Statistics for Censored Environmental Data Using Minitab and R

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  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2012-02-01
  • Publisher: Wiley

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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

Prefacep. ix
Acknowledgmentsp. xi
Introduction to the First Edition: An Accident Waiting To Happenp. xiii
Introduction to the Second Edition: Invasive Datap. xvii
Things People Do with Censored Data that Are Just Wrongp. 1
Why Not Substitute-Missing the Signals that Are Present in the Datap. 3
Why Not Substitute?-Finding Signals that Are Not Therep. 8
So Why Not Substitute?p. 10
Other Common Misuses of Censored Datap. 10
Three Approaches for Censored Datap. 12
Approach 1: Nonparametric Methods after Censoring at the Highest Reporting Limitp. 13
Approach 2: Maximum Likelihood Estimationp. 14
Approach 3: Nonparametric Survival Analysis Methodsp. 17
Application of Survival Analysis Methods to Environmental Datap. 17
Parallels to Uncensored Methodsp. 21
Reporting Limitsp. 22
Limits When the Standard Deviation is Considered Constantp. 23
Insider Censoring-Biasing Interpretationsp. 29
Reporting the Machine Readings of all Measurementsp. 33
Limits When the Standard Deviation Changes with Concentrationp. 34
For Further Studyp. 36
Reporting, Storing, and Using Censored Datap. 37
Reporting and Storing Censored Datap. 37
Using Interval-Censored Datap. 41
Exercisesp. 42
Plotting Censored Datap. 44
Boxplotsp. 44
Histogramsp. 46
Empirical Distribution Functionp. 47
Survival Function Plotsp. 49
Probability Plotp. 52
X-Y Scatterplotsp. 59
Exercisesp. 61
Computing Summary Statistics and Totalsp. 62
Nonparametric Methods after Censoring at the Highest Reporting Limitp. 62
Maximum Likelihood Estimationp. 64
The Nonparametric Kaplan-Meier and Turnbull Methodsp. 70
ROS: A "Robust" Imputation Methodp. 79
Methods in Excelp. 86
Handling Data with High Reporting Limitsp. 86
A Review of Comparison Studiesp. 87
Summing Data with Censored Observationsp. 94
Exercisesp. 98
Computing Interval Estimatesp. 99
Parametric Intervalsp. 100
Nonparametric Intervalsp. 103
Intervals for Censored Data by Substitutionp. 103
Intervals for Censored Data by Maximum Likelihoodp. 104
Intervals for the Lognormal Distributionp. 112
Intervals Using "Robust" Parametric Methodsp. 125
Nonparametric Intervals for Censored Datap. 126
Bootstrapped Intervalsp. 136
For Further Studyp. 140
Exercisesp. 141
What Can be Done When All Data Are Below the Reporting Limit?p. 142
Point Estimatesp. 143
Probability of Exceeding the Reporting Limitp. 144
Exceedance Probability for a Standard Higher than the Reporting Limitp. 148
Hypothesis Tests Between Groupsp. 151
Summaryp. 152
Exercisesp. 152
Comparing Two Groupsp. 153
Why Not Use Substitution?p. 154
Simple Nonparametric Methods After Censoring at the Highest Reporting Limitp. 156
Maximum Likelihood Estimationp. 161
Nonparametric Methodsp. 167
Value of the Information in Censored Observationsp. 178
Interval-Censored Score Tests: Testing Data that Include (DL to RL) Valuesp. 180
Paired Observationsp. 183
Summary of Two-Sample Tests for Censored Datap. 192
Exercisesp. 192
Comparing Three or More Groupsp. 194
Substitution Does Not Work-Invasive Datap. 195
Nonparametric Methods after Censoring at the Highest Reporting Limitp. 196
Maximum Likelihood Estimationp. 199
Nonparametric Method-The Generalized Wilcoxon Testp. 209
Summaryp. 215
Exercisesp. 216
Correlationp. 218
Types of Correlation Coefficientsp. 218
Nonparametric Methods after Censoring at the Highest Reporting Limitp. 219
Maximum Likelihood Correlation Coefficientp. 224
Nonparametric Correlation Coefficient-Kendall's Taup. 227
Interval-Censored Score Tests: Testing Correlation with (DL to RL) Valuesp. 230
Summary: A Comparison Among Methodsp. 232
For Further Studyp. 234
Exercisesp. 235
Regression and Trendsp. 236
Why Not Substitute?p. 237
Nonparametric Methods After Censoring at the Highest Reporting Limitp. 239
Maximum Likelihood Estimationp. 249
Akritas-Theil-Sen Nonparametric Regressionp. 258
Additional Methods for Censored Regressionp. 264
Exercisesp. 266
Multivariate Methods for Censored Datap. 268
A Brief Overview of Multivariate Proceduresp. 269
Nonparametric Methods After Censoring at the Highest Reporting Limitp. 273
Multivariate Methods for Data with Multiple Reporting Limitsp. 288
Summary of Multivariate Methods for Censored Datap. 296
The NADA for R Softwarep. 297
A Brief Overview of R and the NADA Softwarep. 297
Summary of the Commands Available in NADAp. 300
Appendix: Datasetsp. 303
Referencesp. 309
Indexp. 321
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