Geology topics

D. Helsel

Publications and source records attributed to D. Helsel.

3 recordsLinked to original sources

USGS2007

Statistical analysis of water-quality data containing multiple detection limits II: S-language software for nonparametric distribution modeling and hypothesis testing

Analysis of low concentrations of trace contaminants in environmental media often results in left-censored data that are below some limit of analytical precision. Interpretation of values becomes complicated when there are multiple detection limits in the data-perhaps as a result of changing analytical precision over time. Parametric and semi-parametric methods, such as maximum likelihood estimation and robust regression on order statistics, can be employed to model distributions of multiply censored data and provide estimates of summary statistics. However, these methods are based on assumptions about the underlying distribution of data. Nonparametric methods provide an alternative that does not require such assumptions. A standard nonparametric method for estimating summary statistics of multiply-censored data is the Kaplan-Meier (K-M) method. This method has seen widespread usage in the medical sciences within a general framework termed "survival analysis" where it is employed with right-censored time-to-failure data. However, K-M methods are equally valid for the left-censored data common in the geosciences. Our S-language software provides an analytical framework based on K-M methods that is tailored to the needs of the earth and environmental sciences community. This includes routines for the generation of empirical cumulative distribution functions, prediction or exceedance probabilities, and related confidence limits computation. Additionally, our software contains K-M-based routines for nonparametric hypothesis testing among an unlimited number of grouping variables. A primary characteristic of K-M methods is that they do not perform extrapolation and interpolation. Thus, these routines cannot be used to model statistics beyond the observed data range or when linear interpolation is desired. For such applications, the aforementioned parametric and semi-parametric methods must be used.

Computers & Geosciences↗

USGS2005

Baseline models of trace elements in major aquifers of the United States

Trace-element concentrations in baseline samples from a survey of aquifers used as potable-water supplies in the United States are summarized using methods appropriate for data with multiple detection limits. The resulting statistical distribution models are used to develop summary statistics and estimate probabilities of exceeding water-quality standards. The models are based on data from the major aquifer studies of the USGS National Water Quality Assessment (NAWQA) Program. These data were produced with a nationally-consistent sampling and analytical framework specifically designed to determine the quality of the most important potable groundwater resources during the years 1991-2001. The analytical data for all elements surveyed contain values that were below several detection limits. Such datasets are referred to as multiply-censored data. To address this issue, a robust semi-parametric statistical method called regression on order statistics (ROS) is employed. Utilizing the 90th-95th percentile as an arbitrary range for the upper limits of expected baseline concentrations, the models show that baseline concentrations of dissolved Ba and Zn are below 500 ??g/L. For the same percentile range, dissolved As, Cu and Mo concentrations are below 10 ??g/L, and dissolved Ag, Be, Cd, Co, Cr, Ni, Pb, Sb and Se are below 1-5 ??g/L. These models are also used to determine the probabilities that potable ground waters exceed drinking water standards. For dissolved Ba, Cr, Cu, Pb, Ni, Mo and Se, the likelihood of exceeding the US Environmental Protection Agency standards at the well-head is less than 1-1.5%. A notable exception is As, which has approximately a 7% chance of exceeding the maximum contaminant level (10 ??g/L) at the well head.

Applied Geochemistry↗

USGS2005

Statistical analysis of water-quality data containing multiple detection limits: S-language software for regression on order statistics

Trace contaminants in water, including metals and organics, often are measured at sufficiently low concentrations to be reported only as values below the instrument detection limit. Interpretation of these "less thans" is complicated when multiple detection limits occur. Statistical methods for multiply censored, or multiple-detection limit, datasets have been developed for medical and industrial statistics, and can be employed to estimate summary statistics or model the distributions of trace-level environmental data. We describe S-language-based software tools that perform robust linear regression on order statistics (ROS). The ROS method has been evaluated as one of the most reliable procedures for developing summary statistics of multiply censored data. It is applicable to any dataset that has 0 to 80% of its values censored. These tools are a part of a software library, or add-on package, for the R environment for statistical computing. This library can be used to generate ROS models and associated summary statistics, plot modeled distributions, and predict exceedance probabilities of water-quality standards. ?? 2005 Elsevier Ltd. All rights reserved.

Computers & Geosciences↗