U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2011–5013

Prepared in cooperation with the

Massachusetts Department of Environmental Protection 

and the Massachusetts Department of Public Health

Arsenic and Uranium in Water from Private Wells 

Completed in Bedrock of East-Central Massachusetts—

Concentrations, Correlations with Bedrock Units, and 

Estimated Probability Maps
Cover photos:

A quartz-diorite bedrock formation at the road cut northeast of the I-495, I-290 intersection, in 

Marlborough, Massachusetts. Photos by Marcus Waldron.
Arsenic and Uranium in Water from Private 

Wells Completed in Bedrock of East-Central 

Massachusetts—Concentrations, Correlations with 

Bedrock Units, and Estimated Probability Maps

By John A. Colman

Prepared in cooperation with the

Massachusetts Department of Environmental Protection and the

Massachusetts Department of Public Health

Scientific Investigations Report 2011–5013

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2011

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Colman, J.A., 2011, Arsenic and uranium in water from private wells completed in bedrock of east-central 

Massachusetts—Concentrations, correlations with bedrock units, and estimated probability maps: U.S. Geological 

Survey Scientific Investigations Report 2011–5013, 113 p.
iii

Contents

Acknowledgments ...............................................................................................................................................vi

Abstract...................................................................................................................................................................1

Introduction............................................................................................................................................................2

Purpose and Scope.....................................................................................................................................2

Health Effects of Arsenic and Uranium...................................................................................................2

Previous Investigations ..............................................................................................................................4

Investigative Design .............................................................................................................................................4

Study Area.....................................................................................................................................................4

Sampling Distribution..................................................................................................................................5

Sample Collection and the Well-User Questionnaire...........................................................................5

Sample Processing and Analytical Methods.........................................................................................7

Supplemental Data......................................................................................................................................7

Statistical Comparisons..............................................................................................................................7

Arsenic and Uranium Concentrations and Correlations with Bedrock Units...........................................7

Quality Assurance and Other Data Attributes .......................................................................................7

Return Rates of the Water Samples .......................................................................................10

Water Use and Water Quality at Sampled Wells..................................................................10

Arsenic Concentrations............................................................................................................................10

Arsenic Correlations with Bedrock Units .............................................................................................11

Uranium Concentrations ..........................................................................................................................19

Uranium Correlations with Bedrock Units............................................................................................20

Detailed Geologic Quadrangle Mapping of Bedrock Units...............................................................20

Water-Quality Correlations with Ancillary Constituents....................................................................22

Bedrock Units, Geologic Terranes, and Geologic Sources of Arsenic and Uranium..................22

Maps of Estimated Probability for Elevated Arsenic and Uranium in Groundwater.............................24

Arsenic.........................................................................................................................................................24

Uranium .......................................................................................................................................................26

Estimates of the Number of Wells that Exceed USEPA Drinking-Water Standards....................26

Arsenic.........................................................................................................................................30

Uranium .......................................................................................................................................30

Implications for New Supplies, Testing, and Treatment..............................................................................30

Locating Future Bedrock Water Supplies.............................................................................................30

Directing Resources for Water Testing.................................................................................................30

Defining Natural Background Concentrations ....................................................................................30

Summary...............................................................................................................................................................31

References Cited.................................................................................................................................................31

Appendix 1. Abbreviations and Descriptions for Bedrock Units in and Adjacent to the 

 Study Area........................................................................................................................... 35–41

Appendix 2. Letter to Potential Participants in the Study.................................................................43–46

Appendix 3. Probability of Arsenic Exceeding a Given Concentration by Bedrock Unit...........47–62

Appendix 4. Arsenic Log-Normal Fit Statistics by Bedrock Unit .................................................... 63–70

Appendix 5. Probability of Uranium Exceeding a Given Concentration by Bedrock Unit.......... 71–98

Appendix 6. Uranium Log-Normal Fit Statistics by Bedrock Unit................................................. 99–113
iv

Figures

1–3. Maps showing:

1. Arsenic concentrations in public bedrock wells in Massachusetts, 2008.....................3

2. Uranium concentrations in public bedrock wells in Massachusetts, 2008 ...................6

3. Bedrock units and principal faults in the project study area of 

 east-central Massachusetts................................................................................................8–9

4. Graph showing arsenic and uranium sample duplicates collected on the 

 same day and after approximately 80 days, east-central Massachusetts, 2009 ...................12

5. Map showing arsenic concentrations in east-central Massachusetts, 2009 ........................13

6. Graph showing distribution of arsenic concentrations by bedrock unit, with 

 seven or more samples, in the primary and secondary study areas, east-central 

 Massachusetts, 2009..........................................................................................................................14

7. Map showing arsenic concentrations, including Massachusetts Department 

 of Environmental Protection data, showing elevated concentrations west of 

 the Clinton-Newbury fault, east-central Massachusetts ...........................................................15

8. Graph showing distribution of arsenic concentrations by rock type in the 

 elevated-concentration area where differences in concentrations by unit were 

 not significant, east-central Massachusetts.................................................................................16

9. Map showing arsenic concentrations inside and outside the elevated-arsenic 

 area in bedrock units Dl and Sp.......................................................................................................17

10. Graph showing distribution of arsenic concentrations inside and outside the 

 elevated-arsenic area in bedrock units Dl and Sp, east-central Massachusetts.................18

11. Graph showing distribution of arsenic concentrations by bedrock unit east of 

 the Clinton-Newbury fault, east-central Massachusetts ...........................................................18

12. Map showing uranium concentrations in east-central Massachusetts, 2009.......................19

13. Graph showing distribution of uranium concentrations by bedrock unit, with 

 seven or more samples, in the primary and secondary study area, east-central 

 Massachusetts, 2009..........................................................................................................................20

