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Tables of Contents for Modern Statistics for the Life Sciences
Chapter/Section Title
Page #
Page Count
Why use this book
xi
How to use this book
xii
How to teach this text
xiv
An introduction to analysis of variance
1
21
Model formulae and geometrical pictures
1
1
General Linear Models
1
1
The basic principles of ANOVA
2
8
What happens when we calculate a variance?
3
1
Partitioning the variability
4
4
Partitioning the degrees of freedom
8
1
F-ratios
9
1
An example of ANOVA
10
6
Presenting the results
14
2
The geometrical approach for an ANOVA
16
3
Summary
19
1
Exercises
20
2
Melons
20
1
Dioecious trees
21
1
Regression
22
25
What kind of data are suitable for regression?
22
1
How is the best fit line chosen?
23
3
The geometrical view of regression
26
2
Regression-an example
28
5
Confidence and prediction intervals
33
2
Confidence intervals
33
1
Prediction intervals
33
2
Conclusions from a regression analysis
35
5
A strong relationship with little scatter
35
1
A weak relationship with lots of noise
36
2
Small datasets and pet theories
38
1
Significant relationships-but that is not the whole story
39
1
Unusual observations
40
2
Large residuals
40
1
Influential points
41
1
The role of X and Y-does it matter which is which?
42
3
Summary
45
1
Exercises
45
2
Does weight mean fat?
45
1
Dioecious trees
46
1
Models, parameters and GLMs
47
9
Populations and parameters
47
1
Expressing all models as linear equations
48
4
Turning the tables and creating datasets
52
3
Influence of sample size on the accuracy of parameter estimates
54
1
Summary
55
1
Exercises
55
1
How variability in the population will influence our analysis
55
1
Using more than one explanatory variable
56
20
Why use more than one explanatory variable?
56
3
Leaping to the wrong conclusion
56
1
Missing a significant relationship
57
2
Elimination by considering residuals
59
2
Two types of sum of squares
61
4
Eliminating a third variable makes the second less informative
62
2
Eliminating a third variable makes the second more informative
64
1
Urban Foxes-an example of statistical elimination
65
3
Statistical elimination by geometrical analogy
68
4
Partitioning and more partitioning
68
3
Picturing sequential and adjusted sums of squares
71
1
Summary
72
1
Exercises
73
3
The cost of reproduction
73
2
Investigating obesity
75
1
Designing experiments-keeping it simple
76
20
Three fundamental principles of experimental design
76
9
Replication
76
2
Randomisation
78
2
Blocking
80
5
The geometrical analogy for blocking
85
3
Partitioning two categorical variables
85
1
Calculating the fitted model for two categorical variables
86
2
The concept of orthogonality
88
4
The perfect design
88
3
Three pictures of orthogonality
91
1
Summary
92
1
Exercises
93
3
Growing carnations
93
2
The dorsal crest of the male smooth newt
95
1
Combining continuous and categorical variables
96
14
Reprise of models fitted so far
96
1
Combining continuous and categorical variables
97
5
Looking for a treatment for leprosy
97
2
Sex differences in the weight-fat relationship
99
3
Orthogonality in the context of continuous and categorical variables
102
2
Treating variables as continuous or categorical
104
2
The general nature of General Linear Models
106
1
Summary
107
1
Exercises
108
2
Conservation and its influence on biomass
108
1
Determinants of the Grade Point Average
109
1
Interactions--getting more complex
110
17
The factorial principle
110
2
Analysis of factorial experiments
112
3
What do we mean by an interaction?
115
2
Presenting the results
117
10
Factorial experiments with insignificant interactions
117
3
Factorial experiments with significant interactions
120
3
Error bars
123
4
Extending the concept of interactions to continuous variables
127
5
Mixing continuous and categorical variables
127
2
Adjusted Means (or least square means in models with continuous variables)
129
1
Confidence intervals for interactions
130
1
Interactions between continuous variables
131
1
Uses of interactions
132
2
Is the story simple or complicated?
133
1
Is the best model additive?
