1 Welcome to the CLU-IN Internet Seminar Unified Guidance Sponsored by: U.S. EPA Technical Support Project Delivered: October 7, 2010, 2:00 PM - 3:00 PM, EDT (18:00-19:00 GMT) Instructor: Mike Gansecki, U.S. EPA Region 8 Moderator: Jean Balent, U.S. EPA, Technology Innovation and Field Services Division Visit the Clean Up Information Network online at

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UNIFIED GUIDANCE WEBINAR Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities March 2009 Website Location: resources/guidance/sitechar/gwstats/index.htm 3

Covers and Errata Sheet

Purpose of Webinar Present general layout and contents of the Unified Guidance Present general layout and contents of the Unified Guidance How to use this guidance How to use this guidance Issues of interest Issues of interest 5

GENERAL LAYOUT Longleat, England 6

GUIDANCE LAYOUT MAIN TEXT PART I Introductory Information & Design PART II Diagnostic Methods PART III Detection Monitoring Methods PART IV Compliance/Corrective Action Methods APPENDICES– References, Index, Historical Issues, Statistical Details, Programs & Tables 7

PART I INTRODUCTORY INFORMATION & DESIGN RCRA Regulations, Constraints & Issues RCRA Regulations, Constraints & Issues Basic Statistical Concepts Basic Statistical Concepts Groundwater Monitoring Framework Groundwater Monitoring Framework Developing Background Data Developing Background Data Detection Monitoring Design Detection Monitoring Design Compliance/Corrective Action Monitoring Design Compliance/Corrective Action Monitoring Design Summary of Methods Summary of Methods 8

PART II DIAGNOSTIC METHODS Exploratory Data Techniques Exploratory Data Techniques Fitting Distributions Fitting Distributions Outlier Analyses Outlier Analyses Equality of Variance Equality of Variance Spatial Variation Evaluation Spatial Variation Evaluation Temporal Variation Analysis Temporal Variation Analysis Managing Non-Detect Data Managing Non-Detect Data 9

PART III DETECTION MONITORING METHODS Two-sample Tests Two-sample Tests ANOVAs, Tolerance Limits & Trend Tests ANOVAs, Tolerance Limits & Trend Tests Prediction Limit Tests and Managing Multiple Comparisons Prediction Limit Tests and Managing Multiple Comparisons Control Charts Control Charts 10

PART IV COMPLIANCE MONITORING METHODS Mean, Median and Upper Percentile Tests with Fixed Health-based Standards Mean, Median and Upper Percentile Tests with Fixed Health-based Standards Stationary versus Trend Tests Stationary versus Trend Tests Parametric and Non-parametric Options Parametric and Non-parametric Options Strategies under Compliance and Corrective Action Testing Strategies under Compliance and Corrective Action Testing Consideration of Tests with a Background- type Groundwater Protection Standard Consideration of Tests with a Background- type Groundwater Protection Standard 11

HOW TO USE THIS GUIDANCE Man-at-Desk 12

USING THE UNIFIED GUIDANCE Design of a statistical monitoring system versus routine implementation Design of a statistical monitoring system versus routine implementation Flexibility necessary in selecting methods Flexibility necessary in selecting methods Resolving issues may require coordination with the regulatory agency Resolving issues may require coordination with the regulatory agency Later detailed methods based on early concept and design Chapters Later detailed methods based on early concept and design Chapters Each method has background, requirements and assumptions, procedure and a worked example Each method has background, requirements and assumptions, procedure and a worked example 13

The Neumanns Alfred E. Neuman, Cover of MAD #30John von Neumann, taken in the 1940’s 14

Temporal Variation [Chapter 14] Rank von Neumann Ratio Test Background & Purpose A non-parametric test of first-order autocorrelation; A non-parametric test of first-order autocorrelation; an alternative to the autocorrelation function Based on idea that independent data vary in a random but predictable fashion Based on idea that independent data vary in a random but predictable fashion Ranks of sequential lag-1 pairs are tested, using the sum of squared differences in a ratio Ranks of sequential lag-1 pairs are tested, using the sum of squared differences in a ratio Low values of the ratio v indicative of temporal dependence Low values of the ratio v indicative of temporal dependence A powerful non-parametric test even with parametric (normal or skewed) data A powerful non-parametric test even with parametric (normal or skewed) data 15

