United States
Environmental Protection
# % Agency
GROUNDWATER STATISTICS TOOL
USER'S GUIDE
U.S. ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF SOLID WASTE AND EMERGENCY RESPONSE
OFFICE OF SUPERFUND REMEDIATION AND TECHNOLOGY INNOVATION
WASHINGTON, D.C. 20460
September 2014
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Groundwater Statistics Tool User's Guide
TABLE OF CONTENTS
Section Page
1.0 BACKGROUND/PURPOSE 1
1.1 Remediation Monitoring Phase 1
1.2 Attainment Monitoring Phase 2
2.0 OVERVIEW OF THE GROUNDWATER STATISTICS TOOL 4
2.1 Outlier Testing 4
2.2 Normality Testing 4
2.3 Calculations of the Mean, Linear Trend and Upper Confidence Band 4
2.4 Data Sets with No Detected Values 5
3.0 STEP-BY-STEP INSTRUCTIONS FOR USING THE GROUNDWATER STATISTICS
TOOL 6
4.0 EXAMPLES 13
5.0 REFERENCES 16
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Groundwater Statistics Tool User's Guide
TABLES
Table Page
1 Methods for Calculating UCLs on the Mean by Data Set Type 5
2 Methods for Calculating Linear Trends and Confidence Bands by Data Set Type 5
FIGURES
Figure Page
1 Data Input Screen for Trichloroethene Remediation Example 1, All Eight Data Points
Used 17
2 Normality Screen for Trichloroethene Remediation Example 1, All Eight Data Points
Used 18
3 Data Input Screen for Trichloroethene Remediation Example 1, Final Four Data Points
Used 19
4 Outlier Screen for Trichloroethene Remediation Example 1, Final Four Points Used 20
5 Normality Screen for Trichloroethene Remediation Example 1, Final Four Points Used 21
6 Trend Screen for Trichloroethene Remediation Example 1, Final Four Points Used 22
7 UCL Screen for Trichloroethene Remediation Example 1, Final Four Points Used 23
8 Data Input Screen for Trichloroethene Attainment Example 2, First Eight Data Points
Used 24
9 UCL Screen for Trichloroethene Attainment Example 2, First Eight Data Points Used ..25
10 Data Input Screen for Trichloroethene Attainment Example 2,
All Ten Data Points Used 26
11 UCL Screen for Trichloroethene Attainment Example 2, All Ten Data Points Used 27
12 Data Input Screen for Vinyl Chloride Remediation Example 3 28
13 UCL Screen for Vinyl Chloride Remediation Example 3 29
14 Data Input Screen for Vinyl Chloride Attainment Example 4 30
15 UCL Screen for Vinyl Chloride Attainment Example 4 31
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Groundwater Statistics Tool User's Guide
1.0 BACKGROUND/PURPOSE
The Groundwater Statistics Tool is designed to help evaluate contaminant of concern (COC)
concentrations on a well-by-well basis to determine whether a groundwater restoration remedial
action is complete. The tool is designed to support the U.S. Environmental Protection Agency
(EPA) memorandum, "Guidance for Evaluating Completion of Groundwater Restoration
Remedial Actions" (EPA 2013b, referred to as the Groundwater Restoration Completion
Guidance), and comports with principles outlined in the "Recommended Approach for
Evaluating Completion of Groundwater Restoration Remedial Actions at a Groundwater
Monitoring Well" (EPA 2014, referred to as the Recommended Approach). Both of these
guidance documents should be reviewed before using the tool.
The tool is a Microsoft Excel workbook that is intended to evaluate data for a single COC at a
single well. Each Excel worksheet ("screen") is protected to prevent accidental overwriting of
formulas. The tool was developed in Excel 2010; using an older version of Excel or a version
using personal computer (PC) emulation in a non-PC environment may not allow use of all of
the tool's capabilities. The tool should generally be run separately for each well and each COC
being evaluated.
There are two phases of the groundwater restoration process that the tool is designed to
evaluate: the remediation monitoring phase, and attainment monitoring phase.
1.1 Remediation Monitoring Phase
The following text from the Recommended Approach discusses the remediation monitoring
phase:
"As discussed in the Groundwater Restoration Completion Guidance, the remediation
monitoring phase refers to the phase of the remedy where either active or passive remedial
activities are being implemented to reach groundwater cleanup levels selected in a decision
document. During this phase, groundwater sampling and monitoring data typically are
collected to evaluate contaminant migration and changes in COC concentrations over time.
The completion of this phase typically provides stakeholders a decision point for starting
data collection and evaluation of the attainment monitoring phase. If an active treatment
system is being employed at the site, the completion of this phase may also provide
stakeholders with an opportunity to evaluate terminating the system, as appropriate, in the
vicinity of the well or wells where groundwater restoration completion is being evaluated. If
passive systems are being employed at the site, the data used to make the remediation
phase completion conclusion may also be useful as part of the attainment phase evaluation
since active systems are not being employed.
The remediation phase at a monitoring well typically is completed when the data collected
and evaluated demonstrate that the groundwater has reached the cleanup levels for all
COCs set forth in the record of decision (ROD). It is important to note that at any time during
the groundwater remediation, conclusions may be made to remove certain COCs from the
monitoring program based on their COC-specific trends or presence in the well. If certain
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COCs are no longer being evaluated in a well, the rationale for discontinuing monitoring may
be used, in conjunction with the current well data, to make the conclusion that all COCs
have reached their cleanup levels."
The user should note the following considerations regarding data requirements for each well
and COC:
• EPA guidance (2014) recommends a minimum of four data points to evaluate
completion of this phase. In addition, the tool requires a minimum of four detected
results to complete statistical calculations because upper confidence limit (UCL) and
trend calculations require at least four detected results to be reliable.
• EPA guidance (2014) provides the user with an option to use a trend test or a mean test
on the remediation monitoring phase data set. In this situation, the selection of the best
statistical tool is based on the user and best professional judgment.
o Trend test: The time-dependent trend line is calculated for this test. It is
recommended that the trend test generally be used for a data set that has a
protracted steep change in concentration over time with data points that cross
below the cleanup level. A less steep change (or asymptotic condition) may not
lend itself to a trend test. Once the trend is calculated, an upper confidence band
on the trend line should be calculated to allow the user to account for variability
within the data set. The use of the upper confidence band on the trend line
accounts for uncertainty and provides confidence that the COC cleanup level has
been achieved. In general, a 95 percent confidence level is recommended for
calculating the upper confidence band.
o Mean test: It is recommended that the mean test generally be used for the data
set that does not have a steep change in concentration over time. A steep
change would provide high variability in the data set and would tend to elevate
the UCL on the mean. Statistics are used to determine the mean contaminant
concentration from these data for the COC for this test. The UCL is calculated
once the mean is established. The UCL should be compared against the cleanup
level. The use of the UCL value accounts for uncertainty and provides confidence
that the COC cleanup level has been achieved. In general, the 95 percent UCL is
used as the recommended confidence limit.
