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Complex and Confusing
Interested in low concentrations of targets
Heterogeneous samples - variable results
Matrix interference on analysis
Regulations don’t address these problems
Complex and Confusing
What do you need?
Why do you need it?
How will you use it?
Bad or good decisions can come from it?
Complex and Confusing
All data have error.
Nobody can afford absolute certainty.
Tolerable error rates (99 % vs. 95 % certainty)
Without DQOs, decisions are uninformed.
Uninformed decisions - conservative and expensive
Appendix IA Parameters
Dissolved Anions Method 300 or 9056 (pay attention to hold times) + Alkalinity Method 310.1 48 hour hold on NO3
- and NO2- (May need 353.1, 353.2, 353.3)
Dissolved Cations Method 6010B/6020
Field Parameters Specific Conductance Method 160.1 pH Method(s) 150.1 or 9040B Temperature Method 170.1 TOC (Not field parameter) Lab Method 9060
Ask for what you need and want
Appendix IB Parameters Total Elements Method 6010B/6020
Volatiles Method 8260B
Method 624
Ask for what you want Communicate, communicate, communicate
DQO Approach: 3 Phases Planning
Data Quality Objectives (Why sample?)
Quality Assurance Project Plan (“QAPP”)
Implementation
Field Data Collection (Sampling)
Quality Assurance/Quality Control Activities
Assessment
Data Validation
Quality Assurance/Quality Control Activities
Much Work Remains to be Done before We Can Announce
Our Total Failure to Make any Progress
•Implementation
Assessment
Environmental Data:
What does this information tell us?
(Reading between the Regulatory Lines)
Why monitor? Why do statistical analysis?
Understand the hydrological setting.
Detect and deal with environmental impacts.
Understand risks and liabilities.
Focus resources.
Reduce monitoring costs.
The soil profile of a dark brown Chernozemic soil formed under native grassland
“A” horizonTopsoil, organic materialZone of leaching
“B” horizonZone of accumulation
“C” horizonParent material ( rock, gravel, sand)
Detection Monitoring
Includes all Appendix I parameters (Appendix IA and IB).
May be modified, in consultation with local governing body to delete any Appendix I parameter on a Site Specific Basis, if
Removed constituents not reasonably expected to be derived from waste
Detection Monitoring
May add parameters, if
Acceptable analytical method,
Commercially available calibration standard, Analyte is chemically stable,
Reasonable sample collection and preservation technique
Reasonable expectation of detection, and is a good indicator and possible precursor to other more hazardous constitutents that might Be released later.
Detection Monitoring
Department considerations in modifying Appendix I parameters:
Types, quantities, and concentrations of constituents in waste managed at the SWDS and facilities
Mobility, stability, and persistence of constituents, or their reaction products in the unsaturated zone beneath the MSWLF unit.
Detection Monitoring
Department may specify a monitoring frequency during the active life and post-closure.
Minimum of semi-annually, unless approved by the Department.
Considerations:
Lithology of the saturated and unsaturated zone
Hydraulic conductivity of groundwater
Groundwater flow rates and minimum distance of travel
Resource value of the groundwater
Background Data
Owner/operator must acquire a minimum of Eight Quarterly SamplesFrom each well and analyzed for Appendix IA and IB constituents.
Owner/operator must specify in the operating record, one or morestatistical tests for each hazardous constituent.
Changes in these statistical tests shall be reviewed and approved within two weeks of the request and entered into the operating record.
Background Data
Owner/operator must acquire a minimum of Eight Quarterly SamplesFrom each well and analyzed for Appendix IA and IB constituents.
Owner/operator must specify in the operating record, one or morestatistical tests for each hazardous constituent.
Changes in these statistical tests shall be reviewed and approved within two weeks of the request and entered into the operating record.
Statistically Significant Increase over Background
Documentation in Operating Record indicating which constituent is above Background, and forward the Documentation to the Department and localGoverning Body within 14 days.