14. Map showing details of change in geologic remapping of the Ayer, Hudson, and 

 South Groveland 7.5-minute quadrangles compared to the statewide mapping of 

 Zen and others (1983).........................................................................................................................21

15. Boxplots showing associations among constituents measured in bedrock 

 wells in east-central Massachusetts, 2009 ...................................................................................23

16. Graph showing cumulative probabilities for arsenic for two bedrock units east 

 of the Clinton-Newbury fault.............................................................................................................24

17. Map showing probabilities of arsenic concentrations in bedrock well water being 

 greater than 10 micrograms per liter, the U.S. Environmental Protection Agency 

 drinking-water standard for public supplies, east-central Massachusetts ...........................25

18. Graph showing cumulative log-normal distribution functions for uranium in an 

 elevated-concentration bedrock unit, Dfgr, and a low-concentration bedrock unit, 

 Sb, east-central Massachusetts......................................................................................................26

19. Map showing probabilities of uranium concentrations in bedrock well water being 

 greater than 30 micrograms per liter, the U.S. Environmental Protection Agency 

 drinking-water standard for public supplies, east-central Massachusetts ...........................27

20. Map showing inferred locations of private wells and census tracts for towns 

 not included in the inferred private-well study, east-central Massachusetts .......................28
v

Tables

1. Chemical analytical methods used in the arsenic and uranium study, east-central 

 Massachusetts, 2009 ................................................................................................................................10

2. Quality-assurance results for arsenic, iron, manganese, and uranium.........................................11

3. Constituent correlation with bedrock units in statewide-scale (1:250,000) and quadrangle-

 scale (1:24,000), east-central Massachusetts .....................................................................................22

4. Number of wells in each bedrock unit and estimates of number of wells exceeding the 

 arsenic and uranium U.S. Environmental Protection Agency drinking-water standards 

 for public supplies, east-central Massachusetts ...............................................................................29

Conversion Factors and Datums

Multiply By To obtain

Area

square kilometer (km2

) 0.6214 square mile (mi2)

Temperature in degrees Celsius (°C) can be converted to degrees Fahrenheit (°F) 

as follows: °F = (1.8 × °C) + 32

Specific conductance is given in microsiemens per centimeter at 25 degrees Celsius 

(μS/cm at 25 °C).

Concentrations of chemical constituents in water are given in micrograms per liter (μg/L).

Acronyms and Additional Abbreviations

ANOVA analysis of variance

GIS Geographic Information System

MDEP Massachusetts Department of Environmental Protection

MDPH Massachusetts Department of Public Health

MCL maximum contaminant level

μg/L micrograms per liter

μS/cm microsiemens per centimeter

mL milliliter

NWQL National Water Quality Laboratory

USEPA U.S. Environmental Protection Agency

USGS U.S. Geological Survey
vi

Acknowledgments

This investigation would not have been possible without the participation of the 

many well users who sent in water samples for analysis. Discussion and project planning 

with the late Elaine Krueger was instrumental for development of the project. Support 

from the Massachusetts Department of Environmental Protection and the Massachusetts 

Department of Public Health is greatly appreciated.
Arsenic and Uranium in Water from Private 

Wells Completed in Bedrock of East-Central 

Massachusetts—Concentrations, Correlations 

with Bedrock Units, and Estimated 

Probability Maps

By John A. Colman

Abstract 

Two U.S. Environmental Protection Agency drinkingwater standards for public supplies involving groundwater 

contaminants that may derive from bedrock sources were 

promulgated between 2003 and 2006. A new arsenic drinkingwater standard, a maximum contaminant level (MCL) of 

10 micrograms per liter, became effective in January 2006. 

The non-radon radionuclides final standard took effect in 

December 2003, with an MCL for uranium of 30 micrograms 

per liter. This investigation, conducted in cooperation with the 

Massachusetts Department of Environmental Protection and 

the Massachusetts Department of Public Health, assessed the 

concentration ranges of arsenic and uranium in bedrock wells 

with reference to the new concentration standards, and associations of arsenic and uranium with bedrock units of the wells 

of east-central Massachusetts. The investigation focused on 

east-central Massachusetts, because State public bedrock-well 

databases indicate that arsenic concentrations in bedrock well 

water are elevated in that area. The project exploited the wide 

areal coverage of private wells to give the first detailed look 

at concentration distributions of arsenic and uranium through 

the high-arsenic zone of Massachusetts. The results establish 

statistical probabilities for elevated concentrations by bedrock 

unit at the scale of the State geologic map (1:250,000), which 

can guide future well-water testing, treatment, and supply 

development.

Well sampling was from 478 randomly selected wells 

by private-well users who were sent sampling-kit bottles with 

instructions and a water-use questionnaire. Results indicated 

that 13 percent of the randomly selected wells contained water 

with concentrations greater than the drinking-water standard 

established for public wells for arsenic, and 3.5 percent were 

greater than the standard for uranium. Arsenic and uranium did 

not in general co-occur in water of a given well. Of the wells 

with concentrations exceeding the standards, the questionnaire 

results indicated that 66 percent were being used for drinking 

water without treatment for arsenic, and 93 percent were being 

used without treatment for uranium.

Statistical analysis of the results indicated that distributions 

of arsenic and uranium concentrations grouped by bedrock 

unit were log normal. Statistically significant differences were 

found among distributions by bedrock unit for both arsenic and 

uranium. However, a zone of elevated concentrations of arsenic 

was found in groundwater west of the Clinton-Newbury fault 

(a boundary between two geologic terranes), where correlation 

between arsenic concentrations and the bedrock units was not 

significant.