133
1
Summary
134
1
Exercises
134
2
Antidotes
134
1
Weight, fat and sex
135
1
Checking the models I: independence
136
17
Heterogeneous data
137
5
Same conclusion within and between subsets
140
1
Creating relationships where there are none
140
1
Concluding the opposite
141
1
Repeated measures
142
5
Single summary approach
142
3
The multivariate approach
145
2
Nested data
147
1
Detecting non-independence
148
3
Germination of tomato seeds
149
2
Summary
151
1
Exercises
151
2
How non-independence can inflate sample size enormously
151
1
Combining data from different experiments
152
1
Checking the models II: the other three asumptions
153
33
Homogeneity of variance
153
2
Normality of error
155
2
Linearity/additivity
157
1
Model criticism and solutions
157
16
Histogram of residuals
158
2
Normal probability plots
160
3
Plotting the residuals against the fitted values
163
3
Transformations affect homogeneity and normality simultaneously
166
1
Plotting the residuals against each continuous explanatory variable
167
1
Solutions for nonlinearity
168
4
Hints for looking at residual plots
172
1
Predicting the volume of merchantable wood: an example of model criticism
173
5
Selecting a transformation
178
2
Summary
180
1
Exercises
181
5
Stabilising the variance
181
1
Stabilising the variance in a blocked experiment
181
2
Lizard skulls
183
1
Checking the `perfect' model
184
2
Model selection t: principles of model choice and designed experiments
186
23
The problem of model choice
186
3
Three principles of model choice
189
6
Economy of variables
189
2
Multiplicity of p-values
191
1
Considerations of marginality
192
1
Model choice in the polynomial problem
193
2
Four different types of model choice problem
195
1
Orthogonal and near orthogonal designed experiments
196
5
Model choice with orthogonal experiments
196
2
Model choice with loss of orthogonality
198
3
Looking for trends across levels of a categorical variable
201
4
Summary
205
1
Exercises
206
3
Testing polynomials requires sequential sums of squares
206
1
Partitioning a sum of squares into polynomial components
207
2
Model selection II; datasets with several explanatory variables
209
23
Economy of variables in the context of multiple regression
210
7
R-squared and adjusted R-squared
210
3
Prediction Intervals
213
4
Multiplicity of p-values in the context of multiple regression
217
3
The enormity of the problem
217
1
Possible solutions
217
3
Automated mode) selection procedures
220
5
How stepwise regression works
220
1
The stepwise regression solution to the whale watching problem
221
4
Whale Watching: using the GLM approach
225
3
Summary
228
1
Exercises
229
3
Finding the best treatment for cat fleas
229
2
Multiplicity of p-values
231
1
Random effects
232
23
What are random effects?
232
2
Distinguishing between fixed and random factors
232
2
Why does it matter?
234
1
Four new concepts to deal with random effects
234
4
Components of variance
234
1
Expected mean square
235
1
Nesting
236
1
Appropriate Denominators
237
1
A one-way ANOVA with a random factor
238
3
A two-level nested ANOVA
241
3
Nesting
241
3
Mixing random and fixed effects
244
3
Using mock analyses to plan an experiment
247
5
Summary
252
1
Exercises
253
2
Examining microbial communities on leaf surfaces
253
1
How a nested analysis can solve problems of non-independence
254
1
Categorical data
255
26
Categorical data: the basics
255
3
Contingency table analysis
255
2
When are data truly categorical?
257
1
The Poisson distribution
258
7
Two properties of a Poisson process
258
1
The mathematical description of a Poisson distribution
259
2
The dispersion test
261
4
The chi-squared test in contingency tables
265
4
Derivation of the chi-squared formula
265
2
Inspecting the residuals
267
2
General linear models and categorical data
269
9
Using contingency tables to illustrate orthogonality
269
2
Analysing by contingency table and GLMs
271
5
Omitting important variables
276
1
Analysing uniformity
277
1
Summary
278
1
Exercises
279
2
Soya beans revisited
279
1
Fig trees in Costa Rica
280
1
What lies beyond?
281
4
Generalised Linear Models
281
2
Multiple y variables, repeated measures and within-subject factors
283
1
Conclusions
284
1
Answers to exercises
285
32
Chapter 1
285
2
Chapter 2
287
1
Chapter 3
288
1
Chapter 4
289
3
Chapter 5
292
2
Chapter 6
294
1
Chapter 7
295
3
Chapter 8
298
1
Chapter 9
299
9
Chapter 10
308
2
Chapter 11
310
3
Chapter 12
313
1
Chapter 13
314
3
Revision section: The basics
317
15
Populations and samples
317
1
Three types of variability: of the sample, the population and the estimate
318
4
Variability of the sample
318
1
Variability of the population
319
1
Variability of the estimate
319
3
Confidence intervals: a way of precisely representing uncertainty
322
2
The null hypothesis-taking the conservative approach
324
3
Comparing two means
327
4
Two sample t-test
327
1
Alternative tests
328
1
One and two tailed tests
329
2
Conclusion
331
1
Appendix 1: The meaning of p-values and confidence intervals
332
3
What is a p-value?
332
2
What is a confidence interval?
334
1
Appendix 2: Analytical results about variances of sample means
335
4
Introducing the basic notation
335
1
Using the notation to define the variance of a sample
335
1
Using the notation to define the mean of a sample
336
1
Defining the variance of the sample mean
336
1
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
2
Appendix 3: Probability distributions
339
4
Some gentle theory
339
2
Confirming simulations
341
2
Bibliography
343
2
Index
345
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