Begin Assessment Monitoring, or
Provide an Alternative Source Demonstration
Error in sampling, analysis, or natural variations in water
Certified by a qualified groundwater scientist
If not successfully demonstrated begin Assessment Monitoring in 90 days.
Statistical Methods and Requirements
Trend analysis
Control charts
Prediction interval (tolerance intervals)
ANOVA comparison with background
Other……………………….
-------------------------------------------------------------------Regulations……..Type I error = 0.01
99 % Certainty (for each constituent in each well)
Statistical Methods and Requirements
Intrawell Statistics, or
Interwell Statistics
(groups and/or Upgradient – Downgradient)
Analyses of Variance (ANOVA)
Trend Analysis
Nitrate
0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
40.00
0 5 10 15 20 25 30 35
Sampling Event
mil
lig
ram
s/L
iter
Series1
Linear (Series1)
Control ChartsFamily of Charts: Shewhart used 3 sigma (3 standard deviations, 98.5 % probability, others have used the Standard error of the Estimate, etc.)
1 sd 67 % of data fits within limits2 sd 95 % of data fits within limits3 sd 98.5 % of data fits within limits4 sd 99 % of data fits within limits
“….the fact that the criterion which we happen to use has a fine ancestry in highbrow statistical theorems does not justify its use. Such justification must come from empirical evidence that it works. As the practical engineer might say, the proof of the pudding is in the eating.”
Walter A. Shewhart
Control Charts
Criticisms:
Controversial.
Operators expected to determine if a special case has occurred.
Process in control – 0.27% probability that a point will be out of specs(1/0.0027 or 1 in 370.4)
Good at detecting large changes, does not detect small changes efficiently
Strengths:
May work well for non-parametric data
Special control chart CUMSUM does detect small changes
Control Charts
Control Charts
No rma lize d R a tio
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
S a mp le Nu mb e r
Tolerance Interval
A tolerance interval, also known as a tolerance limit, or prediction interval is an interval within which, with some confidence, a specifiedproportion of a population falls. This differs from a confidence intervalin that the confidence interval bounds a population parameter(the mean, for example) with some confidence, while a tolerance intervalbounds a population proportion.
Criticisms:
Difficult to use and interpret…..takes some experience
Strengths:
Works well on non-parametric data
Tolerance Interval
Tolerance Intervals for the Normal Distribution
Fill in the following information:
If I measured a sample of 8 items,and got a mean of 97.07
and a standard deviation of 1.5then I can be 99.0% certain
that 90.0% of the populationwill be contained…
within the interval from: 90.84983 to 103.2902 (a Two-sided Tolerance Interval)
below the value: 102.7091 (an Upper One-sided Tolerance Interval)
above the value: 91.43086 (a Lower One-sided Tolerance Interval)
You can ignore the following intermediate quantities used in the calculation:z(1-p): 1.281551z(1-g): 2.326342
a: 0.613438b: 0.965889
k1: 3.759429
z((1-p)/2): 1.644853ChiSq(g,n-1): 1.239032
k2: 4.146782
Reference:NIST/Sematech Handbook, Section 7.2.6.3
Analyses of Variance (ANOVA)
Parametric – populations behave as a Normal Distribution
Non-parametric – population does not behave Normally
Can it be mathematically transformed to behave Normally ?
log, antilog, power transformation
0
0.002
0.004
0.006
0.008
0.01
-500
-375
-250
-125 0
125
250
375
500
Ndist calc
excel t dist
Hypothesis Testing – Probability and Inferential Statistics
Hypothesis:
Ho : The Landfill is contributing pollutants in excess of standards, and background. Ha : The Landfill is not contributing pollutants in excess of standards, and background.
There are two decisions possible:
(1). Accept the null hypothesis (Ho), (2). Reject the null hypothesis (Ho ), equivalent to “accept the alternate hypothesis (Ha)”.
There are two possible situations either the null hypothesis (Ho ) is true, or it is false.
