Textbook
Statistics for Censored Environmental Data Using Minitab and R, 2nd EditionFebruary 2012, ©2012

Praise for the First Edition
" . . . an excellent addition to an upperlevel undergraduate course on environmental statistics, and . . . a 'musthave' desk reference for environmental practitioners dealing with censored datasets."
—Vadose Zone Journal
Statistical Methods for Censored Environmental Data Using Minitab® and R, Second Edition introduces and explains methods for analyzing and interpreting censored data in the environmental sciences. Adapting survival analysis techniques from other fields, the book translates wellestablished methods from other disciplines into new solutions for environmental studies.
This new edition applies methods of survival analysis, including methods for intervalcensored data to the interpretation of lowlevel contaminants in environmental sciences and occupational health. Now incorporating the freely available R software as well as Minitab® into the discussed analyses, the book features newly developed and updated material including:
A new chapter on multivariate methods for censored data
Use of intervalcensored methods for treating true nondetects as lower than and separate from values between the detection and quantitation limits ("remarked data")
A section on summing data with nondetects
A newly written introduction that discusses invasive data, showing why substitution methods fail
Expanded coverage of graphical methods for censored data
The author writes in a style that focuses on applications rather than derivations, with chapters organized by key objectives such as computing intervals, comparing groups, and correlation. Examples accompany each procedure, utilizing realworld data that can be analyzed using the Minitab® and R software macros available on the book's related website, and extensive references direct readers to authoritative literature from the environmental sciences.
Statistics for Censored Environmental Data Using Minitab® and R, Second Edition is an excellent book for courses on environmental statistics at the upperundergraduate and graduate levels. The book also serves as a valuable reference for¿environmental professionals, biologists, and ecologists who focus on the water sciences, air quality, and soil science.
Acknowledgments xi
Introduction to the First Edition: An Accident Waiting To Happen xiii
Introduction to the Second Edition: Invasive Data xvii
1 Things People Do with Censored Data that Are Just Wrong 1
Why Not Substitute—Missing the Signals that Are Present in the Data 3
Why Not Substitute?—Finding Signals that Are Not There 8
So Why Not Substitute? 10
Other Common Misuses of Censored Data 10
2 Three Approaches for Censored Data 12
Approach 1: Nonparametric Methods after Censoring at the Highest Reporting Limit 13
Approach 2: Maximum Likelihood Estimation 14
Approach 3: Nonparametric Survival Analysis Methods 17
Application of Survival Analysis Methods to Environmental Data 17
Parallels to Uncensored Methods 21
3 Reporting Limits 22
Limits When the Standard Deviation is Considered Constant 23
Insider Censoring–Biasing Interpretations 29
Reporting the Machine Readings of all Measurements 33
Limits When the Standard Deviation Changes with Concentration 34
For Further Study 36
4 Reporting, Storing, and Using Censored Data 37
Reporting and Storing Censored Data 37
Using IntervalCensored Data 41
Exercises 42
5 Plotting Censored Data 44
Boxplots 44
Histograms 46
Empirical Distribution Function 47
Survival Function Plots 49
Probability Plot 52
X–Y Scatterplots 59
Exercises 61
6 Computing Summary Statistics and Totals 62
Nonparametric Methods after Censoring at the Highest Reporting Limit 62
Maximum Likelihood Estimation 64
The Nonparametric Kaplan–Meier and Turnbull Methods 70
ROS: A “Robust” Imputation Method 79
Methods in Excel 86
Handling Data with High Reporting Limits 86
A Review of Comparison Studies 87
Summing Data with Censored Observations 94
Exercises 98
7 Computing Interval Estimates 99
Parametric Intervals 100
Nonparametric Intervals 103
Intervals for Censored Data by Substitution 103
Intervals for Censored Data by Maximum Likelihood 104
Intervals for the Lognormal Distribution 112
Intervals Using “Robust” Parametric Methods 125
Nonparametric Intervals for Censored Data 126
Bootstrapped Intervals 136
For Further Study 140
Exercises 141
8 What Can be Done When All Data Are Below the Reporting Limit? 142
Point Estimates 143
Probability of Exceeding the Reporting Limit 144
Exceedance Probability for a Standard Higher than the Reporting Limit 148
Hypothesis Tests Between Groups 151
Summary 152
Exercises 152
9 Comparing Two Groups 153
Why Not Use Substitution? 154
Simple Nonparametric Methods After Censoring at the Highest Reporting Limit 156
Maximum Likelihood Estimation 161
Nonparametric Methods 167
Value of the Information in Censored Observations 178
IntervalCensored Score Tests: Testing Data that Include (DL to RL) Values 180
Paired Observations 183
Summary of TwoSample Tests for Censored Data 192
Exercises 192
10 Comparing Three or More Groups 194
Substitution Does Not Work—Invasive Data 195
Nonparametric Methods after Censoring at the Highest Reporting Limit 196
Maximum Likelihood Estimation 199
Nonparametric Method—The Generalized Wilcoxon Test 209
Summary 215
Exercises 216
11 Correlation 218
Types of Correlation Coefficients 218
Nonparametric Methods after Censoring at the Highest Reporting Limit 219
Maximum Likelihood Correlation Coefficient 224
Nonparametric Correlation Coefficient—Kendall’s Tau 227
IntervalCensored Score Tests: Testing Correlation with (DL to RL) Values 230
Summary: A Comparison Among Methods 232
For Further Study 234
Exercises 235
12 Regression and Trends 236
Why Not Substitute? 237
Nonparametric Methods After Censoring at the Highest Reporting Limit 239
Maximum Likelihood Estimation 249
Akritas–Theil–Sen Nonparametric Regression 258
Additional Methods for Censored Regression 264
Exercises 266
13 Multivariate Methods for Censored Data 268
A Brief Overview of Multivariate Procedures 269
Nonparametric Methods After Censoring at the Highest Reporting Limit 273
Multivariate Methods for Data with Multiple Reporting Limits 288
Summary of Multivariate Methods for Censored Data 296
14 The NADA for R Software 297
A Brief Overview of R and the NADA Software 297
Summary of the Commands Available in NADA 300
Appendix: Datasets 303
References 309
Index 321
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