Statistics for Censored Environmental Data Using Minitab and R

by Helsel, Dennis R.

• ISBN13: 9780470479889
• ISBN10: 0470479884
• Edition: 2nd
• Format: Hardcover
• Copyright: 2012-02-01
• Publisher: Wiley

Summary

This Second Edition solves a current dilemma that occurs across a wide spectrum of environmental science: how to correctly analyze and interpret censored data (data below detection limits). It adapts survival analysis methods and demonstrates their practical applications when studying trace chemicals in air, water, soils, and biota. This edition features new chapters on plotting data with nondetects, multivariate procedures, and software for data with nondetects, as well as expanded and new sections, including a new section on testing censored data for normal distributions. Environmental professionals and upper-undergraduate and graduate students will rely on this resource.

Author Biography

Dennis R. Helsel, PhD, is owner and Principal Scientist of Practical Stats, where he designs and conducts training courses in environmental statistics for scientists. He has over thirty years of experience working with the U.S. Geological Survey and is the author of numerous published articles on nondetect data and statistical methods in the environmental sciences. Dr. Helsel is the recipient of the Distinguished Service Award from the U.S. Department of the Interior (2007) as well as the Distinguished Achievement Award from the American Statistical Association (2003).

Table of Contents

Preface	p. ix
Acknowledgments	p. xi
Introduction to the First Edition: An Accident Waiting To Happen	p. xiii
Introduction to the Second Edition: Invasive Data	p. xvii
Things People Do with Censored Data that Are Just Wrong	p. 1
Why Not Substitute-Missing the Signals that Are Present in the Data	p. 3
Why Not Substitute?-Finding Signals that Are Not There	p. 8
So Why Not Substitute?	p. 10
Other Common Misuses of Censored Data	p. 10
Three Approaches for Censored Data	p. 12
Approach 1: Nonparametric Methods after Censoring at the Highest Reporting Limit	p. 13
Approach 2: Maximum Likelihood Estimation	p. 14
Approach 3: Nonparametric Survival Analysis Methods	p. 17
Application of Survival Analysis Methods to Environmental Data	p. 17
Parallels to Uncensored Methods	p. 21
Reporting Limits	p. 22
Limits When the Standard Deviation is Considered Constant	p. 23
Insider Censoring-Biasing Interpretations	p. 29
Reporting the Machine Readings of all Measurements	p. 33
Limits When the Standard Deviation Changes with Concentration	p. 34
For Further Study	p. 36
Reporting, Storing, and Using Censored Data	p. 37
Reporting and Storing Censored Data	p. 37
Using Interval-Censored Data	p. 41
Exercises	p. 42
Plotting Censored Data	p. 44
Boxplots	p. 44
Histograms	p. 46
Empirical Distribution Function	p. 47
Survival Function Plots	p. 49
Probability Plot	p. 52
X-Y Scatterplots	p. 59
Exercises	p. 61
Computing Summary Statistics and Totals	p. 62
Nonparametric Methods after Censoring at the Highest Reporting Limit	p. 62
Maximum Likelihood Estimation	p. 64
The Nonparametric Kaplan-Meier and Turnbull Methods	p. 70
ROS: A "Robust" Imputation Method	p. 79
Methods in Excel	p. 86
Handling Data with High Reporting Limits	p. 86
A Review of Comparison Studies	p. 87
Summing Data with Censored Observations	p. 94
Exercises	p. 98
Computing Interval Estimates	p. 99
Parametric Intervals	p. 100
Nonparametric Intervals	p. 103
Intervals for Censored Data by Substitution	p. 103
Intervals for Censored Data by Maximum Likelihood	p. 104
Intervals for the Lognormal Distribution	p. 112
Intervals Using "Robust" Parametric Methods	p. 125
Nonparametric Intervals for Censored Data	p. 126
Bootstrapped Intervals	p. 136
For Further Study	p. 140
Exercises	p. 141
What Can be Done When All Data Are Below the Reporting Limit?	p. 142
Point Estimates	p. 143
Probability of Exceeding the Reporting Limit	p. 144
Exceedance Probability for a Standard Higher than the Reporting Limit	p. 148
Hypothesis Tests Between Groups	p. 151
Summary	p. 152
Exercises	p. 152
Comparing Two Groups	p. 153
Why Not Use Substitution?	p. 154
Simple Nonparametric Methods After Censoring at the Highest Reporting Limit	p. 156
Maximum Likelihood Estimation	p. 161
Nonparametric Methods	p. 167
Value of the Information in Censored Observations	p. 178
Interval-Censored Score Tests: Testing Data that Include (DL to RL) Values	p. 180
Paired Observations	p. 183
Summary of Two-Sample Tests for Censored Data	p. 192
Exercises	p. 192
Comparing Three or More Groups	p. 194
Substitution Does Not Work-Invasive Data	p. 195
Nonparametric Methods after Censoring at the Highest Reporting Limit	p. 196
Maximum Likelihood Estimation	p. 199
Nonparametric Method-The Generalized Wilcoxon Test	p. 209
Summary	p. 215
Exercises	p. 216
Correlation	p. 218
Types of Correlation Coefficients	p. 218
Nonparametric Methods after Censoring at the Highest Reporting Limit	p. 219
Maximum Likelihood Correlation Coefficient	p. 224
Nonparametric Correlation Coefficient-Kendall's Tau	p. 227
Interval-Censored Score Tests: Testing Correlation with (DL to RL) Values	p. 230
Summary: A Comparison Among Methods	p. 232
For Further Study	p. 234
Exercises	p. 235
Regression and Trends	p. 236
Why Not Substitute?	p. 237
Nonparametric Methods After Censoring at the Highest Reporting Limit	p. 239
Maximum Likelihood Estimation	p. 249
Akritas-Theil-Sen Nonparametric Regression	p. 258
Additional Methods for Censored Regression	p. 264
Exercises	p. 266
Multivariate Methods for Censored Data	p. 268
A Brief Overview of Multivariate Procedures	p. 269
Nonparametric Methods After Censoring at the Highest Reporting Limit	p. 273
Multivariate Methods for Data with Multiple Reporting Limits	p. 288
Summary of Multivariate Methods for Censored Data	p. 296
The NADA for R Software	p. 297
A Brief Overview of R and the NADA Software	p. 297
Summary of the Commands Available in NADA	p. 300
Appendix: Datasets	p. 303
References	p. 309
Index	p. 321
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