Modern statistics for the life sciences: [learn to analyse your own data]
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2010
|
| Ausgabe: | Reprint. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XV, 351 S. Ill., graph. Darst. |
| ISBN: | 9780199252312 |
Internformat
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| 100 | 1 | |a Grafen, Alan |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Modern statistics for the life sciences |b [learn to analyse your own data] |c Alan Grafen ; Rosie Hails |
| 250 | |a Reprint. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2010 | |
| 300 | |a XV, 351 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 0 | 7 | |a Biostatistik |0 (DE-588)4729990-3 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-020876877 | ||
Datensatz im Suchindex
| _version_ | 1804143686547668992 |
|---|---|
| adam_text | Titel: Modern statistics for the life sciences
Autor: Grafen, Alan
Jahr: 2010
Contents
Why use this book xi
How to use this book xii
How to teach this text xiv
An introduction to analysis of variance 1
1.1 Model formulae and geometrical pictures 1
1.2 General Linear Models 1
1.3 The basic principles of ANOVA 2
What happens when we calculate a variance? 3
Partitioning the variability 4
Partitioning the degrees of freedom 8
F-ratios 9
1.4 An example of ANOVA 10
Presenting the results 14
1.5 The geometrical approach for an ANOVA 16
1.6 Summary 19
1.7 Exercises 20
Melons 20
Dioecious trees 21
Regression 22
2.1 What kind of data are suitable for regression? 22
2.2 How is the best fit line chosen? 23
2.3 The geometrical view of regression 26
2.4 Regression-an example 28
2.5 Confidence and prediction intervals 33
Confidence intervals 33
Prediction intervals 33
2.6 Conclusions from a regression analysis 35
A strong relationship with little scatter 35
A weak relationship with lots of noise 36
Small datasets and pet theories 38
Significant relationships-but that is not the whole story 39
2.7 Unusual observations 40
Large residuals 40
Influential points 41
2.8 The role of X and V-does it matter which is which? 42
2.9 Summary 45
2.10 Exercises 45
Does weight mean fat? 45
Dioecious trees 46
Models, parameters and GLMs 47
3.1 Populations and parameters 47
3.2 Expressing all models as linear equations 48
3.3 Turning the tables and creating datasets 52
Influence of sample size on the accuracy of parameter estimates 54
3.4 Summary 55
3.5 Exercises 55
How variability in the population will influence our analysis 55
Using more than one explanatory variable 56
4.1 Why use more than one explanatory variable? 56
Leaping to the wrong conclusion 56
Missing a significant relationship 57
4.2 Elimination by considering residuals 59
4.3 Two types of sum of squares 61
Eliminating a third variable makes the second less informative 62
Eliminating a third variable makes the second more informative 64
4.4 Urban Foxes-an example of statistical elimination 65
4.5 Statistical elimination by geometrical analogy 68
Partitioning and more partitioning 68
Picturing sequential and adjusted sums of squares 71
4.6 Summary 72
4.7 Exercises 73
The cost of reproduction 73
Investigating obesity 75
Designing experiments-keeping it simple 76
5.1 Three fundamental principles of experimental design 76
Replication 76
Randomisation 78
Blocking 80
5.2 The geometrical analogy for blocking 85
Partitioning two categorical variables 85
Calculating the fitted model for two categorical variables 86
5.3 The concept of orthogonality 88
The perfect design 88
Three pictures of orthogonality 91
5.4 Summary 92
5.5 Exercises 93
Growing carnations 93
The dorsal crest of the male smooth newt 95
Combining continuous and categorical variables 96
6.1 Reprise of models fitted so far 96
6.2 Combining continuous and categorical variables 97
Looking for a treatment for leprosy 97
Sex differences in the weight-fat relationship 99
6.3 Orthogonality in the context of continuous and categorical variables 102
6.4 Treating variables as continuous or categorical 104
6.5 The general nature of General Linear Models 106
6.6 Summary 107
6.7 Exercises 108
Conservation and its influence on biomass 108
Determinants of the Grade Point Average 109
Interactions-getting more complex 110
7.1 The factorial principle 110
7.2 Analysis of factorial experiments 112
7.3 What do we mean by an interaction? 115
7.4 Presenting the results 117
Factorial experiments with insignificant interactions 117
Factorial experiments with significant interactions 120
Error bars 123
7.5 Extending the concept of interactions to continuous variables 127
Mixing continuous and categorical variables 127
Adjusted Means (or least square means in models with continuous variables) 129
Confidence intervals for interactions 130
Interactions between continuous variables 131
7.6 Uses of interactions 132
Is the story simple or complicated? 133
Is the best model additive? 133
7.7 Summary 134
7.8 Exercises 134
Antidotes 134
Weight, fat and sex 135
Checking the models I: independence 136
8.1 Heterogeneous data 137
Same conclusion within and between subsets 140
Creating relationships where there are none 140
Concluding the opposite 141
8.2 Repeated measures 142
Single summary approach 142
The multivariate approach 145
8.3 Nested data 147
8.4 Detecting non-independence 148
Germination of tomato seeds 149
8.5 Summary 151
8.6 Exercises 151
How non-independence can inflate sample size enormously 151
Combining data from different experiments 152
Checking the models II: the other three assumptions 153
9.1 Homogeneity of variance 153
9.2 Normality of error 155
9.3 Linearity/additivity 157
9.4 Model criticism and solutions 157
Histogram of residuals 158
Normal probability plots 160
Plotting the residuals against the fitted values 163
Transformations affect homogeneity and normality simultaneously 166
Plotting the residuals against each continuous explanatory variable 167
Solutions for nonlinearity 168
Hints for looking at residual plots 172