1.2 Attainment Monitoring Phase
The following text from the Recommended Approach discusses the attainment monitoring
phase:
"The attainment monitoring phase typically occurs after a Region makes a determination
that the remediation monitoring phase is complete. When the attainment monitoring phase
begins, data typically are collected to first evaluate whether the well has reached steady-
state conditions where active remediation activities, if employed, are no longer influencing
the groundwater in the well. Once the groundwater is observed to have reached steady-
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state conditions, data should be collected and evaluated to confirm the attainment
monitoring phase has been completed."
The attainment monitoring phase at a monitoring well typically is complete when contaminant-
specific data provide a technical and scientific basis that:
(1) The contaminant cleanup level for each COC has been achieved; and
(2) The groundwater will continue to meet the contaminant cleanup level for each COC in
the future.
The user should note the following considerations regarding data requirements:
• EPA guidance (2014) recommends a minimum of eight data points generally be used to
evaluate completion of this phase. However, the tool requires a minimum of four data
points to run the attainment monitoring phase calculations to accommodate site-specific
cases. In addition, the tool requires a minimum of four detected results to complete
statistical calculations because UCL and trend calculations require at least four detected
results to be reliable.
• EPA guidance (2014) recommends evaluating data to determine whether steady-state
conditions have been reached for a COC in a well. If steady-state conditions have been
reached, it may be appropriate to include some of the remediation monitoring phase
data points in the data set used to evaluate the attainment monitoring phase.
• EPA guidance (2014) recommends evaluating the attainment monitoring phase by
applying both the UCL on the mean and the trend test.
o UCL on the mean: Statistics are used for this test to determine the mean
contaminant concentration from the data for the COC. The UCL is calculated
once the mean is established. The UCL should be compared with the cleanup
level. Using the UCL value accounts for uncertainty and provides confidence that
the COC cleanup level has been achieved. In general, the 95 percent UCL is
used as the recommended confidence limit.
o Trend: Statistics are used to determine the time-dependent trend line for this test.
The slope of the trend line is used to make a conclusion on future groundwater
conditions. If the trend line has a statistically significant zero or negative slope
(indicating steady-state conditions or decreasing concentrations), it may be
appropriate to conclude that the contaminant concentrations for each COC in
groundwater will remain at or below the cleanup level.
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2.0 OVERVIEW OF THE GROUNDWATER STATISTICS TOOL
The tool is designed to provide a statistical evaluation of a data set to determine that the
expectations outlined in EPA guidance (2013b and 2014) and outlined above in this User's
Guide have been achieved. In addition to providing statistical mean, trend, and UCL
calculations, the tool also tests for detection frequency, outliers, and normality. These tests are
described in the following sub-sections. Most of the statistical tests used in the tool are based
on the "Unified Guidance for Statistical Analysis of Groundwater Monitoring Data at RCRA
Facilities," which will be referred to as the Unified Guidance (EPA 2009).
2.1 Outlier Testing
Outliers are checked with a Dixon's test, which is appropriate for data sets composed of fewer
than 25 samples. For more details on outliers and the mechanics of the Dixon's test, see
Section 12.3 of the Unified Guidance (EPA 2009). A confidence level of 1 percent is
recommended for the Dixon's test and is established as the default in cell A19 of the Data Input
screen. However, alternative confidence levels for the test can be specified (10 percent, 5
percent, or 0.5 percent). Dixon's test is used only to indicate whether a data point can be
considered as an outlier statistically; outliers should not be discarded from the data set unless
there is also a valid, known technical reason for the outlier.
2.2 Normality Testing
The normality of the data set is checked using a Shapiro-Wilk test. For details on normality and
the mechanics of the Shapiro-Wilk test, see Section 10.5 of the Unified Guidance (EPA 2009).
Different levels of confidence are used based on the size of the data set (n=number of samples
in data set):
• n < 10 - use a confidence level of 10 percent
• 10 < n < 20 - use a confidence level of 5 percent
• n > 20 - use a confidence level of 1 percent
2.3 Calculations of the Mean, Linear Trend and Upper Confidence Band
A confidence level of 95 percent is recommended for the mean calculations and represents the
common practice for calculating the UCL on the mean. As shown in Table 1, the UCL on the
mean is calculated in different ways, depending on the characteristics of the data set.
A confidence level of 95 percent is recommended to calculate confidence around a trend line
and represents the common practice for this calculation. The linear trend and upper confidence
band are calculated in different ways, depending on the characteristics of the data set, as
shown in Table 2.
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Table 1. Methods for Calculating UCLs on the Mean by Data Set Type
Detection Frequency
Type of Data Set (Based on Shapiro-Wilk Test of Data)
Normal
Nonparametric
DF = 100%
Student's-t UCL
Chebyshev UCL
0% < DF < 100%
KM Chebyshev UCL
KM Chebyshev UCL
0%
No UCL is calculated
No UCL is calculated
Notes:
KM Kaplan-Meier
DF Detection frequency
UCL Upper confidence limit
Table 2. Methods for Calculating Linear Trends and Confidence Bands by Data Set Type
Detection Frequency
Type of Data Set (Based on Shapiro-Wilk Test on Residuals)
Linear
Nonlinear
DF = 100%
Linear Regression
Theil-Sen line, Mann-Kendall test
0% < DF < 100%
Linear Regression*
Theil-Sen line, Mann-Kendall test
0%
No trend is calculated
No trend is calculated
Notes:
* Before the linear regression is calculated, each nondetect result is substituted with a randomly generated real
number between zero and the reported detection limit. This substitution prevents the introduction of artificially
low variability from multiple identical (or similar) detection limits.
DF Detection frequency
2.4 Data Sets with No Detected Values
As noted in Tables 1 and 2, the tool will not calculate a UCL on the mean, a trend line, or an
upper confidence band if none of the concentrations are above the detection limit. In this
situation, the project team can generally conclude that the phase being evaluated is complete
by visual, or a non-statistical, evaluation if the detection limits for non-detects in the data set are
below the contaminant cleanup level.
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3.0 STEP-BY-STEP INSTRUCTIONS FOR USING THE GROUNDWATER STATISTICS
TOOL
This tool takes the user through one data input and four results screens. Each screen is
protected to prevent accidental overwriting of formulas. These screens are:
1. The "Datajnput" screen.
2. The "Outliers" screen.
3. The "Normality" screen.
4. The "Trend" screen.
5. The "UCL" screen.
In addition to the data input and results screens, the tool provides a screen titled "Example
Data." This screen provides several synthesized data sets that illustrate various functions of the
tool. These example data sets are discussed in the Examples section. Example data sets 5
through 9 can document the tool's performance compared with example results calculated in the
Unified Guidance.
