R — the statistical and graphical environment is rapidly emerging as an important set of teaching and research tools for biologists. This book draws upon the popularity and free availability of R to couple the theory and practice of biostatistics into a single treatment, so as to provide a textbook for biologists learning statistics, R, or both. An abridged description of biostatistical principles and analysis sequence keys are combined together with worked examples of the practical use of R into a complete practical guide to designing and analyzing real biological research. Topics covered include:
- simple hypothesis testing, graphing
- exploratory data analysis and graphical summaries
- regression (linear, multi and non-linear)
- simple and complex ANOVA and ANCOVA designs (including nested, factorial, blocking, spit-plot and repeated measures)
- frequency analysis and generalized linear models.
Linear mixed effects modeling is also incorporated extensively throughout as an alternative to traditional modeling techniques.
The book is accompanied by a companion website www.wiley.com/go/logan/r with an extensive set of resources comprising all R scripts and data sets used in the book, additional worked examples, the biology package, and other instructional materials and links.
Table of Contents:
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
1.2.1 Windows 2
1.2.2 Unix/Linux 2
1.2.3 MacOSX 3
1.3 The R environment 3
1.3.1 The console (command line) 4
1.4 Object names 4
1.5 Expressions, Assignment and Arithmetic 5
1.6 R Sessions and workspaces 6
1.6.1 Cleaning up 6
1.6.2 Workspaces 7
1.6.3 Current working directory 7
1.6.4 Quitting R 8
1.7 Getting help 8
1.8 Functions 9
1.9 Precedence 10
1.10 Vectors - variables 11
1.10.1 Regular or patterned sequences 12
1.10.2 Character vectors 13
1.10.3 Factors 15
1.11 Matrices, lists and data frames 16
1.11.1 Matrices 16
1.11.2 Lists 17
1.11.3 Data frames - data sets 18
1.12 Object information and conversion 18
1.12.1 Object information 18
1.12.2 Object conversion 20
1.13 Indexing vectors, matrices and lists 20
1.13.1 Vector indexing 21
1.13.2 Matrix indexing 22
1.13.3 List indexing 23
1.14 Pattern matching and replacement (character search and replace) 24
1.14.1 grep - pattern searching 24
1.14.2 regexpr - position and length of match 25
1.14.3 gsub - pattern replacement 26
1.15 Data manipulation 26
1.15.1 Sorting 26
1.15.2 Formatting data 27
1.16 Functions that perform other functions repeatedly 28
1.16.1 Along matrix margins 29
1.16.2 By factorial groups 30
1.16.3 By objects 30
1.17 Programming in R 30
1.17.1 Grouped expressions 31
1.17.2 Conditional execution – if and ifelse 31
1.17.3 Repeated execution – looping 32
1.17.4 Writing functions 34
1.18 An introduction to the R graphical environment 35
1.18.1 The plot() function 36
1.18.2 Graphical devices 39
1.18.3 Multiple graphics devices 40
1.19 Packages 42
1.19.1 Manual package management 42
1.19.2 Loading packages 45
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
2.3.1 Import from text file 50
2.3.2 Importing from the clipboard 51
2.3.3 Import from other software 51
2.4 Exporting (writing) data 52
2.5 Saving and loading of R objects 53
2.6 Data frame vectors 54
2.6.1 Factor levels 54
2.7 Manipulating data sets 56
2.7.1 Subsets of data frames – data frame indexing 56
2.7.2 The %in% matching operator 57
2.7.3 Pivot tables and aggregating datasets 58
2.7.4 Sorting datasets 58
2.7.5 Accessing and evaluating expressions within the context of a dataframe 59
2.7.6 Reshaping dataframes 59
2.8 Dummy data sets - generating random data 62
3 Introductory Statistical Principles 65
3.1 Distributions 66
3.1.1 The normal distribution 67
3.1.2 Log-normal distribution 68
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
3.7.1 Least squares (LS) 73
3.7.2 Maximum likelihood (ML) 74
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
4.2.1 Fully randomized treatment allocation 83
4.2.2 Randomized complete block treatment allocation 84
5 Graphical Data Presentation 85
5.1 The plot() function 86
5.1.1 The type parameter 86
5.1.2 The xlim and ylim parameters 87
5.1.3 The xlab and ylab parameters 88
5.1.4 The axes and ann parameters 88
5.1.5 The log parameter 88
5.2 Graphical Parameters 89
5.2.1 Plot dimensional and layout parameters 90
5.2.2 Axis characteristics 92
5.2.3 Character sizes 93
5.2.4 Line characteristics 93
5.2.5 Plotting character parameter - pch 93
5.2.6 Fonts 96
5.2.7 Text orientation and justification 98
5.2.8 Colors 98
5.3 Enhancing and customizing plots with low-level plotting functions 99
5.3.1 Adding points - points() 99
5.3.2 Adding text within a plot - text() 100