Increased sampling in the investigation was directed 

in the regions of three 1:24,000 (7.5-minute) quadrangles 

where recent detailed geologic mapping had been conducted. 

Improved correlations of arsenic and uranium with bedrock 

unit were measured for two of the three quadrangles compared 

to the correlations made for the statewide map. 
2 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Cumulative distribution frequencies of concentrations 

grouped by rock unit or area (zone of elevated arsenic 

concentration) were used to assess the probability of wells 

having concentrations exceeding the drinking-water standards. 

The probabilities were mapped and applied to the estimated 

number of private wells in the study area to determine the 

likely number of wells in the study area with concentrations 

exceeding the standards. For arsenic and uranium, respectively, about 5,700 and 3,300 wells were estimated to contain 

concentrations exceeding the standards. Estimates for arsenic 

may approach the total number for the State, because the study 

area covered the principal known area of elevated arsenic 

concentrations.

Introduction

Two U.S. Environmental Protection Agency (USEPA) 

drinking-water standards involving groundwater contaminants 

that may derive from bedrock sources were promulgated 

between 2003 and 2006. A new maximum contaminant 

level (MCL) standard of 10 micrograms per liter (μg/L) for 

arsenic in drinking water became effective in February 2002, 

with compliance required by January 2006. The non-radon 

radionuclides final rule took effect in December 2003, with 

an MCL for uranium of 30 μg/L. The standards apply to 

public water supplies. In Massachusetts, the Massachusetts 

Department of Environmental Protection (MDEP) recommends that the standards also be used as guidelines for private 

supplies (Massachusetts Department of Environmental 

Protection, 2008).

Private water supply in Massachusetts, exclusive of the 

sand and gravel aquifers of the southeastern part of the State, 

is obtained primarily from wells drilled in bedrock (Hansen 

and Simcox, 1994). Bedrock water sources also are used for 

small commercial water supplies and, in some locations, for 

moderate to large municipal and industrial supplies (Hansen 

and Simcox, 1994; Lyford, and others 2003). Tens of 

thousands of private and public bedrock wells are used in the 

State —91,000 private bedrock wells were estimated for the 

bedrock geologic units investigated in this study.

Arsenic has long been known to be present in water 

from bedrock wells in east-central Massachusetts (Zuena and 

Keane, 1985; Ayotte and others, 2003; 2006), and the State 

straddles an arsenic belt that extends from Connecticut to New 

Brunswick, Canada. Elevated uranium concentrations in water 

from bedrock wells have been associated with igneous rock 

throughout New England, but also are present in water from 

other crystalline rock aquifers in the region (Ayotte and others, 

2007). This investigation, conducted by the U.S. Geological 

Survey (USGS) in cooperation with the Massachusetts 

Department of Environmental Protection (MDEP) and the 

Massachusetts Department of Public Health (MDPH), was 

designed to assess the concentration ranges and associations of 

arsenic and uranium with reference to the new concentration 

standards and to the classifications of the bedrock geologic 

units (hereafter bedrock units) in which the wells are drilled. 

The results can be used to establish statistical probabilities 

for elevated concentrations by bedrock unit, which can guide 

future well-water testing, treatment, and supply development.

Purpose and Scope

Information about bedrock associations of arsenic and 

uranium with bedrock well water are needed in Massachusetts 

to guide future well-water testing, treatment, and supply development. Probability distributions of well-water contaminants 

by bedrock unit will indicate the likelihood of contamination at a given concentration. Maps of these probabilities 

can be used to determine the likelihood of the presence of 

elevated arsenic or uranium concentrations in water of new 

wells in a given location or for directing testing priorities for 

existing wells. 

The study encompasses the east-central arsenic belt in 

Massachusetts (fig. 1), the location of nearly all contamination 

of bedrock wells in the State by arsenic from a natural source. 

Many but not all wells contaminated by uranium are included 

in the same area, although igneous rocks, and likely uranium 

contamination, also occur outside the arsenic belt. 

The principal focus of this report is the collection and 

interpretation of new data from 478 private bedrock wells. 

The amount of existing unpublished MDEP data from public 

bedrock wells is large, however, and may substantially supplement the number of observations per bedrock unit. The public 

bedrock-well data were used for qualitative analysis of the 

extent of contamination of bedrock units. The newly collected 

data were used to compute statistics of contaminant distribution. A reporting goal is to produce maps showing the probability statistic that concentrations of arsenic or uranium in 

well water exceed the drinking-water standards. 

Health Effects of Arsenic and Uranium

Health effects from exposure to elevated concentrations 

of arsenic in drinking water have been established from studies 

in countries with very elevated levels of arsenic in water 

supplies, especially Taiwan (Smith and others, 1992; Lamm 

and others, 2003). Inorganic arsenic is well documented as a 

human carcinogen of the bladder, lungs, and skin (Centeno 

and others, 2007). Inorganic arsenic has also been demonstrated to affect many other organ systems, including the 

gastrointestinal, hepatic, cardiovascular, nervous, renal, and 

hematopoietic systems. A recent interest in arsenic in drinking 

water in the northeastern part of the United States relates to 

possible correlations with increased rates of bladder cancer in 

the region (Devasa and others, 1999; Ayotte and others, 2006). 

