Threshold-dependent sample sizes for selenium assessment with stream fish tissue

Nathaniel P Hitt, David R. Smith

Research output: Contribution to journalArticle

Abstract

Natural resource managers are developing assessments of selenium (Se) contamination in freshwater ecosystems based on fish tissue concentrations. We evaluated the effects of sample size (i.e., number of fish per site) on the probability of correctly detecting mean whole-body Se values above a range of potential management thresholds. We modeled Se concentrations as gamma distributions with shape and scale parameters fitting an empirical mean-to-variance relationship in data from southwestern West Virginia, USA (63 collections, 382 individuals). We used parametric bootstrapping techniques to calculate statistical power as the probability of detecting true mean concentrations up to 3mg Se/kg above management thresholds ranging from 4 to 8mg Se/kg. Sample sizes required to achieve 80% power varied as a function of management thresholds and Type I error tolerance (α). Higher thresholds required more samples than lower thresholds because populations were more heterogeneous at higher mean Se levels. For instance, to assess a management threshold of 4mg Se/kg, a sample of eight fish could detect an increase of approximately 1mg Se/kg with 80% power (given α=0.05), but this sample size would be unable to detect such an increase from a management threshold of 8mg Se/kg with more than a coin-flip probability. Increasing α decreased sample size requirements to detect above-threshold mean Se concentrations with 80% power. For instance, at an α-level of 0.05, an 8-fish sample could detect an increase of approximately 2 units above a threshold of 8mg Se/kg with 80% power, but when α was relaxed to 0.2, this sample size was more sensitive to increasing mean Se concentrations, allowing detection of an increase of approximately 1.2 units with equivalent power. Combining individuals into 2- and 4-fish composite samples for laboratory analysis did not decrease power because the reduced number of laboratory samples was compensated for by increased precision of composites for estimating mean conditions. However, low sample sizes (<5 fish) did not achieve 80% power to detect near-threshold values (i.e., <1mg Se/kg) under any scenario we evaluated. This analysis can assist the sampling design and interpretation of Se assessments from fish tissue by accounting for natural variation in stream fish populations.

Original languageEnglish (US)
Pages (from-to)143-149
Number of pages7
JournalIntegrated Environmental Assessment and Management
Volume11
Issue number1
DOIs
StatePublished - Jan 1 2015

Fingerprint

selenium
fish
management
tissue
environmental pollution
bootstrapping
tolerance
freshwater ecosystem
natural resources
manager
scenario
natural resource
interpretation

All Science Journal Classification (ASJC) codes

  • Geography, Planning and Development
  • Environmental Science(all)

Cite this

@article{29b50a3b0b6e4a22b906b4f2becc1061,
title = "Threshold-dependent sample sizes for selenium assessment with stream fish tissue",
abstract = "Natural resource managers are developing assessments of selenium (Se) contamination in freshwater ecosystems based on fish tissue concentrations. We evaluated the effects of sample size (i.e., number of fish per site) on the probability of correctly detecting mean whole-body Se values above a range of potential management thresholds. We modeled Se concentrations as gamma distributions with shape and scale parameters fitting an empirical mean-to-variance relationship in data from southwestern West Virginia, USA (63 collections, 382 individuals). We used parametric bootstrapping techniques to calculate statistical power as the probability of detecting true mean concentrations up to 3mg Se/kg above management thresholds ranging from 4 to 8mg Se/kg. Sample sizes required to achieve 80{\%} power varied as a function of management thresholds and Type I error tolerance (α). Higher thresholds required more samples than lower thresholds because populations were more heterogeneous at higher mean Se levels. For instance, to assess a management threshold of 4mg Se/kg, a sample of eight fish could detect an increase of approximately 1mg Se/kg with 80{\%} power (given α=0.05), but this sample size would be unable to detect such an increase from a management threshold of 8mg Se/kg with more than a coin-flip probability. Increasing α decreased sample size requirements to detect above-threshold mean Se concentrations with 80{\%} power. For instance, at an α-level of 0.05, an 8-fish sample could detect an increase of approximately 2 units above a threshold of 8mg Se/kg with 80{\%} power, but when α was relaxed to 0.2, this sample size was more sensitive to increasing mean Se concentrations, allowing detection of an increase of approximately 1.2 units with equivalent power. Combining individuals into 2- and 4-fish composite samples for laboratory analysis did not decrease power because the reduced number of laboratory samples was compensated for by increased precision of composites for estimating mean conditions. However, low sample sizes (<5 fish) did not achieve 80{\%} power to detect near-threshold values (i.e., <1mg Se/kg) under any scenario we evaluated. This analysis can assist the sampling design and interpretation of Se assessments from fish tissue by accounting for natural variation in stream fish populations.",
author = "Hitt, {Nathaniel P} and Smith, {David R.}",
year = "2015",
month = "1",
day = "1",
doi = "10.1002/ieam.1579",
language = "English (US)",
volume = "11",
pages = "143--149",
journal = "Integrated Environmental Assessment and Management",
issn = "1551-3777",
publisher = "SETAC Press",
number = "1",

}

Threshold-dependent sample sizes for selenium assessment with stream fish tissue. / Hitt, Nathaniel P; Smith, David R.