Step 1: On the "Datajnput" screen, enter descriptive data into cells B4 to B21, D7 to F26, and
I24 to L24. Descriptive data capture information to describe the site, the monitoring phase being
evaluated, the COC, and related information that describe the site and purpose of the
evaluation. The cells for entering descriptive data are color-coded green; cells in blue are locked
and show outputs that the user cannot alter. Control buttons are located in cells that are color-
coded red; use these control buttons to move forward and backward through the tool. Follow the
instructions below for data entry:
a. Enter the name of the site in cell B4. No restrictions.
b. Enter the operating unit (OU) in cell B5 (if applicable). No restrictions.
c. Select the type of evaluation in cell B6. This value should be either "Remediation" or
"Attainment," and there is a drop-down menu to aid in the selection.
d. Enter the date of the evaluation in cell B7. There are no restrictions on how the date is
entered. Examples include: March 1, 2014, 3/1/2014, 3/1/14, March 2014.
e. Enter the name of the person performing the evaluation in cell B8. No restrictions.
f. Enter the COC in cell B10. No restrictions.
g. Enter the well name or number in cell B11. No restrictions.
h. Enter the units for date in cell B12. This value should be "Day," "Month," "Year," or
"Date," and there is a drop-down menu to aid in the selection. The entries are expected
to be dates, or may be days, months, or years from a starting value (which may be zero).
If cell B12 is set to some value other than "Date" when dates have already been entered
into the data entry table in column D, the values will be displayed as large integer values
because of the way Excel handles dates.
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i. Enter the units for concentration in cell B13. No restrictions. These units should be the
same as the units for the cleanup level in cell B16.
j. Enter the confidence level desired in cell B15 using the drop-down menu to aid in the
selection. The default is the recommended confidence level of 95 percent.
k. Enter the cleanup level for the COC in cell B16. This value should be a positive real
number and should be extracted from the remedy decision document.
I. Enter the type of cleanup level being compared in cell B17/B18 (for example, Maximum
Contaminant Level [MCL] or risk-based concentration). No restrictions. The type of
cleanup level should be extracted from the remedy decision document.
m. Enter the risk of false outlier rejection in cell B19. This value should be "0.5%," "1%,"
"5%," or "10%," and there is a drop-down menu to aid in the selection. The default is 1
percent. Selecting a higher value increases the likelihood that a data point may be
falsely flagged as a potential outlier; selecting a lower value decreases this likelihood.
n. Random Seed: Cell B20 is a placeholder for a random seed. The random seed is used
to calculate imputed values for non-detect data points. The random seed is also used to
calculate the time-dependent upper confidence band for nonparametric data sets using a
bootstrap procedure. In general, the user should leave this value blank when the data
are initially entered. If non-detects are present in the data set or if it is determined that
the data set in nonparametric, the tool will automatically generate a random seed. Since
the random seed is generated off an internal clock, the value (assuming nothing is
entered during data entry) will be different each time the tool is run. After a data set
analysis is conducted, the user should document the random seed value. Documenting
this value will allow the results to be replicated. If you desire to replicate results, you may
enter this random seed value (a positive real number) in cell B20 for subsequent data
calculations.
o. Enter the number of significant figures to use for reporting UCLs and predicted
concentrations in cell B21. This value should be a positive whole number greater than
zero. The tool restricts the number of significant figures to be between 1 and 3, since
analytical precision is not expected to exceed three significant figures. The default value
is 2. A drop-down menu is provided to assist with the selection.
p. Time and concentration data may be entered manually into the data entry table in cells
D7 to F26 using the keyboard; however, the preferred method is to enter data by
copying and pasting from another Excel spreadsheet (as long as the organization is the
same and only the three columns, D through F, are pasted into the data entry table) to
reduce input error. Excel's "paste values" method can be used to avoid overwriting the
formatting of the cells.
The tool's data entry table is set up for a maximum of 20 data points. If more than 20
data points are available, it is recommended that only the most recent 20 be used. If the
user wants to conduct a trend analysis of more than 20 data points, other software tools
such as ProUCL (EPA 2013a) or MAROS (AFCEE 2006) can be used.
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1. Enter the measurement dates in column D between rows 7 to 26. These dates
are expected to be actual dates, or may be days, months, or years from a
starting value (which may be zero). A few notes regarding the data set:
i. The type of date input (day, month, or actual date) should be consistent
throughout the data set. This allows for accurate trend analysis.
ii. All data should be entered in increasing chronological order (oldest to
newest).
iii. If duplicate data are available for a specific date, only one data entry for
that date should be made.
2. Enter the measured concentrations in column E between rows 7 and 26. These
values are restricted to real numbers greater than zero.
i. If the date corresponds to a duplicate sampling event, it is recommended
that the user enter either the maximum concentration or the average
concentration in the concentration field, as agreed by the project team.
ii. If the measurement is categorized as a non-detect, it is recommended
that the user enter the reporting limit for the analytical method. The user
should NOT enter zero or an arbitrary number.
3. Enter the data qualifier in column F between rows 7 and 26. Use either "U" or
"ND" for undetected or nondetected results. Based on the qualifier, column G will
be populated with a "yes" or "no" to indicate whether the concentration is a
detected result (for a "yes") or a detection limit for a nondetected result (for a
"no"). Blank cells are allowed, and qualifiers do not need to be entered if they are
not applicable.
q. In cells I24 to L24, enter the minimum and maximum values for the date and
concentration axes of plots shown on the various reports. The default selection is "Auto,"
which will use Excel's automatic setting for the charts. Adjusting these values can make
the data plots easier to view.
Step 2: Review the Data Review and Recommendations section at the bottom of the
"Datajnput" screen. If no recommendations appear in red text, the data are ready for statistical
analysis. If recommendations appear in red text, the user should follow the recommendations
before proceeding with the statistical analysis. Although the statistical analysis can be run
without addressing the recommendations, error messages will result.
Step 3: Click the button labeled "Next Step: Check for Outliers." The tool will run Dixon tests to
check for outliers and will display the results of the tests on the "Outliers" screen.
a. Rows 5 and 6 show the number of data points and the selected risk of false rejection,
both of which were previously entered on the "Datajnput" screen.
b. Row 7 shows the critical value used for the Dixon's test, which is based on the number
of data points and the selected risk of false rejection.
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c. Row 8 shows the outlier type being tested. Both low concentration (column B) and high
concentration (column C) outliers are tested.
d. Row 9 shows the test statistic. For details on how the test statistic is calculated, refer to
Section 12.3 of the Unified Guidance (EPA 2009). The test statistic is compared with the
critical value to determine whether the lowest concentration data point is a potential low
outlier or the highest concentration data point is a potential high outlier.
e. Row 10 shows the result of the test. "Yes" is displayed if a potential outlier is indicated;
otherwise "No" is displayed.
f. Row 11 uses the results of the normality testing (which will be shown on the next screen)
to indicate whether the Dixon's test is valid. Since Dixon's test requires that the data are
normally distributed, the test is not valid and should not be used to justify an outlier when
the data are not normally distributed. Nonparametric outlier tests may be used, but these
tests are not included in this tool.
g. If row 10 of the "Outliers" screen indicates no potential outliers, the user may proceed by
clicking the button labeled "Next Step: Normality Screen."
h. If row 10 of the "Outliers" screen indicates that potential outliers are present in the data
set and row 11 indicates that the Dixon's test is valid for that potential outlier, the user
may want to consider revising the data set to remove the outlier. Outliers should be
removed only if a valid technical reason for the outlier is known and the project team or
user concludes an acceptable reason exists to remove the outlier. There are two options
for proceeding in the presence of an outlier:
i. Elect to remove the outlier. The outlier can be removed from the data set in one
of two ways: 1) click the button labeled "Previous Step: Data Input Screen" to
return to the "Data Input" screen or 2) click the button labeled "Next Step:
Normality Screen", where a pop up box will be displayed. To get back to the
"Data Input" screen, a "N" should be entered in the prompt.