Epidemiological results demonstrating links between arsenic 

and health problems involve concentrations greater than the 

current USEPA drinking-water standard by an order of magnitude or more (National Research Council, 2001). Risk levels at 
Introduction 3

Primary study

area boundary

Secondary

study area

boundary

Boston

Harbor

Buzzards Bay

EXPLANATION

Arsenic, in micrograms per liter—Black-border symbols indicate 

concentrations greater than the U.S. Environmental Protection Agency

public drinking-water standard

Town boundary

< 1

1 – < 5

5 – < 10

10 – < 20

20 – 1,000

73°00' 72°00' 71°00'

42°30'

42°00'

41°30'

Base geology from Zen and others (1983), digitized by Nicholson and others (2007), 

scale 1:250,000, NAD 1983, StatePlane Massachusetts Mainland FIPS 2001,

Lambert Conformal Conic projection

0 50 MILES

0 25

25

50 KILOMETERS

CAPE COD 

BAY

NANTUCKET

SOUND

ATLANTIC

OCEAN

RHODE

ISLAND

NEW YORK VERMONT

MASSACHUSETTS

NEW HAMPSHIRE

CONNECTICUT

Figure 1. Arsenic concentrations in public bedrock wells in Massachusetts, 2008. Data from the Massachusetts 

Department of Environmental Protection. See figure 3 and appendix 1 for explanation of bedrock units in the east-central 

part of Massachusetts. <, less than
4 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

the standard are determined by extrapolation from the higher 

exposure studies. The National Research Council review 

for the National Academy of Science estimated the bladder 

cancer risk at about 12 to 23 per 10,000 persons with lifetime 

consumption of drinking water at 10 μg/L, the current public 

supply drinking-water standard. Lung cancer risk is estimated 

at about 14 to 19 per 10,000 persons at 10 μg/L (National 

Research Council, 2001). 

Little is known about the long-term health effects on 

humans of exposure to low-level environmental uranium. 

Studies of occupationally exposed persons, such as uranium 

miners, have shown that the major health effect of uranium in 

the body is renal (kidney) toxicity (Leggett, 1989; Taylor and 

Taylor, 1997).

A discussion of the health effects of uranium in New 

England can also consider the effects of radium and radon, 

which are associated with uranium in crystalline bedrock 

aquifers (Ayotte and others, 2007). The association arises 

from the radioactive decay chain of uranium, which results in 

radium, through several radioactive decay product precursors. 

Radium decays directly to short-half-lived radon (3.8 days). 

Decay of radon results in four short-lived daughters and then 

longer-lived lead (22 years). Where uranium in drinking water 

is measured greater than the standard, analyses for radium 

and radon also could be done. Depending on the analysis 

technique, differential costs of analyses of the radionuclides 

means that uranium analysis may be an inexpensive indicator 

(when compared to gross alpha analysis) for determining the 

presence or absence of other radionuclides. 

Previous Investigations

Several previous water-quality investigations exist 

for arsenic in New England and areas of Massachusetts. 

Investigations of uranium are more limited and cover 

the entire Northeast. The first published investigation to 

address the concerns of arsenic concentrations in private 

bedrock wells of New England referred to southeastern 

New Hampshire (Boudette and others, 1985). Bedrock and 

anthropogenic sources were analyzed, and the conclusion 

was drawn that the source was probably anthropogenic. 

A similar investigation of arsenic wells in Buxton, Maine, 

concluded that the likely source was bedrock (Marvinney and 

others, 1994). A three-town investigation in southern New 

Hampshire, very similar to the present Massachusetts investigation, reported the percentages of arsenic samples with 

concentrations greater than the 10 μg/L standard by bedrock 

unit (Montgomery and others, 2003). Several New Englandbased investigations have evaluated the risk for arsenic occurrence in the region—number of wells affected and probability 

maps of concentrations greater than or equal to 5 μg/L (for 

example, Karagas and others, 2002; Ayotte and others, 2003; 

2006). Ayotte (2006) used a logistic regression based on many 

geologic, hydrologic, and anthropologic statistics for the 

region. A nationwide investigation of contaminants in private 

wells of selected aquifers included distribution plots of 

arsenic concentrations for the New England bedrock aquifer 

(DeSimone, 2009). The New England aquifer was the only 

aquifer investigated in the eastern United States with elevated 

concentrations of arsenic in private wells.

One survey of arsenic in private wells from 

Massachusetts is available from an investigation in Pepperell, 

Massachusetts (SEA Consultants, 1985). Water was analyzed 

from 300 wells, and 12 percent of them had concentrations 

that exceeded the 50‐μg/L USEPA standard that was in effect 

at that time. Attempts to distinguish natural sources of arsenic 

in bedrock from anthropogenic sources, such as pesticides 

applied to orchards, were not successful.

 Finally, a geologically based review of arsenic presence 

in the Northeast was published by Peters (2008). The investigation discusses arsenic presence in overburden and bedrock 

wells from natural and anthropogenic sources. Peters (2008) 

showed that arsenic concentrations were not correlated with 

iron concentrations in bedrock well water, and that elevated 

arsenic concentrations were associated with contacts between 

metamorphic and intrusive igneous rock.

Uranium was included in the DeSimone (2009) survey of 

private wells, including several overstandard samples in the 

New England crystalline-rock aquifers, but the study involved 

few samples from Massachusetts. In an investigation summarizing uranium and radon data from the northern United States, 

a correlation was found between uranium, radium, and radon 

in the New England bedrock aquifer (Ayotte and others 2007). 

Of the nine northern aquifers investigated, median concentrations of radon and uranium were highest and third highest, 

respectively, in the New England bedrock aquifer. 

Investigative Design

The investigative design followed that of Montgomery 

and others (2003) in southeastern New Hampshire, addressing 

the correlations between bedrock units and concentrations 

of arsenic and uranium. The intent in this study was to cover 

the known elevated-arsenic areas in Massachusetts so that the 

assessment of arsenic contamination in the State would be 

advanced as much as possible. However, future studies may be 

necessary to characterize other parts of the State with limited 

areas of elevated arsenic.