In: Integrated Environmental Assessment and Management, Vol. 11, No. 1, 01.01.2015, p. 143-149.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Threshold-dependent sample sizes for selenium assessment with stream fish tissue

AU - Hitt, Nathaniel P

AU - Smith, David R.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Natural resource managers are developing assessments of selenium (Se) contamination in freshwater ecosystems based on fish tissue concentrations. We evaluated the effects of sample size (i.e., number of fish per site) on the probability of correctly detecting mean whole-body Se values above a range of potential management thresholds. We modeled Se concentrations as gamma distributions with shape and scale parameters fitting an empirical mean-to-variance relationship in data from southwestern West Virginia, USA (63 collections, 382 individuals). We used parametric bootstrapping techniques to calculate statistical power as the probability of detecting true mean concentrations up to 3mg Se/kg above management thresholds ranging from 4 to 8mg Se/kg. Sample sizes required to achieve 80% power varied as a function of management thresholds and Type I error tolerance (α). Higher thresholds required more samples than lower thresholds because populations were more heterogeneous at higher mean Se levels. For instance, to assess a management threshold of 4mg Se/kg, a sample of eight fish could detect an increase of approximately 1mg Se/kg with 80% power (given α=0.05), but this sample size would be unable to detect such an increase from a management threshold of 8mg Se/kg with more than a coin-flip probability. Increasing α decreased sample size requirements to detect above-threshold mean Se concentrations with 80% power. For instance, at an α-level of 0.05, an 8-fish sample could detect an increase of approximately 2 units above a threshold of 8mg Se/kg with 80% power, but when α was relaxed to 0.2, this sample size was more sensitive to increasing mean Se concentrations, allowing detection of an increase of approximately 1.2 units with equivalent power. Combining individuals into 2- and 4-fish composite samples for laboratory analysis did not decrease power because the reduced number of laboratory samples was compensated for by increased precision of composites for estimating mean conditions. However, low sample sizes (<5 fish) did not achieve 80% power to detect near-threshold values (i.e., <1mg Se/kg) under any scenario we evaluated. This analysis can assist the sampling design and interpretation of Se assessments from fish tissue by accounting for natural variation in stream fish populations.

AB - Natural resource managers are developing assessments of selenium (Se) contamination in freshwater ecosystems based on fish tissue concentrations. We evaluated the effects of sample size (i.e., number of fish per site) on the probability of correctly detecting mean whole-body Se values above a range of potential management thresholds. We modeled Se concentrations as gamma distributions with shape and scale parameters fitting an empirical mean-to-variance relationship in data from southwestern West Virginia, USA (63 collections, 382 individuals). We used parametric bootstrapping techniques to calculate statistical power as the probability of detecting true mean concentrations up to 3mg Se/kg above management thresholds ranging from 4 to 8mg Se/kg. Sample sizes required to achieve 80% power varied as a function of management thresholds and Type I error tolerance (α). Higher thresholds required more samples than lower thresholds because populations were more heterogeneous at higher mean Se levels. For instance, to assess a management threshold of 4mg Se/kg, a sample of eight fish could detect an increase of approximately 1mg Se/kg with 80% power (given α=0.05), but this sample size would be unable to detect such an increase from a management threshold of 8mg Se/kg with more than a coin-flip probability. Increasing α decreased sample size requirements to detect above-threshold mean Se concentrations with 80% power. For instance, at an α-level of 0.05, an 8-fish sample could detect an increase of approximately 2 units above a threshold of 8mg Se/kg with 80% power, but when α was relaxed to 0.2, this sample size was more sensitive to increasing mean Se concentrations, allowing detection of an increase of approximately 1.2 units with equivalent power. Combining individuals into 2- and 4-fish composite samples for laboratory analysis did not decrease power because the reduced number of laboratory samples was compensated for by increased precision of composites for estimating mean conditions. However, low sample sizes (<5 fish) did not achieve 80% power to detect near-threshold values (i.e., <1mg Se/kg) under any scenario we evaluated. This analysis can assist the sampling design and interpretation of Se assessments from fish tissue by accounting for natural variation in stream fish populations.

UR - http://www.scopus.com/inward/record.url?scp=84940544592&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84940544592&partnerID=8YFLogxK

U2 - 10.1002/ieam.1579

DO - 10.1002/ieam.1579

M3 - Article

C2 - 25208918

AN - SCOPUS:84940544592

VL - 11

SP - 143

EP - 149

JO - Integrated Environmental Assessment and Management

JF - Integrated Environmental Assessment and Management

SN - 1551-3777

IS - 1

ER -