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 <div style="float:right;margin:0 0 2em 2em;">__TOC__</div>
 '''Related Article(s):'''
 *[[Long-Term Monitoring (LTM)]]
 *[[Long-Term Monitoring (LTM) - Data Variability]]
-'''CONTRIBUTOR(S):''' [[Dr. Thomas McHugh]] and [[Dr. David Adamson, P.E.]]
+'''Contributor(s):''' [[Dr. Thomas McHugh]] and [[Dr. David Adamson, P.E.]]
 '''Key Resource(s):'''
-*[[Media:ITRC-2013-Groundwater_Stat_Mon.pdf|Groundwater statistics and monitoring compliance, statistical tools for the project life cycle]]<ref name="ITCR2013">ITRC, 2013. Groundwater statistics and monitoring compliance, statistical tools for the project life cycle. GSMC-1. Washington, D.C.: Interstate Technology & Regulatory Council, Groundwater Statistics and Monitoring Compliance Team. [[Media:ITRC-2013-Groundwater_Stat_Mon.pdf|Report pdf]]</ref>
 *[https://www.serdp-estcp.org/Program-Areas/Environmental-Restoration/Contaminated-Groundwater/Monitoring/ER-201209 Methods for minimization and management of variability in long-term groundwater monitoring results-ER-201209]<ref name="McHugh2015">McHugh, T.E., Kulkarni, P.R., Beckley, L.M., Newell, C.J., Strasters, B., 2015. Methods for minimization and management of variability in long-term groundwater monitoring results. A new method to optimize monitoring frequency and evaluate long-term concentration trends, Technical Report, Task 2 & 3.  ER-201209. [https://www.serdp-estcp.org/Program-Areas/Environmental-Restoration/Contaminated-Groundwater/Monitoring/ER-201209 ER-201209]</ref>
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 Site managers often use parametric or non-parametric statistica methods to analyze LTM groundwater concentration vs. time data. [[wikipedia: Parametric statistics | Parametric statistical methods]] incorporate specific assumptions regarding the data distribution (e.g., a normal distribution or a log normal distribution), while [[wikipedia: Nonparametric statistics | non-parametric methods]] do not. Parametric methods are more accurate and powerful for the analysis of datasets that satisfy the specified assumptions. However, non-parametric methods are more accurate for datasets that do not satisfy the required assumptions that are incorporated into the specific parametric methods. Site managers commonly choose between one parametric method (linear regression) and two non-parametric methods (Mann-Kendall and Theil-Sen Slope Estimator<ref>Gilbert, R.O., 1987. Statistical methods for environmental pollution monitoring. John Wiley & Sons. ISBN 978-0-471-28878-7</ref>) to evaluate concentration trends over time. Mann-Kendall can only be used to evaluate the concentration trend (i.e., are concentrations increasing or decreasing?) with linear regression and the Theil-Sen Slope Estimator can be used to evaluate both concentration trends and attenuation rates. When evaluating concentration vs. time with groundwater monitoring data, the long-term concentration trend is most commonly assumed to be first-order (e.g., exponential decay). This first-order attenuation rate is estimated using linear regression or the Theil-Sen Slope Estimator on natural log transformed concentration data (i.e., Ln(C)) vs. time. The site manager may conduct trend analysis for individual monitoring wells or for the plume as a whole (i.e., using a representation of plume mass or average plume concentration).
-Most statistics software packages can be used for parametric or non-parametric trend analysis. In addition, organizations have developed a number of free software programs specifically for analysis of environmental monitoring data (see Appendix D of ITRC, 2013)<ref name="ITCR2013"/>. Commonly used software tools include:
+Most statistics software packages can be used for parametric or non-parametric trend analysis. In addition, organizations have developed a number of free software programs specifically for analysis of environmental monitoring data (see Appendix D of ITRC, 2013)<ref name="ITCR2013" />. Commonly used software tools include:
 *<u>Microsoft Excel</u>: Parametric trend analyses can be conducted using Excel functions or the Data Analysis Tool Pack add-in that is part of the Excel software package, but may not be installed on your computer if the default installation option was chosen.