Study Area

The primary study area (fig. 1), in east-central 

Massachusetts, was chosen to include the area of elevated 

results (greater than or equal to the USEPA drinking-water 

standard for public supplies, 10 μg/L) of arsenic in public 

wells (primarily bedrock) published from the MDEP database 

(Ayotte and others, 2003). Data reviewed after initiation 

of the project (J.A. Cerutti, Massachusetts Department of 

Environmental Protection, written commun., 2008; Ayotte, 
Investigative Design 5

2006) indicated additional elevated concentrations to the 

east of the principal study area and one elevated value in the 

northwest (fig. 1). The primary study area was augmented 

with a secondary study area (fig. 1) to cover the elevated 

concentrations in the east. By including the areas of known 

elevated concentration, the investigation would define arsenic 

occurrence in the principal areas of Massachusetts where 

concentrations could be expected to exceed the drinkingwater standard. 

Although the project study areas were determined on the 

basis of concentrations of arsenic in bedrock wells, the areas 

were also appropriate for investigation of uranium (fig. 2). 

MDEP data show that the arsenic-defined areas include 

many of the elevated concentrations of uranium in the State. 

The MDEP uranium coverage is less extensive than that for 

arsenic, so uranium concentrations are unknown in some 

areas. Not all of the bedrock units that may have elevated 

uranium were characterized in the present investigation; 

however, enough elevated-concentration units were included 

that correlations between uranium and bedrock unit would be 

apparent if uranium were controlled by rock type.

The distribution of bedrock units of crystalline igneous 

and metamorphic rocks in the study area is complex (fig. 3). 

The study area is crossed by major faults that divide parts of 

three geologic terranes that include the Merrimack belt, the 

Nashoba zone and the Milford-Dedham zone (Hatch, 1991, 

p. v, fig. 2). The primary study area includes most of the 

Merrimack belt, which extends from the Connecticut Valley 

belt (indicated by the Merrimack belt western boundary 

in fig. 3) to the Clinton-Newbury fault (fig. 3), and the 

western half of the Nashoba zone, which extends from the 

Clinton-Newbury fault to the Bloody Bluff fault (fig. 3). 

The secondary study area includes the remainder of the 

Nashoba zone and the western edge of the Milford-Dedham 

zone, which begins at the Bloody Bluff fault and extends to 

the east.

Geologic units are as defined in the digitized version 

(Nicholson and others, 2007) of the bedrock map of 

Massachusetts (Zen and others, 1983). The use of these 

maps to define geologic units for wells is, of course, only as 

accurate as could be determined from a 1:250,000-scale map. 

There is the chance that wells near a bedrock boundary may 

not be correctly assigned to a bedrock unit. Bedrock wells are 

on the order of 100 m deep and unscreened in their bedrock 

portions. As such, they may encounter geologic units at depth 

that are different from units as mapped at the surface. But, 

due to the scale of the map (1:250,000), only the major rock 

type is shown at the location of the borehole. For example, a 

borehole study in a 305-m deep well in Tyngsborough, Mass., 

is located in the Ayer Granite bedrock unit SOad, but the borehole contains xenoliths of the host metasedimentary Berwick 

Formation (unit Sb) (Pierce and others, 2007). The level of 

detail seen in boreholes cannot be displayed on a State-scale 

map, and detailed studies of individual boreholes are beyond 

the scope of this regional study.

Sampling Distribution

Well locations were chosen for the study areas by 

stratified random selection across the bedrock units. Previous 

arsenic-concentration data (Ayotte and others, 2003; Joseph 

Cerutti, unpub. data, 2008) indicated that arsenic was more 

prevalent in the 69 bedrock units of the primary study area, 

so more sampling was directed at this area. One sampling 

objective was to collect at least seven samples per bedrock 

unit so that statistical inference could be made even for small 

units. So that large units would have coverage throughout 

their extent, a second objective was applied to supplement 

the initial seven samples by an additional one sample per 

20 km2 for units 20 km2 and larger. The largest unit, the 

Paxton Formation (Sp), is 822 km2, so the sampling objective for this unit was 48 wells. In the secondary area, the 

selection objective was 5 wells for each of the 12 bedrock 

units investigated.

Although a minimum of seven sites per unit in the 

primary study area was desired, some small units did not have 

this number of private wells (or even residences) available. 

Also, areas with public water supplies were necessarily 

excluded from the investigation, which left gaps in data for 

some units. These unavoidable exclusions of sampled areas 

biased the study toward areas where bedrock wells existed.

Wells were selected using randomly generated geo -

coordinates and matching closest Google-Earth determined 

locations of well addresses to well lists provided by the 

Massachusetts Department of Conservation and Recreation. 

Locations of the selected sites were moved from the street 

locations provided by Google Earth to positions of the building 

at that address using field observations of addresses and buildings, and georeferenced ORTHO photos (Massachusetts Office 

of Geographic Information (MassGIS), 2005). 

Increased sampling in the investigation was directed 

in the regions of three 1:24,000 (7.5 minute) quadrangles 

where recent detailed geologic mapping had been conducted. 

Comparisons of correlations of arsenic and uranium with 

geologic units based on 1:250,000-scale mapping to those 

based on more recent 1:24,000-scale mapping could indicate 

the efficacy of remapping for arsenic and uranium delineation 

and for correlation with bedrock.

