Quantification of the uncertainties associated with environmental geochemical prediction, such as the function of sample size, remains a concern when performing impact assessments, more specifically Environmental Impact Assessments (EIA). While the determination of sample size in the EIA is limited, there is a definite need for the development of a statistical method, together with a protocol, to address geochemical sample sizing and representative analyses. Based on Central Limit Theorem, this article proposes a statistical method to determine sample sizes, by use of the Vaal River tailing dams in the Witwatersrand Basin and slag dumps of Transalloys Co., Witbank, South Africa, as case studies. It also discusses factors such as confidence intervals, acceptable sampling errors, etc., that could influence sample size estimation, and recommends a trade-off strategy to reduce the sample size for economic reasons. A sample size determination formula was derived at to be used for EIA research and practical work, namely <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="267_2025_2195_Article_IEq1.gif" Format="GIF" Height="30" Rendition="HTML" Resolution="72" Type="Linedraw" Width="96" /> </InlineMediaObject> <EquationSource Format="TEX">$n={(\frac{{Z}_{\alpha /2}\times S}{d})}^{2}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>=</mo> <msup> <mrow> <mo stretchy="true">(</mo> <mfrac> <mrow> <msub> <mrow> <mi>Z</mi> </mrow> <mrow> <mi>α</mi> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mo>×</mo> <mi>S</mi> </mrow> <mrow> <mi>d</mi> </mrow> </mfrac> <mo stretchy="true">)</mo> </mrow> <mn>2</mn> </msup> </mrow> </math></EquationSource> </InlineEquation> (n - sample number taken), <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="267_2025_2195_Article_IEq2.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="32" /> </InlineMediaObject> <EquationSource Format="TEX">${{Z}_{\alpha/2}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mrow> <mi>Z</mi> </mrow> <mrow> <mi>α</mi> <mo>/</mo> <mn>2</mn> </mrow> </msub> </math></EquationSource> </InlineEquation>- obtained from confidence level, S - standard deviation from the sample, d - sampling error, and a benchmark for sampling error was proposed: <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="267_2025_2195_Article_IEq3.gif" Format="GIF" Height="26" Rendition="HTML" Resolution="72" Type="Linedraw" Width="110" /> </InlineMediaObject> <EquationSource Format="TEX">${d}_{{benchmark}}=\frac{S}{\sqrt{n}}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mrow> <mi>d</mi> </mrow> <mrow> <mi mathvariant="italic">benchmark</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mi>S</mi> </mrow> <mrow> <msqrt> <mrow> <mi>n</mi> </mrow> </msqrt> </mrow> </mfrac> </mrow> </math></EquationSource> </InlineEquation> for stakeholders to make wise decisions.

Sampling Size Determination: Application in Geochemical Sampling for Environmental Impact Assessment

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发表日期：

2025年5月26日

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Meng Zhou,
Elizabeth Chihobve,
Baojin Zhao,
Zhen Song

摘要

Quantification of the uncertainties associated with environmental geochemical prediction, such as the function of sample size, remains a concern when performing impact assessments, more specifically Environmental Impact Assessments (EIA). While the determination of sample size in the EIA is limited, there is a definite need for the development of a statistical method, together with a protocol, to address geochemical sample sizing and representative analyses. Based on Central Limit Theorem, this article proposes a statistical method to determine sample sizes, by use of the Vaal River tailing dams in the Witwatersrand Basin and slag dumps of Transalloys Co., Witbank, South Africa, as case studies. It also discusses factors such as confidence intervals, acceptable sampling errors, etc., that could influence sample size estimation, and recommends a trade-off strategy to reduce the sample size for economic reasons. A sample size determination formula was derived at to be used for EIA research and practical work, namely $n={(\frac{{Z}_{\alpha /2}\times S}{d})}^{2}$ $n = {(\frac{Z_{α / 2} \times S}{d})}^{2}$ (n - sample number taken), ${{Z}_{\alpha/2}}$ $Z_{α / 2}$ - obtained from confidence level, S - standard deviation from the sample, d - sampling error, and a benchmark for sampling error was proposed: ${d}_{{benchmark}}=\frac{S}{\sqrt{n}}$ $d_{benchmark} = \frac{S}{\sqrt{n}}$ for stakeholders to make wise decisions.