Upon returning to the "Data Input" screen to remove the outlier(s) from the data
set, the user should first delete the "date" (column D) and "concentration"
(column E) values for the outlier(s). The user should then "Copy" the date and
concentration values for all data that was collected chronologically after the
outlier(s). The user should then paste the copied cells into the table starting in
the row where the original outlier(s) was deleted. The user should then delete the
data in the final row(s) to ensure there is no duplicative data in the set (however,
the entire row should not be deleted).
Note: When modifying the data set, do not use the "Cut" function.
ii. Retain full data set. If the user elects to retain the outlier(s) and move forward
with the statistical analysis, the user should click the button labeled "Next Step:
Normality Screen" and enter "Y" into the prompt field.
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Step 4: The tool will run three Shapiro-Wilk tests on the data set to determine whether the data
and the residuals appear to be normally distributed. The three test results are shown on the
"Normality" screen. The first column is for the full data set and is used to determine which UCL
calculation method (normal or nonparametric) should be used. The second column is for the
data set minus the potential outliers and is used only to determine whether the Dixon test is
valid. Dixon's test is not considered valid if the data set minus the potential outliers does not
appear to be normal. If no outliers exist, the column for the data set minus potential outliers will
not be populated with results. The third column is for the residuals and is used to test whether
parametric or non-parametric methods are used for fitting the trend. The following results are
shown for each test:
a. Rows 7 and 8 show the number of data points and the selected alpha values for the
Shapiro-Wilk test. The number of data points was previously calculated in cell B23 on
the "Datajnput" screen. The alpha value for the Shapiro-Wilk test is equal to 100
percent minus the confidence level previously entered in cell B15 on the "Datajnput"
screen.
b. Rows 9, 10 and 11 show the slopes, intercepts and correlation coefficients (R) of the
normal Q-Q plot. These are shown for informational purposes only.
c. Row 12 shows the exact Shapiro-Wilk test values. For more detail on how the test value
is calculated, see Section 10.5 of the Unified Guidance (EPA 2009).
d. Row 13 shows the critical values for each test, which is based on the number of data
points and the Shapiro-Wilk alpha values. For more detail on how the critical value is
determined, see Section 10.5 of the Unified Guidance (EPA 2009).
e. Row 14 shows the result of the tests. If the exact test value is lower than the critical
value, the conclusion of the test is that the data (or the residuals, for the third column) do
not appear normal. If the exact test value is equal to or greater than the critical value, the
conclusion of the test is that the data (or the residuals, for the third column) appear
normal.
The user may now proceed to either the "Trend" screen, the "UCL" screen or return to the
"Outliers" screen by using the buttons at the bottom of the screen.
An error message will appear if the trend predicts negative concentrations during the time
period of the measurements entered into the tool. In this case, the message will inform the user
that the data set cannot be evaluated by the tool. This situation can occur when there is a steep
trend in the data that ends (or starts) near a concentration of zero. This situation is not expected
to occur commonly; if it does occur, there are two ways to correct the situation.
1. Data points can be removed from the data set. Often, a case may be observed where a
group of data points within the data set has a steeply decreasing trend and these data
points are followed by a group of data points with a less steep trend, In this case, the
early points where the concentration is decreasing rapidly should be removed, while the
number of data points recommended for the decision (as described in Section 1) is
maintained. Data points at the end of the data set should not be removed.
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2. Normalizing transformations of the data may be attempted to account for the change in
slope. This tool (or another tool such as ProUCL [EPA 2013a]) may still be used for
trend testing, but the data must be transformed outside the tool and imported into the
tool. For example, the logarithms of the concentration can be calculated and imported
into the tool to perform a logarithmic transformation. The user may want to consult a
statistician for assistance with this process. In this situation, the UCL must be calculated
on the untransformed data; only the trend should be calculated using the transformed
data. For more details on other transformations that can be attempted with the data, see
Section 3.2.4 of the Unified Guidance (EPA 2009).
Step 5: Inspect the results on the "Trend" screen.
• If the trend is found to be linear, the trend will be evaluated using the ordinary least
squares method. The following outputs will be shown:
o The data set will be shown in columns B and C of the table. The predicted
concentrations from the ordinary least squares method, the residuals (difference
between the measured and predicted concentrations), and the calculated values
of the 95 upper confidence band for each data point will also be shown in
columns D, E, and F of the table.
o The slope, intercept and R-squared values of the linear regression trend line will
be shown in cells 17, 18, and 19.
o The test statistic will be shown in cell 111. For details on calculation of the test
statistic, see Section 17.3.1 of the Unified Guidance (EPA 2009).
o The critical value of the test will be shown in cell 112. The critical value is based
on the number of data points and the confidence level selected on the "Data
Input" screen, and will have the same sign as the slope.
o The test result will be shown in cell 110. If the critical value is positive and the test
statistic is greater than the critical value, the conclusion is that the trend is
increasing; otherwise, the conclusion is that there is no trend. If the critical value
is negative and the test statistic is lower than the critical value, the conclusion is
that the trend is decreasing; otherwise, the conclusion is that there is no trend.
o If the trend is increasing, the date at which the concentration is predicted to
exceed the cleanup level is shown in cell 113. If the trend is not increasing, the
message "Not applicable - slope is not statistically increasing" will be displayed.
• If the trend is not found to be linear, the trend will be evaluated using the Mann-Kendal
test using a Theil-Sen slope. The following outputs will be shown:
o The data set will be shown in columns B and C of the table. The predicted
concentrations from the ordinary least squares method, the residuals (difference
between the measured and predicted concentrations), and the calculated values
of the upper confidence band for each data point will also be shown in columns
D, E, and F of the table.
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o The critical value of the test will be shown in cell 112. The critical value is based
on the number of data points and the confidence level selected on the "Data
Input" screen and will have the same sign as the slope.
o The test statistic and normalized S value will be shown in cells 18 and 19. For
details on the calculation of these values, see Section 17.3.2 of the Unified
Guidance (EPA 2009).
o The slope and intercept of the Theil-Sen trend line will be shown in cells L7 and
L8.
o If the trend is increasing, the date at which the concentration is predicted to
exceed the cleanup level is shown in cell L9. If the trend is not increasing, the
message "Not applicable - slope is not statistically increasing" will be displayed.
• The trend line is displayed on a plot. The confidence band on the trend will also be
displayed.
The user may now proceed to the "UCL" screen.
Step 6: Inspect the results on the "UCL" screen. The screen shows the calculated UCL, the
value of the upper confidence band at the final sampling event, and the result of the trend
calculations. It also includes a summary of the data entered on the "Datajnput" screen and
shows the appropriate trend information. If nondetects are present, the tool displays a table that
summarizes the data and the imputed values assigned by the tool.