-*<u>[https://www.epa.gov/land-research/proucl-software ProUCL (Free)]</u>: Supports parametric and non-parametric analyses<ref> Singh, A., Maichle, R. and Lee, S.E., 2006. On the computation of a 95% upper confidence limit of the unknown population mean based upon data sets with below detection limit observations. U.S. Environmental Protection Agency, EPA-600-R-06-022. [[Media:Singh_EPA-2006-Computation.pdf|Report pdf]]</ref>.
+*<u>[https://www.epa.gov/land-research/proucl-software ProUCL (Free)]</u>: Supports parametric and non-parametric analyses<ref> Singh, A., Maichle, R. and Lee, S.E., 2006. On the computation of a 95% upper confidence limit of the unknown population mean based upon data sets with below detection limit observations. U.S. Environmental Protection Agency, EPA-600-R-06-022. [//www.enviro.wiki/images/4/4c/Singh_EPA-2006-Computation.pdf Report pdf]</ref>.
-*<u>[[http://www.gsi-net.com/en/software/free-software/monitoring-and-remediation-optimization-system-maros-version-2-2.html MAROS (Free)]</u>: Supports spatial data averaging for whole plume trend analysis<ref >AFCEC (Air Force Civil Engineer Center), 2012. Monitoring and remediation optimization system (MAROS) software, user's guide and technical manual. In: Air Force Center for Environmental Excellence. [http://www.gsi-net.com/en/software/free-software/monitoring-and-remediation-optimization-system-maros-version-2-2.html MAROS]</ref>.
+*<u>[[http://www.gsi-net.com/en/software/free-software/monitoring-and-remediation-optimization-system-maros-version-2-2.html MAROS (Free)]</u>: Supports spatial data averaging for whole plume trend analysis<ref>AFCEC (Air Force Civil Engineer Center), 2012. Monitoring and remediation optimization system (MAROS) software, user's guide and technical manual. In: Air Force Center for Environmental Excellence. [http://www.gsi-net.com/en/software/free-software/monitoring-and-remediation-optimization-system-maros-version-2-2.html MAROS]</ref>.
 *<u>[http://www.gsi-net.com/en/software/free-software/gsi-mann-kendall-toolkit.html Mann-Kendall Tool Kit (Free)]</u>: Evaluates concentration trends using the Mann-Kendall statistical test<ref>Connor, J.A., Farhat, S.K. and Vanderford, M., 2014. GSI Mann‐Kendall toolkit for quantitative analysis of plume concentration trends. Groundwater, 52(6), 819-820. [http://dx.doi.org/10.1111/gwat.12277 doi: 10.1111/gwat.12277]</ref>.
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 [[File:Adamson-Article 2-Table 1.PNG|thumbnail|right|600 px|Table 1. Monitoring data required to determine long-term attenuation rate.]]
-Researchers analyzed historical monitoring records from 20 sites in order to characterize the range of monitoring data requirements at different sites as part of an ESTCP-funded project<ref name="McHugh2015"/>. At each site, they used historical monitoring data to determine attenuation rate and the site-specific magnitude of short-term variability. Next, they used these values to determine how much monitoring data were required to characterize the long-term attenuation rate within a defined level of accuracy or confidence (Table 1).
+Researchers analyzed historical monitoring records from 20 sites in order to characterize the range of monitoring data requirements at different sites as part of an ESTCP-funded project<ref name="McHugh2015" />. At each site, they used historical monitoring data to determine attenuation rate and the site-specific magnitude of short-term variability. Next, they used these values to determine how much monitoring data were required to characterize the long-term attenuation rate within a defined level of accuracy or confidence (Table 1).
 This evaluation showed that '''''characterization of long-term trends with either medium confidence or medium accuracy almost always requires four or more years of quarterly monitoring data'''''. The researchers defined medium confidence as a p-value = 0.1, lower than the typical threshold for statistical confidence of 0.05. Longer monitoring times would be required to obtain p-values of 0.05 in most monitoring wells. Additional key findings were:
 *It is important to recognize that apparent trends characterized using too little data can be misleading and may result in inappropriate management decisions.
 *When evaluating [[Monitored Natural Attenuation (MNA) | natural attenuation]], there are often situations where the project manager can be confident that contaminant concentrations are decreasing, but highly uncertain as to when numerical clean-up goals will be attained.