Because of these facts the possible errors are:
Situation
Ho is True Ho is False_Decision
Accept Ho correct Type II error (Beta)
Reject Ho Type I error (alpha) correct
Hypothesis Testing – Probability and Inferential Statistics
The Type I (alpha) error occurs when Ho is true, but we reject it.
This error would occur when the Landfill is contributing pollutants to water above standards and background, but we conclude that it is not. The consequences of the Type I (alpha) error are the most severe. This error would mislead an understanding of the actual impacts to water resources and public health. In addition, the Type I (alpha) error would be the most embarrassing error to the agency.
The Type II (Beta) error occurs when Ho is false, but we accept it.
This error would occur when the Landfill is not contributing pollutants above standards and background, but we conclude that it is. The Type II error (Beta) is less embarrassing to the organization, but carries a large opportunity cost by unnecessarily alarming residents of the area and possibly causing unnecessary remediation activities.
Hard to imagine good and bad from Groundwater Statistics !!!!!!!
Hypothesis Testing – Probability and Inferential Statistics
Ho - The two well populations are not statistically equivalent
Ha - The two well populations are statistically equivalent
90 % Certainty 95 % Certainty 99 % Certainty
Accept Ho Accept Ho Accept Ho
Well Data on Lead
-100
0
100
200
300
400
500
600
700
1 11 21 31 41 51 61 71 81 91 101
111
121
131
141
151
161
171
181
191
201
Lead Concentration (ug/L)
Pro
bab
ility Upgradient Well
Dow ngradient Well
Hypothesis Testing – Probability and Inferential Statistics
Ho - The two well populations are not statistically equivalent
Ha - The two well populations are statistically equivalent
90 % Certainty 95 % Certainty 99 % Certainty
Reject Ho Accept Ho Accept Ho
Well Data on Lead
-100
0
100
200
300
400
500
600
700
1 11 21 31 41 51 61 71 81 91 101
111
121
131
141
151
161
171
181
191
201
Lead Concentration (ug/L)
Pro
bab
ility Upgradient Well
Dow ngradient Well
Hypothesis Testing – Probability and Inferential Statistics
Ho - The two well populations are not statistically equivalent
Ha - The two well populations are statistically equivalent
90 % Certainty 95 % Certainty 99 % Certainty
Reject Ho Reject Ho Accept Ho
Well Data on Lead
-100
0
100
200
300
400
500
600
700
1 12 23 34 45 56 67 78 89 100
111
122
133
144
155
166
177
188
199
Lead Concentration (ug/L)
Pro
bab
ility Upgradient Well
Dow ngradient Well
Hypothesis Testing – Probability and Inferential Statistics
Ho - The two well populations are not statistically equivalent
Ha - The two well populations are statistically equivalent
90 % Certainty 95 % Certainty 99 % Certainty
Reject Ho Reject Ho Reject Ho
Well Data on Lead
-100
0
100
200
300
400
500
600
700
1 11 21 31 41 51 61 71 81 91 101
111
121
131
141
151
161
171
181
191
201
Lead Concentration (ug/L)
Pro
bab
ility Upgradient Well
Dow ngradient Well
Injecting Common Sense into Statistic Evaluations
If determination is that constituent concentration is > Background
- Is it consequential ?
- Is result above GW standard, or tending toward > GW standard ?
- Look over the data, is it cogent?
- Is there a failure, or misrepresentation of the statistical protocol?
- Resample, errors happen and GW variations are the norm.