12
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Groundwater Statistics Tool User's Guide
4.0 EXAMPLES
As noted earlier, several example data sets are provided on the "Example Data" screen. Each
data set is discussed briefly in the sections below. The last eight examples are not meant
specifically to test the remediation and attainment decisions, although a decision will be shown
on the "UCL" screens based on the settings for the decision type, cleanup level, and confidence
levels. For Examples 5 through 9 from (), the corresponding results in the Unified Guidance
(EPA 2009) may differ slightly from the results calculated by the tool because of differences in
rounding. Figures at the end of this guide show screenshots for Examples 1 through 4.
• Example Data Set 1. This data set is for trichloroethene and consists of eight data
points. These data are for the remediation monitoring phase at a 95 percent confidence
level. There are two sub-examples here:
o If all eight points are used, the data set is not normally distributed and the
residuals are not normally distributed; therefore, the 95 percent UCL and trends
will be calculated using nonparametric methods. The 95 percent upper
confidence band at the final sampling event is found to be below the cleanup
level (MCL of 5 parts per billion [ppb]), but the fit to the data results in predictions
of negative concentrations, and an error message is generated when the user
clicks the "Next Step: Trend Screen" on the "Normality" screen. Screen shots of
the "Datajnput" and "Normality" screens for this case are shown in Figures 1
and 2.
o If only the last four data points are used, where the data are closer to the MCL
and more linear, the 95 percent upper confidence band at the final sampling
event will be below the MCL, and no negative concentrations are predicted.
Although the overall 95 percent UCL of the data set is above the MCL, only one
criterion must be met to proceed to attainment. Screen shots of the "Data,"
Outlier," "Normality," "Trend," and "UCL" screens for this case are shown in
Figures 3 through 7.
• Example Data Set 2. This data set is a continuation of the previous data set for
trichloroethene and consists of 10 data points for the attainment monitoring phase.
Again, there are two sub-examples here:
o If only the first eight points are used, the data set is found to have a statistically
significant decreasing trend, but the calculated 95 percent UCL is not below the
MCL. Screen shots of the "Data" and "UCL" screens for this case are shown in
Figures 8 and 9.
o If all 10 data points are used, the data set is found to satisfy both attainment
criteria identified in Section 1.2; the trend is statistically significant and
decreasing, and the 95 percent UCL is below the MCL. In fact, this scenario is
also the case after nine sampling events. Screen shots of the "Data" and "UCL"
screens for this case are shown in Figures 10 and 11.
13
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Groundwater Statistics Tool User's Guide
• Example Data Set 3. This data set is for vinyl chloride at the same hypothetical site as
for examples 1 and 2 and is for the remediation monitoring phase. The concentration is
observed to be increasing toward the MCL and there is a slight elevated result at the
seventh event. Although the upper confidence band exceeds the MCL of 2 ppb, the 95
percent UCL does not. Only one criterion must be met to proceed to attainment, so the
remediation monitoring phase is considered complete. Screen shots of the "Data" and
"UCL" screens for this case are shown in Figures 12 and 13.
• Example Data Set 4. This data set is a continuation of the previous data set for vinyl
chloride and consists of 10 data points for the attainment monitoring phase. The first two
data points are the last two from the remediation monitoring phase, which is consistent
with the "Recommended Approach" (EPA 2014). Although all 10 points could be used,
both the UCL and slope criteria for the attainment monitoring phase are met if only the
first eight are used. Screen shots of the "Data" and "UCL" screens for this case are
shown in Figures 14 and 15.
• Example Data Set 5. This data set is Example 12-3 from Section 12.3 of the Unified
Guidance (EPA 2009). The data are the logged concentrations from the example. There
are 20 data points, and the 20th data point is an outlier at the 95 percent confidence
level. Additional calculations can be examined for this example, but it is intended to
illustrate the tool's use in checking the outlier calculations.
• Example Data Set 6. This data set is modified from the previous data set by subtracting
each concentration from 10 ppb. There are 20 data points, and the 20th data point is an
outlier at the 95 percent confidence level. Additional calculations can be examined for
this example, but it is intended for use in checking the outlier calculations.
• Example Data Set 7. This data set is from Example 10-2 in Section 10.5.1 of the Unified
Guidance (EPA 2009). The data set has 20 data points and is not normal at the 99
percent confidence level. The example can be checked by proceeding to the "Normality"
screen and comparing the test results against the example in the Unified Guidance.
Additional calculations can be examined for this example, but it is intended for use in
checking the normality calculations. If trend or UCL calculations are attempted, this
example will generate an error message because negative concentrations are predicted
for the early data points.
• Example Data Set 8. This data set is from Example 17-5 in Section 17.3.1 of the Unified
Guidance (EPA 2009). The data set has 19 data points with normal residuals. It can be
used to illustrate the linear regression and compare it against the results for the example
in the Unified Guidance. The trend is shown to be statistically increasing at the 99
percent confidence level in the example.
• Example Data Set 9. This data set is from Example 21-7 in Section 21.3.1 of the Unified
Guidance (EPA 2009). The data set has 10 data points, with normal residuals. It can be
used to illustrate both the linear regression and the upper confidence band calculations
and compare them against the example. The upper confidence band is calculated at the
95 percent confidence level in the example.
14
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Groundwater Statistics Tool User's Guide
• Example Data Set 10. This data set is the same as example data set 9, described
above, with one change. One additional result is added, a nondetect at a detection limit
of 2 ppb. This data set can be used to illustrate UCLs calculated based on the
nonparametric Kaplan-Meier (KM) Chebyshev UCL. In this example, the residuals are
still normal, so the trend will be calculated using linear regression but using an imputed
value for the nondetect result. If a system-generated random seed predicts negative
concentrations, use a random seed of 62311.421888.
• Example Data Set 11. This data set is the same as example data set 9, described
above, with changes. The last two results are changed to nondetect results with a
detection limit of 15 ppb, and three additional identical results are added. This data set
can be used to illustrate UCLs calculated based on the nonparametric KM Chebyshev
UCL. In this example, the residuals are not normal, so the trend will be calculated using
the Theil-Sen option with a Mann-Kendall test for statistical significance. If a system-
generated random seed predicts negative concentrations, use a random seed of
62311.421888.
• Example Data Set 12. This data set is based on Example 21-8 in Section 21.3.2 of the
Unified Guidance (EPA 2009). The data set has 10 data points, with normal residuals;
the final data point has been altered from the original example so that the trend is not
statistically significant at the 95 percent confidence level; this data set illustrates how the
output will appear if the trend is not found to be statistically significant.
15
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Groundwater Statistics Tool User's Guide
5.0 REFERENCES
Air Force Center for Environmental Excellence (AFCEE). 2006. Monitoring and Remediation
Optimization Systems (MAROS) Software Version 2.2 User Guide. March.
U.S. Environmental Protection Agency (EPA). 2009. Statistical Analysis of Groundwater
Monitoring Data at RCRA Facilities - Unified Guidance. EPA 530/R-09-007. March.
Accessed on line in January 2014 at:
http://www.epa.qov/osw/hazard/correctiveaction/resources/quidance/sitechar/qwstats/
EPA. 2013a. ProUCL Version 5.0.00 Technical Guide, Statistical Software for Environmental
Applications for Data Sets with and without Nondetect Observations. September.