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 ==Trade-off Between Monitoring Frequency and Duration==
 Although the absolute time (or number) of monitoring events required to characterize long-term attenuation rate depends on the short-term variability and the attenuation rate, the trade-off between monitoring frequency and time is independent of these parameters. If you reduce monitoring frequency (e.g., from quarterly to semi-annual monitoring), then you need to extend the total monitoring time in order to characterize the long-term attenuation rate with the same level of confidence or accuracy. The trade-off between monitoring frequency and time required to characterize the long-term trend is defined by the mathematics of linear regression and is the same at every site<ref name="McHugh2016">McHugh , T.E., Kulkarni, P.R., and Newell, C.J., 2016.  Time Vs. Money: A Quantitative Evaluation of Monitoring Frequency Vs. Monitoring Duration. Groundwater, 54, 692–698. [http://dx.doi.org/10.1111/gwat.12407 doi: 10.1111/gwat.12407]</ref>. At all sites, five years of semi-annual monitoring data (10 monitoring events total) provides the same information about the long-term attenuation as four years of quarterly monitoring data (16 monitoring events) regardless of the inherent level of event-to-event variability at the site. Thus, switching from quarterly to semi-annual monitoring will reduce the number of monitoring events needed to characterize the long-term trend by 38%, but the amount of time needed will increase by 25%. The trade-off between monitoring frequency and monitoring duration is summarized in Table 2.
-[[File:Adamson-Article 2-Table 2-Trade-off.PNG|thumbnail|center|600 px|Table 2. Trade-off between monitoring frequency and time. Note: Relative cost is the same as the relative total number of monitoring events required (i.e., based on the assumption that cost is proportional to number of monitoring events) (see McHugh et al., 2006<ref name="McHugh2016"/> for derivation of these relationships).]]
+[[File:Adamson-Article 2-Table 2-Trade-off.PNG|thumbnail|center|600 px|Table 2. Trade-off between monitoring frequency and time. Note: Relative cost is the same as the relative total number of monitoring events required (i.e., based on the assumption that cost is proportional to number of monitoring events) (see McHugh et al., 2006<ref name="McHugh2016" /> for derivation of these relationships).]]
 ==Summary==
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 ==References==
-<references/>
+<references />
 ==See Also==
 *[http://www.graphpad.com/quickcalcs/linear1/ Linear Regression Calculator]<br />
 *[http://www.singlecaseresearch.org/calculators/theil-sen The Thiel-Sen Calculator]<br />
 *[http://www.danielsoper.com/statcalc/calculator.aspx?id=1 A-Priori Sample Size For Multiple Regression Calculator]
-*[https://www.serdp-estcp.org/Program-Areas/Environmental-Restoration/Contaminated-Groundwater/Monitoring/ER-200629   Adaptive Long-Term Monitoring at Environmental Restoration Sites]
+*[https://www.serdp-estcp.org/Program-Areas/Environmental-Restoration/Contaminated-Groundwater/Monitoring/ER-200629 Adaptive Long-Term Monitoring at Environmental Restoration Sites]
-*[https://www.serdp-estcp.org/Program-Areas/Environmental-Restoration/Contaminated-Groundwater/Monitoring/ER-200714  Demonstration and Validation of GTS Long-Term Monitoring Optimization Software at Military and Government Sites]
+*[https://www.serdp-estcp.org/Program-Areas/Environmental-Restoration/Contaminated-Groundwater/Monitoring/ER-200714 Demonstration and Validation of GTS Long-Term Monitoring Optimization Software at Military and Government Sites]

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−	'''CONTRIBUTOR(S):''' [[Dr. ~~Thomas McHugh \|~~ Thomas McHugh]] and [[Dr. David Adamson, P.E. ~~\| David Adamson~~]]	+	'''CONTRIBUTOR(S):''' [[Dr. Thomas McHugh]] and [[Dr. David Adamson, P.E.]]

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−	'''CONTRIBUTOR(S):''' [[Dr. Thomas McHugh]] and [[Dr. David Adamson, P.E.]]	+	'''CONTRIBUTOR(S):''' [[Dr. Thomas McHugh \| Thomas McHugh]] and [[Dr. David Adamson, P.E. \| David Adamson]]

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Long-Term Monitoring (LTM) - Data Analysis - Revision history

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