Sample Collection and the Well-User 

Questionnaire

Samples were collected by private well users during 

spring and summer of 2009, using bottles included in a 

sampling kit mailed to the residence at the location of the 

well. The kit included two labeled 125-mL bottles, a business 

reply Tyvek® envelope, and a questionnaire to determine 

water-use practices at the site, as well as to inform the bottle 

recipients about the program and how to collect the water 

sample (app. 2). Twice as many sampling kits were mailed 

out compared to the number required to meet the sampling 
6 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Town boundary

EXPLANATION

< 1

1 – < 15

15 – < 30

30 – < 60

60 – 230

Uranium, in micrograms per liter—

Black-border symbols indicate concentrations 

greater than the U.S. Environmental Protection 

Agency public drinking-water standard.

73°00' 72°00' 71°00'

42°30'

Base geology from Zen and others (1983), digitized by Nicholson and others (2007),

scale 1:250,000, NAD 1983, StatePlane Massachusetts Mainland FIPS 2001,

Lambert Conformal Conic projection

42°00'

41°30'

0 50 MILES

0 25

25

50 KILOMETERS

Primary study

area boundary

Secondary

study area

boundary

Figure 2. Uranium concentrations in public bedrock wells in Massachusetts, 2008. Data from the Massachusetts 

Department of Environmental Protection. See figure 3 and appendix 1 for explanation of bedrock units in the east-central 

part of Massachusetts. <, less than
Arsenic and Uranium Concentrations and Correlations with Bedrock Units 7

objective for each rock type. A 50-percent return rate was 

expected, based on return rates from a similar investigation in 

New Hampshire (Montgomery and others, 2003). Well users 

were given 1 month to reply before a followup card was sent. 

If no reply had been received by 2 months after the followup 

card, the site was dropped from the study.

Sample Processing and Analytical Methods

All samples were collected by the residents living 

at the addresses selected for sampling. The samples were 

returned in a Tyvek® envelope by mail to the USGS office in 

Northborough, Mass. Samples intended for trace-constituent 

analysis were acidified to a pH less than 2 in the Northborough 

laboratory with 0.4-mL analytical-grade concentrated nitric 

acid (HNO3). The acidified samples were sent to the USGS 

National Water Quality Laboratory (NWQL) in Denver, Colo., 

for analysis as listed in table 1. At the laboratory, samples 

were subject to an in-bottle acid digestion before analysis so 

that results represented total constituent values.

Supplemental Data

Additional data (1997 to 2007) on arsenic and uranium 

in bedrock wells were retrieved from the database of the 

MDEP (Joseph Cerutti, unpub. data, 2008) (figs. 1 and 2). 

The data were from analyses of water in public wells and 

were screened to include only data from bedrock wells. 

Although the results likely were relevant to the investigation, 

some differences prevented a simple combination of the 

data with that collected during this investigation. Different 

and multiple laboratories (State certified) were used for the 

analyses for MDEP data than were used for the USGS data. 

Greater water use may be expected from the public wells 

in the MDEP database compared to the private wells in the 

USGS database. The MDEP data were used to help define the 

areal distribution of arsenic and uranium but were not used in 

statistical summaries of occurrence of these constituents. 

Statistical Comparisons

Parametric statistical tests were used, which are 

appropriate if normality or any other specific distribution 

(log normal in this investigation) can be assumed (Iman and 

Conover, 1983). Analysis of associations of concentration with 

bedrock unit was determined by one-way analysis of variance 

(ANOVA) on log-transformed concentration data, using the 

statistical software package Minitab 16®. Cumulative distribution functions with 95-percent confidence intervals were 

determined for concentration populations grouped by bedrock 

unit by fitting data to a log-normal distribution, using the 

statistical software package Minitab 16® with the options for 

distribution analysis, and arbitrary data censoring. For bedrock 

units with fewer than five analyses with concentrations 

exceeding the analytical reporting limit, the option to assume 

a common scale was used in the distribution fitting.

The statistical software package SPLUS® was used to 

compare geologic mapping techniques and the correlation with 

arsenic and uranium concentrations. The comparisons were 

made with a multiple linear regression of log-transformed data.

Arsenic and Uranium Concentrations 

and Correlations with Bedrock Units

The ranges and correlations of arsenic and uranium 

concentrations among bedrock units are the focus of this 

project. The project objective is to use the correlations to guide 

future well-water testing, treatment, and supply development. 

Quality Assurance and Other Data Attributes

During the investigation, 60 quality-assurance samples 

were analyzed for iron, manganese, arsenic, and uranium. 

The quality-assurance samples included sampling-bottle and 

preservation-acid blanks, a standard-reference sample, resampling, duplicate sampling, and sample splits (table 2). Qualityassurance results of the blank samples showed that possible 

contamination did not occur during sampling, during sample 

handing, or from sampling materials (the bottles and preservation acid). All concentrations measured for the four samplingbottle blanks during the study were below the reporting limits 

(table 1) for the respective analytes (table 2). Four samples of 

standard reference solution (USGS T-195) submitted to the 

NWQL as blind samples were generally within 5 percent of 

the known values. Average percent errors (average, in percent, 

of the absolute difference between replicate pairs divided by 

the average of the replicates) increased for all elements in the 

comparison series: split samples, duplicate samples separated 

by 5 minutes, and duplicate samples separated by months 

(average interval of 80 days). The error increase reflected 

variability in samples over time—small, but measureable for 

samples collected within 5 minutes, and larger for samples 

collected months apart. 