EPA. 2013b. Guidance for Evaluating Completion of Groundwater Restoration Remedial
Actions. OSWER 9355.0-129. From: James E. Woolford, Director, Office of Superfund
Remediation and Technology Innovation; and Reggie Cheatham, Director, Federal
Facilities Restoration and Reuse Office. To: Superfund National Policy Managers,
Regions 1 -10; and Federal Facility Leadership Council. November 25.
EPA. 2014. Recommended Approach for Evaluating Completion of Groundwater Restoration
Remedial Actions at a Groundwater Monitoring Well. OSWER 9283.1-44. Draft.
16
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Groundwater Statistics Tool User's Guide
Figure 1. Data Input Screen for Trichloroethene Remediation Example 1, All Eight Data Points Used
I
Groundwater Statistics Tool
Data input worksheet
Site Name
Operating Unit (OU)
Type of Evaluation
Date of Evaluation
Person performing analysis
Chemical of Concern
Well Name/Number
Date Units
Concentration Units
Confidence Level Desired
Cleanup Level
Source of cleanup level (e.g. MCL
or risk-based concentration)
Risk of False Outlier Rejection
Random Seed (may be left blank)
Significant figures to use
Number of data points
Number of detected results
Number of nondetect results
Detection frequency:
Test
Test
Remediation
6/11/2014
RT
TCE
1
Month
ug/L
95%
MCL
1%
62311 42188
100%
Date (Month)
TCE
Concentration
(ug/L)
Data
Qualifier
Detected?
(Yes or No)
1
93
Yes
2
82
Yes
3
52
Yes
4
19
Yes
5
6.1
Yes
6
4.2
Yes
7
2.8
Yes
8
1.8
Yes
Data Review
Recommendations
Are all necessary data fields entered, and in proper format?
Yes
None
Are at least 4 data points present for statistical analysis?
Yes
None
Are detection limits for nondetects < maximum detected value?
Yes
None
Are all data within chart axis limits?
Yes
None
Pressing the "Check for Outliers" button to the right will open a worksheet that shows the results of a Dixons's test for outliers
| Next Step: Check for Outliers i
17
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Groundwater Statistics Tool User's Guide
Figure 2. Normality Screen for Trichloroethene Remediation Example 1, All Eight Data Points Used
Groundwater Statistics Tool
Normality Testing Worksheet
Normal Q-Q Plot
Trend and UCL calculations cannot be performed because negative
concentrations are predicted by the linear regression. See the User Guide
for discussion of possible solutions.
OK
-5
-10
-15
-20
-25
Quantile
-2
-1
0
Quantile
Previous Step: Outliers Screen
Next Step: Trend Screen
Skip Step: UCL Screen
18
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Groundwater Statistics Tool User's Guide
Figure 3. Data Input Screen for Trichloroethene Remediation Example 1, Final Four Data Points Used
Groundwater Statistics Tool
Data input worksheet
Site Name
Test
Date (Month)
TCE
Concentration
(ug/L)
Data
Qualifier
Detected?
(Yes or No)
Operating Unit (OU)
Test
~ Detected Data
Type of Evaluation
Remediation
Date of Evaluation
6/11/2014
5
6.1
Yes
7
6 -
*53
•2- 4 ¦
e
.2
e 3
I 2"
3
1 "
~
Person performing analysis
RT
6
4.2
Yes
7
2.8
Yes
Chemical of Concern
TCE
8
18
Yes
Well Name/Number
1
~
~
~
Date Units
Month
Concentration Units
uq/L
Confidence Level Desired
95%
Cleanup Level
5
Source of cleanup level (e.g. MCL
or risk-based concentration)
MCL
0
i i
Risk of False Outlier Rejection
1%
4 b a
Month
Random Seed (may be left blank)
62311.42188
Significant figures to use
3
Axis Values
Time
Concentration
Number of data points
4
Min
Max
Min
Max
Number of detected results:
4
4
9
Auto
Auto
Number of nondetect results
0
Reset Concentration Axis
Detection frequency:
100%
Data Review
Recommendations
Are all necessary data fields entered, and in proper format?
Yes
None
Are at least 4 data points present for statistical analysis?
Yes
None
Are detection limits for nondetects < maximum detected value?
Yes
None
Are all data within chart axis limits?
Yes
None
Pressing the "Check for Outliers" button to the right will open a worksheet that shows the results of a Dixons's test for outliers Next Step: Check for Outliers
19
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Groundwater Statistics Tool User's Guide
Figure 4. Outlier Screen for Trichloroethene Remediation Example 1, Final Four Points Used
Groundwater Statistics Tool
Outlier testing worksheet
Dixon's Outlier Test Results
Number of data points
4
Risk of false rejection
1%
Critical value
0.889
Outlier type
Low
High
Test statistic
0.2326
0.4419
Potential Outlier?
No
No
Validity of Dixon'sTest
Valid
Box and Whiskers Plot
7 -
6 "
¦ Values Outside 3 IQR
5
4 "
3 -
• Values Outside 1.5 IQR
~ ValuesWithin 1.5 IQR
Bo* (Interquartile Range) and
Whiskers
~
~
2
1 -
Minimum and Maximum Values
Median Value
Previous Step: Data Input Screen
Next Step: Normality Screen
20
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Groundwater Statistics Tool User's Guide
Figure 5. Normality Screen for Trichloroethene Remediation Example 1, Final Four Points Used
Groundwater Statistics Tool
Normality Testing Worksheet
Normality Test
Results
Parameter
All Data
Minus Outliers
Residuals
Number of data points
4
4
4
Shapiro-Wilk alpha value
10%
N/A
10%
Slope
2.571909632
N/A
0.326533343
Intercept
3.725
N/A
-1.95195E-15
Correlation, R
0989994895
N/A
0 900838346
Exact Test Value
0.975731601
N/A
0768965808
Critical Value
0.792
N/A
0 792
Conclude sample distribution:
Appears normal
N/A
Does not appear normal
Normal Q-Q Plot
.2
E
e
8
c
3
Normal Q-Q Plot, Residuals
0.4
Previous Step: Outliers Screen
Next Step: Trend Screen
Skip Step: UCL Screen
21
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Groundwater Statistics Tool User's Guide
Figure 6. Trend Screen for Trichloroethene Remediation Example 1, Final Four Points Used
Groundwater Statistics Tool
Trend test results for datasets nonparametrically distributed residuals
i
t
(Days)
C(ugfL)
C
Predicted
Residual
Upper Confidence
Band
1
5
G.1
5.G
0.5
G.1
2
G
4.2
4.18
0.02
4.67
3
7
2.8
2.76
0.04
3.23
4
8
18
1.34
0.46
1.8
5
e
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Mann-Kendall
Test Result
Decreasing
Test Statistic (S)
-6
Normalized S
-1.698
Critical Value
1.645
Theil-Sen
Slope
Intercept
When is the
concentration
predicted to
exceed the
cleanup level?