9.5 Predicting the volume of merchantable wood:
an example of model criticism 173
9.6 Selecting a transformation 178
9.7 Summary 180
9.8 Exercises 181
Stabilising the variance 181
Stabilising the variance in a blocked experiment 181
Lizard skulls 183
Checking the perfect model 184
10 Model selection I: principles of model choice and
designed experiments 186
10.1 The problem of model choice *86
10.2 Three principles of model choice 189
Economy of variables 189
Multiplicity of p-values 191
Considerations of marginality 192
Model choice in the polynomial problem 193
10.3 Four different types of model choice problem 195
10.4 Orthogonal and near orthogonal designed experiments 196
Model choice with orthogonal experiments 196
Model choice with loss of orthogonality 198
10.5 Looking for trends across levels of a categorical variable 201
10.6 Summary 205
10.7 Exercises 206
Testing polynomials requires sequential sums of squares 206
Partitioning a sum of squares into polynomial components 207
11 Model selection II: datasets with several explanatory variables 209
11.1 Economy of variables in the context of multiple regression 210
R-squared and adjusted R-squared 210
Prediction Intervals 213
11.2 Multiplicity of p-values in the context of multiple regression 217
The enormity of the problem 217
Possible solutions 217
11.3 Automated model selection procedures 220
How stepwise regression works 220
The stepwise regression solution to the whale watching problem 221
11.4 Whale Watching: using the GLM approach 225
11.5 Summary 228
11.6 Exercises 229
Finding the best treatment for cat fleas 229
Multiplicity of p-values 231
12 Random effects 232
12.1 What are random effects? 232
Distinguishing between fixed and random factors 232
Why does it matter? 234
12.2 Four new concepts to deal with random effects 234
Components of variance 234
Expected mean square 235
Nesting 236
Appropriate Denominators 237
12.3 A one-way ANOVA with a random factor 238
12.4 A two-level nested ANOVA 241
Nesting 241
12.5 Mixing random and fixed effects 244
12.6 Using mock analyses to plan an experiment 247
12.7 Summary 252
12.8 Exercises 253
Examining microbial communities on leaf surfaces 253
How a nested analysis can solve problems of non-independence 254
13 Categorical data 255
13.1 Categorical data: the basics 255
Contingency table analysis 255
When are data truly categorical? 257
13.2 The Poisson distribution 258
Two properties of a Poisson process 258
The mathematical description of a Poisson distribution 259
The dispersion test 261
13.3 The chi-squared test in contingency tables 265
Derivation of the chi-squared formula 265
Inspecting the residuals 267
13.4 General linear models and categorical data 269
Using contingency tables to illustrate orthogonality 269
Analysing by contingency table and GLMs 271
Omitting important variables 276
Analysing uniformity 277
13.5 Summary 278
13.6 Exercises 279
Soya beans revisited 279
Fig trees in Costa Rica 280
14 What lies beyond? 281
14.1 Generalised Linear Models 281
14.2 Multiple y variables, repeated measures and within-subject factors 283
14.3 Conclusions 284
15 Answers to exercises 285
Chapter 1 285
Chapter 2 287
Chapter 3 288
Chapter 4 289
Chapters 292
Chapter 6 294
Chapter 7 295
Chapter 8 298
Chapter 9 299
Chapter 10 308
Chapter 11 310
Chapter 12 313
Chapter 13 314
Revision section: The basics 317
R1.1 Populations and samples 317
R1.2 Three types of variability: of the sample, the population and
the estimate 318
Variability of the sample 318
Variability of the population 319
Variability of the estimate 319
R1.3 Confidence intervals: a way of precisely representing uncertainty 322
R1.4 The null hypothesis-taking the conservative approach 324
R1.5 Comparing two means 327
Two sample t-test 327
Alternative tests 328
One and two tailed tests 329
R1.6 Conclusion 331
Appendix 1: The meaning of p-values and confidence intervals 332
Whatisap-value? 332
What is a confidence interval? 334
Appendix 2: Analytical results about variances of sample means 335
Introducing the basic notation 335
Using the notation to define the variance of a sample 335
Using the notation to define the mean of a sample 336
Defining the variance of the sample mean 336
To illustrate why the sample variance must be calculated with n -1 in
its denominator (rather than n) to be an unbiased estimate of the
population variance 337
Appendix 3: Probability distributions 339
Some gentle theory 339
Confirming simulations 341
Bibliography 343
Index 345
|
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| isbn | 9780199252312 |
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| spelling | Grafen, Alan Verfasser aut Modern statistics for the life sciences [learn to analyse your own data] Alan Grafen ; Rosie Hails Reprint. Oxford [u.a.] Oxford Univ. Press 2010 XV, 351 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Biostatistik (DE-588)4729990-3 gnd rswk-swf Biostatistik (DE-588)4729990-3 s DE-604 Hails, Rosemary Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020876877&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Modern statistics for the life sciences [learn to analyse your own data] |
| title_auth | Modern statistics for the life sciences [learn to analyse your own data] |
| title_exact_search | Modern statistics for the life sciences [learn to analyse your own data] |
| title_full | Modern statistics for the life sciences [learn to analyse your own data] Alan Grafen ; Rosie Hails |
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| title_full_unstemmed | Modern statistics for the life sciences [learn to analyse your own data] Alan Grafen ; Rosie Hails |
| title_short | Modern statistics for the life sciences |
| title_sort | modern statistics for the life sciences learn to analyse your own data |
| title_sub | [learn to analyse your own data] |
| topic | Biostatistik (DE-588)4729990-3 gnd |
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