Variability of concentrations over time was investigated 

by analysis of 48 duplicate samples. USGS personnel visited 

12 randomly chosen wells where three samples were collected 

at each well: duplicate samples within 5 minutes and a third 

sample to compare with the original sample collected by 

the well user. Results showed that repeatability for samples 

collected sequentially at one visit was very good, but that 

substantial variation can occur for a well sampled over time 

(fig. 4). Sampling error from additional sources is possible in 

resampling over time, including the possibility of sampling 

from different water taps by mistake.
Pr

Sp

OZn

Sb

Water

Dht

Zdgr

OZmo

Zsg

Dl

Jpc

Zdh

So

PzZc

Spss

Se

Ssqd

Zdigb

Zv

OZm

Ogl Zdi

Opc

Sgr

Dpgr

OZnb

Trn

SOngd

Ops

Dfgr

SOagr

Zpg

Dfgrg

Zgr

Zb

PzZr

SOcgr

SOqgr

Dcgr

OZfm

igd

Zhg DSw

Zpd

Zm

Pgr

Dchgr

OZsh

Zmgd

Pw

SOad

Dbmdg

Zdpq

Ztgd

Opsa

Oa

Zmgr

DZl Dpgg

Zpmq

Zssy

DSdi

Spqr

Dfgd

Sagr Jtc

mgr

Sacgr

SZtb

Dbi

Drgr

Zpmg

Zwgr

Sngr

De

Zvf

Spsq

Ssaqd

Opv

Dbmd

Zw

OZmg

Dwm

Opbg

Sts

Deg

Zpm

SOcb

Opf

OZf

Zgb

St

SObo

Drh

Sbs

Dbmdt

DSna

OZt

Zmm

Zrdi

PzZrb

Zdngr

Ebw

Pp

DSnl

Dbh

u

grg

Dw

Dlf

Dpgb

DSnu

Dfgds

Pwv

Jd

SObgr

Je

DSn

Opau

Dl+Ops

Spa

Sc

Dcygr

Dgr

Dea

Ddi

Tre

Spbc

OZma

Opvs

Sfs

Dmgr

Ongb

Jn

Spbs

Prc

Eg

OZty

Jec

gr

SOvh

gd

gf

Sf

Jsc

Zdhs

Ph

Jhb

DSnr

Pcm

Jsi

hg

Dhgr

Dlm

Dev

gb

am Dlo

Sfss

Eh

Ddn

Opa

Dbt

qd

OZmoa

Opu

Oau

Oaq

OZmou

Dbd

Dbp

Dft

Zmmu Boston

Harbor

Primary study

area boundary

Secondary study area boundary

0 50 MILES

0 25

25

50 KILOMETERS

Taconic-Berkshire zone

Rowe-Hawley zone

Connecticut Valley belt Merrimack belt

Geologic terranes in Massachuset

72°00' 71°00'

42°40'42°20'

Base geology from Zen and others (1983), digitized by Nicholson and others (2007), scale 1:250,000, NAD 1983, StatePlane Massachusetts Mainland FIPS 2001,Lambert Conformal Conic projection
Merrimack beBloody Bluff faClinton-Newb

sedimentary bresedimentary rocserpentinite slate syenite tonalite tuff ultramafic intrusschist rhyolite sandstone quartzite 

pegmatite Dpeperidotite Dbp OZmou Zmmuphyllite Dgm Se SObo Sts SZtbporphyry SObgrquartz diorite Dbiquartz monzodiorite Dbmd Dbmdt

granodiorite Dgd gd igd Ztgdgranofels De gf Sf Sp Spbc Spbsgranulite Deghornblendite Dbh Oaumafic gneiss Dchh Dlo hg Opvmafic volcanic rock PzZrbmarble Dlmmetasedimentary rock Sb Sometavolcanic rock Zvmica schist Dev Dl+Ops Ops Opsa OZty Sbs Sfssmonzonite Dwmmudstone DSnumylonite Jfgparagneiss OZma

granitic gneiss Dbmdg Dchgr Dfgd Dfgds Dfgrg Dhgr Dht grg

Ogl Opc OZf OZmg Zdh 

granite Dcgr Cmgr Drgr gr mgr Pgr Sacgr Sagr Sgr 

Sngr SOad SOagr Zdgr Zdngr Zgr Zmgd ZmgrZpg Zsg Zwgr

alkali-granite (alaskite) Dcygr Dpgr SOcgr SOqgr Zagr Zhgamphibolite am Dea Oa Opa OZm OZmoa OZnb Spaandesite DSnaargillite Ebw Eh PzZcarkose Jm Jn Trnaugen gneiss Opaubasalt DSnlbiotite gneiss Opau Opvs OZfm OZmo Zpm Zpmgcalc-silicate rock Sfsconglomerate Jecdacite Dbddiabase Jddiorite Ddi Ddn di DSdi Ssaqd Zdi Zdigb Zrdifelsic gneiss Dlf Opffelsic metavolcanic rock Zvfgabbro Dpgb gb Ongb Zgbgneiss Drh OZsh OZtf Zpd

Rock type Bedrock Rock type Bedrock Rock type 

EXPLANATION

Figure 3. Bedrock units and principal faults in the project study area of east-central Massachusetts. See appendix 1 for explanation of bedroMap colors from Moyer and others, 2005.
10 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Table 1. Chemical analytical methods used in the arsenic and uranium study, east-central Massachusetts, 2009.