-1.42
12.7
Not
applicable -
slope is not
statistically
increasing
Trend Line
~ Detected Data O Nondetected Data
TheH-Sen Cleanup Level
¦ — Upper Confidence Band
Previous Step: Normality Screen
Next Step: UCL Screen
22
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Groundwater Statistics Tool User's Guide
Figure 7. UCL Screen for Trichloroethene Remediation Example 1, Final Four Points Used
Groundwater Statistics Tool
UCL calculations and summary statistics for data sets that are normally distributed
Site Name
Test
Trend and UCL Lines
Operating Unit (OU)
Test
Type of Evaluation
Remediation
~ Detected Data Theil-Sen
Date of Evaluation
6/11/2014
7
Cleanup Level — - Upper Confidence Band
Person performing analysis
RT
4k
6 -
3 5
1
3
.a
! 3 -
e
8
1 2"
i •
Chemical of Concern
TCE
Well Name/Number
1
\ N.
Date Units
Month
X v
N. \
\ N
\ \
x ^
\
\ X
Concentration Units
ug/L
Confidence Level
95%
Number of results
4
Number < cleanup level
3
Are any potential outliers present?
No
Mean of concentration
3.73
1 1 1 1
Standard deviation of concentration
1 86
Month
t-value for UCL calculation
2.353
95% Upper Confidence Limit (UCL)
5.92
When is the
concentration
predicted to exceed
the MCL?
Not applicable - slope is not
statistically increasing
Method for calculating UCL
Student's t UCL
Value of 95% Upper Confidence Band
value at final samplinq event
1.8
Trend calculation method
Theil-Sen/Mann-Kendall
Message: None.
Cleanup level
5
Source of cleanup level
MCL
Is the trend decreasing or statistically
insiqnificant?
Yes
Restart Data Input Screen Skip Back Two Steps: Normality Screet Previous Step: Trend Screen
23
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Groundwater Statistics Tool User's Guide
Figure 8. Data Input Screen for Trichloroethene Attainment Example 2, First Eight Data Points Used
Groundwater Statistics Tool
Data input worksheet
Site Name
Test
Date (Month)
TCE
Concentration
(ug/L)
Data
Qualifier
Detected?
(Yes or No)
Operating Unit (OU)
Test
~ Detected Data
Type of Evaluation
Attainment
~
Date of Evaluation
6/11/2014
9
4.3
Yes
Concentration (ug/L)
i m nj w 4* ui vi
~
Person performing analysis
RT
10
6.1
Yes
11
4.6
Yes
~
Chemical of Concern
TCE
12
4.5
Yes
Well Name/Number
1
13
5.3
Yes
~ T ~
~
~
~
Date Units
Month
14
3.9
Yes
Concentration Units
uq/L
15
3 3
Yes
16
2.1
Yes
Confidence Level Desired
95%
Cleanup Level
5
Source of cleanup level (e.g. MCL
or risk-based concentration)
MCL
o
i
Risk of False Outlier Rejection
1%
o 13
Month
Random Seed (may be left blank)
62311.42188
Significant figures to use
3
Axis Values
Time
Concentration
Number of data points
8
Min
Max
Min
Max
Number of detected results
8
8
17
Auto
Auto
Number of nondetect results
0
Reset Concentration Axis
Detection frequency:
100%
Data Review
Recommendations
Are all necessary data fields entered and in proper format?
Yes
None
Are at least 4 data points present for statistical analysis?
Yes
None
Are detection limits for nondetects < maximum detected value?
Yes
None
Are ail data within chart axis limits?
Yes
None
Pressing the "Check for Outliers" button to the right will open a worksheet that shows the results of a Dixons's test for outliers. Next Step: Check for Outliers
24
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Groundwater Statistics Tool User's Guide
Figure 9. UCL Screen for Trichloroethene Attainment Example 2, First Eight Data Points Used
Groundwater Statistics Tool
UCL calculations and summary statistics for data sets that are normally distributed
Site Name
Test
Operating Unit (OU)
Test
Type of Evaluation
Attainment
Date of Evaluation
6/11/2014
Person performing analysis
RT
Chemical of Concern
TCE
Well Name/Number
1
Date Units
Month
Concentration Units
ug/L
Confidence Level
95%
Number of results
8
Number < cleanup level
6
Are any potential outliers present?
No
Mean of concentration
4.26
Standard deviation of concentration
1.22
t-value for UCL calculation
1.895
Trend Line
« Detected Data
— Cleanup Level
Ordinary Least Squares
Upper Confidence Band
95% Upper Confidence Limit (UCL)
Method for calculating UCL
Value of 95% Upper Confidence Band
value at final sampling event
Trend calculation method
Cleanup level
Source of cleanup level
Is the trend decreasing or statistically
insignificant?
5.08
Student's t UCL
449
Ordinary Least Squares
MCL
Yes
When is the
concentration
predicted to exceed
the MCL?
Not applicable - slope is not
statistically increasing
Message: None.
Restart: Data Input Screen
Skip Back Two Steps: Normality Screer
Previous Step: Trend Screen
25
-------
Groundwater Statistics Tool User's Guide
Figure 10. Data Input Screen for Trichloroethene Attainment Example 2, All Ten Data Points Used
Groundwater Statistics Tool
Data input worksheet
Site Name
Test
Date (Month)
TCE
Concentration
(ug'L)
Data
Qualifier
Detected?
(Yes or No)
Operating Uriit(OU)
Test
~ Detected Data
Type of Evaluation
Attainment
Date of Evaluation
6/11/2014
9
4.3
Yes
Concentration (ug/L)
) m ro u> ¦*» in a* vj
I I I K 1 8 ©
~
~
Person performing analysis
RT
10
6.1
Yes
11
4.6
Yes
Chemical of Concern
TCE
12
4.5
Yes
~
~
~
~
~
~
~
~
Well Name/Number
1
13
5.3
Yes
Date Units
Month
14
3.9
Yes
Concentration Units
ug/L
15
3.3
Yes
16
2.1
Yes
Confidence Level Desired
95%
17
1.4
Yes
Cleanup Level
5
18
0.85
Yes
Source of cleanup level (e.g. MCL
or risk-based concentration)
MCL
01
¦ *
Risk of False Outlier Reiection
1%
o 13 IS
Month
Random Seed (may be left blank)
62311 42188
Significant figures to use
3
Axis Values
Time
Concentration
Number of data points
10
Min
Max
Min
Max
Number of detected results
10
8
19
Auto
Auto
Number of nondetect results
0
Reset Concentration Axis
Detection frequency
100%
Data Review
Recommendations
Are all necessary data fields entered, and in proper format?
Yes
None
Are at least 4 data points present for statistical analysis?
Yes
None
Are detection limits for nondetects < maximum detected value?
Yes
None
Are all data within chart axis limits?
Yes
None
Pressing the "Check for Outliers" button to the right will open a worksheet that shows the results of a Dixons's test for outliers Next Step: Check for Outliers
26
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Groundwater Statistics Tool User's Guide
Figure 11. UCL Screen for Trichloroethene Attainment Example 2, All Ten Data Points Used
Groundwater Statistics Tool
UCL calculations and summary statistics for data sets that are normally distributed
Site Name
Test
Trend Line
Operating Unit (OU)
Test
Type of Evaluation
Attainment
c/11/9(114
~ Detected Data Ordinary Least Squares
Cleanup Level UDoer Confidence Band
Person performing analysis
RT
8
N
K
%
\ ~
7
6
5 -
I 4
E
c 3 "
8
<3 2
Chemical of Concern
TCE
Well Name/Number
1
Date Units
Month
" -
~
/ /•*
Concentration Units
ug/L
Confidence Level
95%
Number of results
10
Number < cleanup level
8
Are any potential outliers present?