Temporal Variation [Chapter 14] Rank von Neumann Ratio Test Requirement & Assumptions An unresolved problem occurs when a substantial fraction of tied observations occurs An unresolved problem occurs when a substantial fraction of tied observations occurs Mid-ranks are used for ties, but no explicit adjustment has been developed Mid-ranks are used for ties, but no explicit adjustment has been developed Test may not be appropriate with a large fraction of non-detect data; most non-parametric tests may not work well Test may not be appropriate with a large fraction of non-detect data; most non-parametric tests may not work well Many other non-parametric tests are also available in the statistical literature, particularly with normally distributed residuals following trend removal Many other non-parametric tests are also available in the statistical literature, particularly with normally distributed residuals following trend removal 16

Temporal Variation [Chapter 14] Rank von Neumann Ratio Procedure 17

Rank von Neumann Example 14-4 Arsenic Data 18

Rank von Neumann Ex.14-4 Solution 19

DIAGNOSTIC TESTING Preliminary Data Plots [Chapter 9] 20

Additional Diagnostic Information Data Plots [Chapter 9] – Indicate no likely outliers; data are roughly normal, symmetric and stationary with no obvious unequal variance across time (to be tested) Data Plots [Chapter 9] – Indicate no likely outliers; data are roughly normal, symmetric and stationary with no obvious unequal variance across time (to be tested) Correlation Coefficient Normality Test [Section 10.6] Correlation Coefficient Normality Test [Section 10.6] r =.99; p[r] >.1 Accept Normality Equality of Variance [Chapter 11] - see analyses below Equality of Variance [Chapter 11] - see analyses below Outlier Tests [Chapter 12]- not necessary Outlier Tests [Chapter 12]- not necessary Spatial Variation [Chapter 13]–spatial variation not relevant for single variable data sets Spatial Variation [Chapter 13]–spatial variation not relevant for single variable data sets 21

Additional Diagnostic Information Von Neumann Ratio Test [Section ] Von Neumann Ratio Test [Section ] ν = 1.67 No first-order autocorrelation Pearson Correlation of Arsenic vs. Time Pearson Correlation of Arsenic vs. Time [p.3-12]; r =.09 No apparent linear trend One-Way ANOVA Test for Quarterly Differences One-Way ANOVA Test for Quarterly Differences [Section ];F = 1.7, p(F) =.22 Secondary ANOVA test for equal variance F =.41; p(F) =.748 No significant quarterly mean differences and equal variance across quarters 22

Additional Diagnostic Information One-Way ANOVA Test for Annual Differences [Chapter 14]; One-Way ANOVA Test for Annual Differences [Chapter 14]; F = 1.96; p(F) =.175 Secondary ANOVA test for equal variance F = 1.11; p(F) =.385 No significant annual mean differences and equal variance across years No significant annual mean differences and equal variance across years Non-Detect Data [Chapter 15]– all quantitative data; evaluation not needed Non-Detect Data [Chapter 15]– all quantitative data; evaluation not neededConclusions Arsenic data are satisfactorily independent temporally, random, normally distributed, stationary and of equal variance Arsenic data are satisfactorily independent temporally, random, normally distributed, stationary and of equal variance 23

ISSUES ISSUES The Thinker, Musee Rodin in Paris 24

ISSUES OF INTEREST RCRA REGULATORY STATISTICAL ISSUES RCRA REGULATORY STATISTICAL ISSUES DEVELOPING AND UPDATING BACKGROUND DATA DEVELOPING AND UPDATING BACKGROUND DATA USE OF SYSTEM-WIDE FALSE POSITIVE AND POWER CONTROL DESIGN USE OF SYSTEM-WIDE FALSE POSITIVE AND POWER CONTROL DESIGN APPROPRIATE HYPOTHESES, METHODS, STATISTICAL PARAMETERS, FALSE POSITIVE AND POWER LEVELS FOR COMPLIANCE MONITORING FIXED GWPS TESTING APPROPRIATE HYPOTHESES, METHODS, STATISTICAL PARAMETERS, FALSE POSITIVE AND POWER LEVELS FOR COMPLIANCE MONITORING FIXED GWPS TESTING CHOICES OF PARAMETRIC AND NON-PARAMETRIC DISTRIBUTIONS CHOICES OF PARAMETRIC AND NON-PARAMETRIC DISTRIBUTIONS USE OF OTHER STATISTICAL METHODS AND SOFTWARE, e.g., ProUCL® USE OF OTHER STATISTICAL METHODS AND SOFTWARE, e.g., ProUCL® 25

