Statistics for Environmental Biology and

Statistics for Environmental Biology & Toxicology presents & illustrates statistical methods appropriate for the analysis of environmental data obtained in biological or toxicological experiments. Beginning with basic probability & statistical inferences, this text progresses through non-linear & generalized linear models, trend testing, time-to-event data & analysis of cross-classified tabular & categorical data. For the more complex analyses, extensive examples-including SAS & S-PLUS programming code-are provided to assist the reader when implementing the methods in practice.

Preface

xi

1 Basic probability and statistical distributions

1

(45)

1.1 Introductory concepts in probability

1

(10)

1.2 Families of discrete distributions

11

(9)

1.3 Families of continuous distributions

20

(8)

1.4 The exponential class of distributions

28

(2)

1.5 Families of multivariate distributions

30

(6)

1.6 Summary

36

(1)

Exercises

37

(9)

2 Fundamentals of statistical inference

46

(55)

2.1 Introductory concepts in statistical estimation

47

(2)

2.2 Nature and properties of estimators

49

(1)

2.3 Techniques for constructing statistical estimators

50

(7)

2.4 Statistical inference - Testing hypotheses

57

(8)

2.5 Statistical inference - Confidence intervals

65

(10)

2.6 Confidence intervals for some special distributions

75

(9)

2.7 Semi-parametric inference

84

(8)

2.8 Summary

92

(1)

Exercises

92

(9)

3 Fundamental issues in experiment design

101

(24)

3.1 Basic terminology in experiment design

101

(8)

3.2 The experimental unit

109

(2)

3.3 Random sampling and randomization

111

(3)

3.4 Sample sizes and optimal animal allocation

114

(2)

3.5 Dose selection

116

(5)

3.6 Summary

121

(1)

Exercises

122

(3)

4 Data analysis of treatment-versus-control differences

125

(52)

4.1 Two-sample comparisons - Testing hypotheses

125

(32)

4.2 Two-sample comparisons - Confidence intervals

157

(11)

4.3 Summary

168

(1)

Exercises

169

(8)

5 Treatment-versus-control multiple comparisons

177

(36)

5.1 Comparing more than two populations

177

(7)

5.2 Multiple comparisons via Bonferroni's inequality

184

(3)

5.3 Multiple comparisons with a control - Normal sampling

187

(9)

5.4 Multiple comparisons among binomial populations

196

(5)

5.5 Multiple comparisons with a control - Poisson sampling

201

(3)

5.6 All-pairwise multiple comparisons

204

(3)

5.7 Summary

207

(1)

Exercises

208

(5)

6 Trend testing

213

(75)

6.1 Simple linear regression for normal data

214

(9)

6.2 Williams' test for normal data

223

(4)

6.3 Trend tests for proportions

227

(15)

6.4 Cochran-Armitage trend test for counts

242

(3)

6.5 Overdispersed discrete data

245

(16)

6.6 Distribution-free trend testing

261

(4)

6.7 Nonparametric tests for nonmonotone (`umbrella') trends

265

(5)

6.8 Summary

270

(1)

Exercises

271

(17)

7 Dose-response modeling and analysis

288

(72)

7.1 Dose-response models on a continuous scale

289

(24)

7.2 Dose-response models on a discrete scale

313

(15)

7.3 Potency estimation for dose-response data

328

(14)

7.4 Comparing dose-response curves

342

(5)

7.5 Summary

347

(1)

Exercises

347

(13)

8 Introduction to generalized linear models

360

(52)

8.1 Review of classical linear models

361

(6)

8.2 Generalizing the classical linear model

367

(4)

8.3 Generalized linear models

371

(7)

8.4 Examples and illustrations

378

(25)

8.5 Summary

403

(1)

Exercises

403

(9)

9 Analysis of cross-classified tabular categorical data

412

(50)

9.1 RxC contingency tables

413

(1)

9.2 Statistical distributions for categorical data

414

(4)

9.3 Statistical tests of independence in RxC tables

418

(17)

9.4 Log-linear models and relationships to generalized linear models

435

(3)

9.5 Tables of proportions

438

(13)

9.6 Summary

451

(1)

Exercises

451

(11)

10 Incorporating historical control information

462

(16)

10.1 Guidelines for using historical control data

462

(2)

10.2 Two-sample hypothesis testing - Normal distribution sampling

464

(2)

10.3 Two-sample hypothesis testing - Binomial sampling

466

(5)

10.4 Trend testing with historical controls

471

(3)

10.5 Summary

474

(1)

Exercises

475

(3)

11 Survival-data analysis

478

(57)

11.1 Lifetime distributions

479

(1)

11.2 Estimating the survivor function

480

(22)

11.3 Nonparametric methods for comparing survival curves

502

(5)

11.4 Regression models for survival data

507

(18)

11.5 Summary

525

(1)

Exercises

526

(9)

References

535

(29)

Subject Index

564

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Statistics for Environmental Biology and Toxicology

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Table of Contents

Supplemental Materials