No
Mean of concentration
3 64
0
1 1 1 1
I
Standard deviation of concentration
1.71
8 10 12 14 16 18
Month
t-value for UCL calculation
1.833
95% Upper Confidence Limit (UCL)
4.63
When is the
concentration
predicted to exceed
the MCL?
Not applicable - slope is not
statistically increasing
Method for calculating UCL
Student's t UCL
Value of 95% Upper Confidence Band
value at final samplinq event
2.7
Trend calculation method
Ordinary Least Squares
Message: None.
Cleanup level
5
Source of cleanup level
MCL
Is the trend decreasing or statistically
insiqnincant?
Yes
I Restart: Data Input Screen | Skip Back Two Steps: Normality Screer Previous Step: Trend Screen
27
-------
Groundwater Statistics Tool User's Guide
Figure 12. Data Input Screen for Vinyl Chloride Remediation Example 3
Groundwater Statistics Tool
Data input worksheet
Site Name
Test
Operating Unit (OU)
Test
Type of Evaluation
Remediation
Date of Evaluation
6/11/2014
Person performing analysis
RT
Chemical of Concern
VC
Well Name/Number
1
Date Units
Month
Concentration Units
ug/L
Confidence Level Desired
95%
Cleanup Level
2
Source of cleanup level (e.g. MCL
or risk-based concentration)
MCL
Risk of False Outlier Rejection
1%
Random Seed (may be left blank)
6231142188
Significant figures to use
3
Number of data points:
8
Number of detected results
8
Number of nondetect results
0
Detection frequency:
100%
Date (Month)
VC
Concentration
(ug/L)
Data
Qualifier
Detected?
(Yes or No)
1
0.15
Yes
2
0.21
Yes
3
041
Yes
4
0.82
Yes
5
1.1
Yes
6
1.3
Yes
7
2.1
Yes
8
1.7
Yes
Data Review
Recommendations
Are all necessary data fields entered and in proper format?
Yes
None
Are at least 4 data points present for statistical analysis?
Yes
None
Are detection limits for nondetects < maximum detected value?
Yes
None
Are all data within chart axis limits?
Yes
None
Pressing the "Check for Outliers" button to the right will open a worksheet that shows the results of a Dixons's test for outliers
Next Step: Check for Outliers |
28
-------
Groundwater Statistics Tool User's Guide
Figure 13. UCL Screen for Vinyl Chloride Remediation Example 3
Groundwater Statistics Tool
UCL calculations and summary statistics for data sets that are normally distributed
Site Name
Test
Operating Unit (OU)
Test
Type of Evaluation
Remediation
Date of Evaluation
6/11/2014
Person performing analysis
RT
Chemical of Concern
VC
Well Name/Number
1
Date Units
Month
Concentration Units
ug/L
Confidence Level
95%
Number of results
8
Number < cleanup level
7
Are any potential outliers present?
No
Mean of concentration
0 974
Standard deviation of concentration
0.709
t-value for UCL calculation
1.895
Trend Line
2.5
* Deteaed Data
Cleanup Level
Ordinary Least Squares
Upper Confidence Band
95% Upper Confidence Limit (UCL)
1.45
When is the
concentration
predicted to exceed
the MCL?
8.21
Method for calculating UCL
Student's t UCL
Value of 95% Upper Confidence Band
value at final samplinq event
2 32
Trend calculation method
Ordinary Least Squares
Message: None.
Cleanup level
2
Source of cleanup level
MCL
Is the trend decreasing or statistically
insignificant?
No
Restart Data Input Screen
Skip Back Two Steps: Normality Screei
Previous Step: Trend Screen
29
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Groundwater Statistics Tool User's Guide
Figure 14. Data Input Screen for Vinyl Chloride Attainment Example 4
Groundwater Statistics Tool
Data input worksheet
!
Site Name
Test
Date (Month)
VC
Concentration
(ug/L)
Data
Qualifier
Detected?
(Yes or No)
Data
Operating Unit (OU)
Test
Type of Evaluation
Attainment
Date of Evaluation
6/11/2014
7
2.1
Yes
2.5
2
GT
j? 1.5
s
A
£ i
e
8
3 0.5
~
Person performing analysis
RT
8
1.7
Yes
9
1.8
Yes
~
~
~
~
~
~
~
~
~
Chemical of Concern
VC
10
1.9
Yes
Well Name/Number
1
11
1.8
Yes
Date Units
Month
12
1.7
Yes
Concentration Units
ug/L
13
1.7
Yes
14
16
Yes
Confidence Level Desired
95%
15
16
Yes
Cleanup Level
2
16
1.3
Yes
Source of cleanup level (e.g. MCL
or risk-based concentration)
MCL
0
' 1
Risk of False Outlier Rejection
1%
b 11 lb
Chart Area , Month
Random Seed (may be left blank)
62311 42188
Significant figures to use
3
Axis Values
Time
Concentration
Number of data points
10
Min
Max
Min
Max
Number of detected results:
10
6
17
Auto
Auto
Number of nondetect results
0
Reset Concentration Axis
Detection frequency
100%
Data Review
Recommendations
Are all necessary data fields entered, and in proper format?
Yes
None
Are at least 4 data points present for statistical analysis?
Yes
None
Are detection limits for nondetects < maximum detected value?
Yes
None
Are all data within chart axis limits?
Yes
None
Pressing the "Check for Outliers" button to the right will open a worksheet that shows the results of a Dixons's test for outliers Next Step: Check for Outliers
30
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Groundwater Statistics Tool User's Guide
Figure 15. UCL Screen for Vinyl Chloride Attainment Example 4
Groundwater Statistics Tool
Site Name
Test
Operating Unit (OU)
Test
Type of Evaluation
Attainment
Date of Evaluation
6/11/2014
Person performing analysis
RT
Chemical of Concern
VC
Well Name/Number
1
Date Units
Month
Concentration Units
ug/L
Confidence Level
95%
Number of results
10
Number < cleanup level
9
Are any potential outliers present?
No
Mean of concentration
1.72
Standard deviation of concentration
0.21
t-value for UCL calculation
1.833
Trend Line
« Detected Data
Cleanup Level
Ordinary Least Squares
Upper Confidence Band
0.5
95% Upper Confidence Limit (UCL)
1.84
Method for calculating UCL
Student's t UCL
Value of 95% Upper Confidence Band
value at final samplinq event
1.64
Trend calculation method
Ordinary Least Squares
Cleanup level
2
Source of cleanup level
MCL
Is the trend decreasing or statistically
insiqnificant?
Yes
When is the
concentration
predicted to exceed
the MCL?
Not applicable - slope is not
statistically increasing
Message: None.
Restart Data Input Screen
Skip Back Two Steps: Normality Screei
Previous Step: Trend Screen
31
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