5.3.3 Adding text to plot margins - mtext() 101
5.3.4 Adding a legend - legend() 102
5.3.5 More advanced text formatting 104
5.3.6 Adding axes - axis() 107
5.3.7 Adding lines and shapes within a plot 108
5.4 Interactive graphics 113
5.4.1 Identifying points - identify() 113
5.4.2 Retrieving coordinates - locator() 114
5.5 Exporting graphics 114
5.5.1 Postscript - poscript() and pdf() 114
5.5.2 Bitmaps - jpeg() and png() 115
5.5.3 Copying devices - dev.copy() 115
5.6 Working with multiple graphical devices 115
5.7 High-level plotting functions for univariate (single variable) data 116
5.7.1 Histogram 116
5.7.2 Density functions 117
5.7.3 Q-Q plots 118
5.7.4 Boxplots 119
5.7.5 Rug charts 120
5.8 Presenting relationships 120
5.8.1 Scatterplots 120
5.9 Presenting grouped data 125
5.9.1 Boxplots 125
5.9.2 Boxplots for grouped means 125
5.9.3 Interaction plots - means plots 126
5.9.4 Bargraphs 127
5.9.5 Violin plots 128
5.10 Presenting categorical data 128
5.10.1 Mosaic plots 128
5.10.2 Association plots 129
5.11 Trellis graphics 129
5.11.1 scales() parameters 132
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
7.3.1 Linear models with factorial variables 156
7.3.2 Linear model hypothesis testing 162
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
8.1.1 Product moment correlation coefficient 169
8.1.2 Null hypothesis 169
8.1.3 Assumptions 169
8.1.4 Robust correlation 169
8.1.5 Confidence ellipses 170
8.2 Simple linear regression 170
8.2.1 Linear model 171
8.2.2 Null hypotheses 171
8.2.3 Assumptions 172
8.2.4 Multiple responses for each level of the predictor 173
8.2.5 Model I and II regression 173
8.2.6 Regression diagnostics 176
8.2.7 Robust regression 176
8.2.8 Power and sample size determination 177
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
9.5.1 Polynomial regression 211
9.5.2 Nonlinear regression 214
9.5.3 Diagnostics 214
9.6 Robust regression 214
9.7 Model selection 214
9.7.1 Model averaging 215
9.7.2 Hierarchical partitioning 218
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
10.0.1 Fixed versus random factors 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
11.2.1 Factor A - the main treatment effect 285
11.2.2 Factor B - the nested factor 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
11.11.1 Error strata (aov) 293
11.11.2 Linear mixed effects models (lme and lmer) 294
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
12.2.1 Model 1 - fixed effects 315
12.2.2 Model 2 - random effects 316
12.2.3 Model 3 - mixed effects 317
12.3 Analysis of variance 317
12.3.1 Quasi F-ratios 320
12.3.2 Interactions and main effects tests 321
12.4 Assumptions 321
12.5 Planned and unplanned comparisons 321
12.6 Unbalanced designs 322
12.6.1 Missing observations 322
12.6.2 Missing combinations - missing cells 324
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
13.2.1 Factor A - the main within block treatment effect 364
13.2.2 Factor B - the blocking factor 364
13.3 Analysis of variance 364
13.4 Assumptions 365
13.4.1 Sphericity 366
13.4.2 Block by treatment interactions 368
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
14.1.1 Factor A - the main between block treatment effect 400
14.1.2 Factor B - the blocking factor 401
14.1.3 Factor C - the main within block treatment effect 401
14.1.4 AC interaction - the within block interaction effect 402
14.1.5 BC interaction - the within block interaction effect 402
14.2 Linear models 402
14.2.1 One between (α), one within (γ) block effect 402
14.2.2 Two between (α, γ), one within (δ) block effect 402
14.2.3 One between (α), two within (γ , δ) block effects 403
14.3 Analysis of variance 403
14.4 Assumptions 403
14.5 Other issues 408
14.5.1 Robust alternatives 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
15.1.1 Factor A - the main treatment effect 450
15.1.2 Factor B - the covariate effect 450
15.2 Linear models 450
15.3 Analysis of variance 451
15.4 Assumptions 452
15.4.1 Homogeneity of slopes 453
15.4.2 Similar covariate ranges 454
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
16.1.1 Assumptions 469
16.2 Goodness of fit tests 469
16.2.1 Homogeneous frequencies tests 469
16.2.2 Distributional conformity - Kolmogorov-Smirnov tests 469
16.3 Contingency tables 469
16.3.1 Odds ratios 470
16.3.2 Residuals 472
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
17.2.1 Logistic model 485
17.2.2 Null hypotheses 487
17.2.3 Analysis of deviance 488
17.2.4 Multiple logistic regression 488
17.3 Count data - Poisson generalized linear models 489
17.3.1 Poisson regression 489
17.3.2 Log-linear Modelling 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
