological data sets 477
17 Generalized Linear Models (GLM) 483
17.1 Dispersion (over or under) 485
17.2 Binary data - logistic (logit) regression 485
17.3 Count data - Poisson generalized linear models 489
17.4 Assumptions 492
17.5 Generalized additive models (GAM's) - non-parametric GLM 493
17.6 GLM and R 494
17.7 Further reading 495
17.8 Key for GLM 495
17.9 Worked examples of real biological data sets 498
Bibliography 531
R index 535
Statistics index 541