RCRA REGULATORY STATISTICAL ISSUES Four-successive sample requirements and independent Sampling Data Four-successive sample requirements and independent Sampling Data Interim Status Indicator Testing Requirements Interim Status Indicator Testing Requirements 1 & 5% Regulatory Testing Requirements 1 & 5% Regulatory Testing Requirements Use of ANOVA and Tolerance Intervals Use of ANOVA and Tolerance Intervals April 2006 Regulatory Modifications April 2006 Regulatory Modifications 26

DEVELOPING AND UPDATING BACKGROUND DATA In development (e.g., permit or plan), consider all historical sample data In development (e.g., permit or plan), consider all historical sample data Larger background sample sizes preferable Larger background sample sizes preferable Consider all diagnostic conditions, especially outliers Consider all diagnostic conditions, especially outliers For updating, need 4-8 samples not significantly different (use a Student-t or Mann-Whitney test to check) For updating, need 4-8 samples not significantly different (use a Student-t or Mann-Whitney test to check) Special considerations for repeat test data Special considerations for repeat test data 27

USE OF SYSTEM-WIDE FALSE POSITIVE AND POWER CONTROL DESIGN Applied to detection monitoring system design for comparisons to background (or for two-sample background-type GWPS compliance tests) Applied to detection monitoring system design for comparisons to background (or for two-sample background-type GWPS compliance tests) Uses a design 10% annual Sitewide False Positive Rate [SWFPR] apportioned to the number of annual statistical tests (number of wells, relevant constituents and annual test frequency) Uses a design 10% annual Sitewide False Positive Rate [SWFPR] apportioned to the number of annual statistical tests (number of wells, relevant constituents and annual test frequency) Reference power curves based on a 1-of-1 prediction limit test 1, 2, or 4 times per year Reference power curves based on a 1-of-1 prediction limit test 1, 2, or 4 times per year Fully developed for prediction limits, but applicable to tolerance interval and control chart detection tests Fully developed for prediction limits, but applicable to tolerance interval and control chart detection tests 28

HYPOTHESES, METHODS, STATISTICAL PARAMETERS, FALSE POSITIVE AND POWER LEVELS FOR COMPLIANCE MONITORING FIXED GWPS TESTING The guidance identifies testing hypotheses based on RCRA regulations; these may differ in other State and regulatory programs The guidance identifies testing hypotheses based on RCRA regulations; these may differ in other State and regulatory programs Choices of statistical parameter to compare to a GWPS variable Choices of statistical parameter to compare to a GWPS variable Regulatory agency can determine significance and power criteria, perhaps on a program level Regulatory agency can determine significance and power criteria, perhaps on a program level 29

CHOICES OF PARAMETRIC AND NON- PARAMETRIC DISTRIBUTIONS Under detection monitoring development, distribution choices are primarily determined by data patterns Under detection monitoring development, distribution choices are primarily determined by data patterns Different choices can result in a single system Different choices can result in a single system In compliance and corrective action monitoring, the regulatory agency may determine which parametric distribution is appropriate in light of how a GWPS should be interpreted In compliance and corrective action monitoring, the regulatory agency may determine which parametric distribution is appropriate in light of how a GWPS should be interpreted 30

USE OF OTHER STATISTICAL METHODS AND SOFTWARE, e.g., ProUCL® The Unified Guidance provides a reasonable suite of methods, but by no means exhaustive The Unified Guidance provides a reasonable suite of methods, but by no means exhaustive Statistical literature references to other possible tests are provided Statistical literature references to other possible tests are provided The guidance suggests use of R-script and ProUCL for certain applications. Many other commercial and proprietary software may be available. The guidance suggests use of R-script and ProUCL for certain applications. Many other commercial and proprietary software may be available. 31

Lewis Hine photo, Power House Mechanic 32

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