Uggradient WellMW-1 Metals
Parameter Al Sb As Ba Be B Cd Cr Co CuAction Level: 5 0.006 0.050 2.000 0.004 0.750 0.005 0.100 0.050 1.000
A P P P P A P P A SOne-tail 0.05Two-tail 0.10 Avg 0.000 0.258 0.004 0.106 0.000 0.000 0.000 0.000 0.000 0.008
Std Dev 0.000 0.150 0.010 0.102 0.000 0.000 0.000 0.000 0.000 0.015n-1 = 1 6.31 95% UCL 0.000 0.368 0.011 0.181 0.000 0.000 0.000 0.000 0.000 0.019n-1 = 2 2.92 95% UCL Test Pass FAIL Pass Pass Pass Pass Pass Pass Pass Passn-1 = 3 2.35 n samples taken 7.000 7.000 7.000 7.000 7.000 7.000 7.000 7.000 7.000 7.000n-1 = 4 2.13 "n" needed 0.000 1.322 0.186 0.011 0.000 0.000 0.000 0.000 0.000 0.001n-1 = 5 2.02 "n" Test Pass Pass Pass Pass Pass Pass Pass Pass Pass Passn-1 = 6 1.94 t n-1 used 1.940 1.940 1.940 1.940 1.940 1.940 1.940 1.940 1.940 1.940
Above Std PASS FAIL PASS PASS PASS PASS PASS PASS PASS PASS
MW-2Metals
Parameter Al Sb As Ba Be B Cd Cr Co CuAction Level: 5.000 0.006 0.050 2.000 0.004 0.750 0.005 0.100 0.050 1.000
A P P P P A P P A SOne-tail 0.05Two-tail 0.10 Avg 0.000 0.281 0.073 2.636 0.007 0.000 0.000 0.143 0.068 0.102
Std Dev 0.000 0.224 0.104 2.024 0.009 0.000 0.000 0.136 0.070 0.096n-1 = 1 6.31 95% UCL 0.000 0.466 0.150 4.120 0.013 0.000 0.000 0.243 0.120 0.172n-1 = 2 2.92 95% UCL Test Pass FAIL FAIL FAIL FAIL Pass Pass FAIL FAIL Passn-1 = 3 2.35 n samples taken 7.000 6.000 7.000 7.000 7.000 7.000 7.000 7.000 7.000 7.000n-1 = 4 2.13 "n" needed 0.000 2.694 74.997 38.148 41.488 0.000 0.000 38.042 57.619 0.043n-1 = 5 2.02 "n" Test Pass Pass FAIL FAIL FAIL Pass Pass FAIL FAIL Passn-1 = 6 1.94 t n-1 used 1.940 2.020 1.940 1.940 1.940 1.940 1.940 1.940 1.940 1.940
Above Std Pass FAIL FAIL FAIL FAIL Pass Pass FAIL FAIL PassF* #DIV/0! 2.234 102.987 396.614 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! 43.022
F table value 4.280 6.390 4.280 4.280 4.280 4.280 4.280 4.280 4.280 4.280F 95% Equiv Variance #DIV/0! Yes No No #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! No9.280 t pooled #DIV/0! -1.505 -6.042 14.058 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! -6.2666.390 tpooled table 1.800 1.800 1.800 1.800 1.800 1.800 1.800 1.800 1.800 1.8005.050 Statisticallydifferent? #DIV/0! No No Yes #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! No4.280 Unequiv Variance #DIV/0! No Yes Yes #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! Yes
t se/sd #DIV/0! -2.126 -0.025 2.497 0.007 #DIV/0! #DIV/0! 0.143 0.068 -0.121Statisticallydifferent? #DIV/0! No No Yes No #DIV/0! #DIV/0! No No No
Downgradient Well 1Element Std (mg/L) Std Type P or F Upgradient Variance = Upgrad Statistically differ from Upgrad
Al 5.000 A PassSb 0.006 P PassAs 0.050 P PassBa 2.000 P PassBe 0.004 P PassB 0.750 A PassCd 0.005 P PassCr 0.100 P PassCo 0.050 A PassCu 1.000 S PassFe 0.300 S FAIL FAIL Yes NoPb 0.050 P PassMn 0.050 S FAIL FAIL Yes NoNi 0.200 P PassSe 0.050 P PassAg 0.050 P PassTi 0.002 P PassV 0.100 A PassZn 2.000 A PassLi 2.500 A PassHg 0.002 P Pass