Modern statistics for the life sciences:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2008
|
| Edition: | Reprinted |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XV, 351 S. Ill., graph. Darst. |
| ISBN: | 9780199252312 |
Staff View
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| 100 | 1 | |a Grafen, Alan |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Modern statistics for the life sciences |c Alan Grafen ; Rosie Hails |
| 250 | |a Reprinted | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2008 | |
| 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 | 4 | |a Mathematical statistics | |
| 650 | 0 | 7 | |a Biostatistik |0 (DE-588)4729990-3 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Hails, Rosemary |e Verfasser |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-017013886 | ||
Record in the Search Index
| _version_ | 1804138464107560960 |
|---|---|
| adam_text | 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
10
14
16
19
20
20
21
22
22
23
26
28
33
33
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
У
—
does it matter which is which?
42
2.9
Summary
45
1.4
An example of ANOVA
Presenting the results
1.5
The geometrical approach for an ANOVA
1.6
Summary
1.7
Exercises
Melons
Dioecious trees
Regression
2.1
What kind of data are suitable for regression?
2.2
How is the best fit line chosen?
2.3
The geometrical view of regression
2.4
Regression
—
an example
2.5
Confidence and prediction intervals
Confidence intervals
Prediction intervals
vi
Contents
2.10
Exercises
45
Does weight mean fat?
45
Dioecious trees
46
3
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
4
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
5
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
6
Combining continuous and categorical variables
96
6.
ι
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
Contents
vii
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
7
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
8
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
9
Checking the models II: the other three assumptions
1
53
9.1
Homogeneity of variance
153
9.2
Normality of error
155
9.3
Linearity/additivity
157
viii
Contents
9.4
Model criticism and solutions
157
Histogram of residuals
158
Normal probability plots 1
60
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 1?8
9.7
Summary 180
9.8
Exercises
181
Stabilising the variance
181
Stabilising the variance in a blocked experiment
181
Lizard skulls
1
83
Checking the perfect model
184
10
Model selection I: principles of model choice and
designed experiments
186
10.1
The problem of model choice
186
10.2
Three principles of model choice
18
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
Contents
¡Χ
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
Contents
Chapter
4 289
Chapters
292
Chapter
6 294
Chapter
7 295
Chapter
8 298
Chapter
9 2
Chapter
10 308
Chapter
11 31°
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
What ¡sap-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
η
-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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| spelling | Grafen, Alan Verfasser aut Modern statistics for the life sciences Alan Grafen ; Rosie Hails Reprinted Oxford [u.a.] Oxford Univ. Press 2008 XV, 351 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Mathematical statistics Biostatistik (DE-588)4729990-3 gnd rswk-swf Biostatistik (DE-588)4729990-3 s DE-604 Hails, Rosemary Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017013886&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Grafen, Alan Hails, Rosemary Modern statistics for the life sciences Mathematical statistics Biostatistik (DE-588)4729990-3 gnd |
| subject_GND | (DE-588)4729990-3 |
| title | Modern statistics for the life sciences |
| title_auth | Modern statistics for the life sciences |
| title_exact_search | Modern statistics for the life sciences |
| title_full | Modern statistics for the life sciences Alan Grafen ; Rosie Hails |
| title_fullStr | Modern statistics for the life sciences Alan Grafen ; Rosie Hails |
| title_full_unstemmed | Modern statistics for the life sciences Alan Grafen ; Rosie Hails |
| title_short | Modern statistics for the life sciences |
| title_sort | modern statistics for the life sciences |
| topic | Mathematical statistics Biostatistik (DE-588)4729990-3 gnd |
| topic_facet | Mathematical statistics Biostatistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017013886&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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