[NWQL, U.S. Geological Survey National Water Quality Laboratory, Denver, Colo.; NA, not applicable; oC, degrees Celsius]

Constituent Units Method Reporting

limit Method reference

Acid neutralizing 

capacity

Milligrams per liter as 

calcium carbonate

Auto titrator at the USGS 

Northborough lab

NA Rounds, 2006

Conductance Microsiemens per 

centimeter at 25 °C

Orion conductance probe at the USGS 

Northborough lab

NA Radtke and others, 2005

pH pH log units Initial pH from alkalinity titration at the 

USGS Northborough lab

NA Ritz and Collins, 2008

Arsenic Micrograms per liter In-bottle acid digestion followed by 

collision/reaction cell inductively 

coupled plasma/collider mass 

spectrometry at NWQL

0.2 Garbarino and others, 2006; 

Garbarino and Struzeski, 1998

Iron Micrograms per liter In-bottle acid digestion followed by 

inductively coupled plasma-atomic 

emission spectroscopy at NWQL

14 Garbarino and others, 2006; 

Garbarino and Struzeski, 1998

Manganese Micrograms per liter In-bottle acid digestion followed by 

inductively coupled plasma/collider 

mass spectrometry at NWQL

0.4 Garbarino and others, 2006; 

Garbarino and Struzeski, 1998

Uranium Micrograms per liter In-bottle acid digestion followed by 

inductively coupled plasma/mass 

spectrometry at NWQL

0.02 Garbarino and others, 2006; 

Garbarino and Struzeski, 1998

Return Rates for the Water Samples

Of the total 1,580 sample kits sent to well users, samples 

from 478 wells were returned, a 30-percent return rate. The low 

return rate resulted in several bedrock units that had too few 

samples for statistical analysis. 

Water Use and Water Quality at Sampled Wells

Results from the returned questionnaires indicate 

that 91 percent of the respondents use their well water for 

drinking. Many users treat the water in some way including 

softening, radon removal, arsenic removal, and reverse 

osmosis. Of the respondents with wells having arsenic 

concentrations exceeding the drinking-water standard, 

however, 66 percent were using water for drinking without 

treatment. Of the respondents with wells having uranium 

concentrations exceeding the standard, 93 percent were using 

water for drinking without treatment. The statistic included 

one respondent that was not using the water for drinking 

because it had not been tested. Thus, none of the respondents 

with wells having uranium concentrations exceeding the 

standard were treating the water for uranium removal.

Arsenic Concentrations

Arsenic concentrations in the complete dataset ranged 

from less than 0.2 μg/L (less than the laboratory reporting 

limit) in 24 percent of all samples tested to 1,540 μg/L. Of 

the 344 randomly selected samples (excluding intensive 

quadrangle sampling), 13 percent exceeded the 10 μg/L 

drinking-water standard. For randomly selected samples from 

the primary study area, a slightly larger fraction of samples, 
Arsenic and Uranium Concentrations and Correlations with Bedrock Units 11

Table 2. Quality-assurance results for arsenic, iron, manganese, and uranium.

[USGS, U.S. Geological Survey]

Quality-assurance 

measure

Details Number of 

samples Result

Bottle blanks Sample bottles had been sent out in 

mailers, and were preserved with acid

4 All concentrations were less than 

the method detection limit

Standard reference samples USGS standard reference water sample, 

number T-195

4 Mean relative errors were

Arsenic: 4.9 percent

Iron: 2.4 percent

Manganese: 0.62 percent

Uranium: 5.6 percent

Sample splits One sample split for two analyses 13 Mean relative errors were 

Arsenic: 3.8 percent

Iron: 1.8 percent

Manganese: 6.2 percent

Uranium: 0.74 percent

Duplicates at one time Samples collected sequentially on one 

sampling occasion

13 Mean relative errors were 

Arsenic: 5.8 percent

Iron: 11.3 percent

Manganese: 15.1 percent

Uranium: 3.3 percent

Duplicates over time Two samples collected on different 

sampling days

13 Mean relative errors were 

Arsenic: 49.5 percent

Iron: 80.1 percent

Manganese: 61.2 percent

Uranium: 74.3 percent

15 percent, exceeded the standard. Concentrations of arsenic 

were not elevated in the 18 samples west of the primary study 

area, but some elevated concentrations were measured in the 

secondary study area, located east of the primary study area 

(fig. 5). Elevated concentrations can exist near low concentrations in the same bedrock unit, similar to distributions 

measured in other New England studies (Montgomery and 

others, 2003).

Arsenic Correlations with Bedrock Units

Arsenic concentrations in well water vary depending 

on the bedrock unit (fig. 6). Generally, concentrations are 

not narrowly distributed but rather extend above and below 

the median concentration for the bedrock unit by an order of 

magnitude or more. Although there are no bedrock units with 

elevated concentrations that do not also include low concentrations, there are some units with only low concentrations. 

One of the lowest-concentration units, Ops, is on the western 

edge of the study area, confirming the western limit to the 

elevated-concentration area in east-central Massachusetts. 

Each of the rock classifications of metamorphic, metamorphic 

with igneous intrusive, and igneous includes low-concentration and elevated-concentration units.

The variation within a bedrock unit indicates that median 

concentrations cannot be used for accurate predictions of 

concentrations in a unit. Concentrations in bedrock units are 

generally log normally distributed, so parametric statistical 

tests can be used to determine whether bedrock units and 

concentrations are related, or if distributions among bedrock 

units are significantly different. If a relation exists, probabilities of a bedrock well containing a given concentration may be 

calculated for each bedrock unit from cumulative distribution 

frequencies.
12 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Line of equivalence

0

2

4

6

8

10

12

0

5

10

15

20

25

0 5 10 15 20 25 0 5

20 4 6 8 10 12 20 4 6 8 10 12

Arsenic, in micrograms per liter Uranium, in micrograms per liter

Uranium, in micrograms per liter

Arsenic, in micrograms per liter

One-time duplicates

One-time duplicates

Time duplicates

Time duplicates

10 15 20 25

Figure 4. Arsenic and uranium sample duplicates collected on the same day and after about 

80 days, east-central Massachusetts, 2009.
Arsenic and Uranium Concentrations and Correlations with Bedrock Units 13

Pr

Sp

OZn

Zdgr

Sb

Dht

OZmo

Zsg

Dl

Zgg

So

PzZc

Spss

Se

Ssqd

Zdigb

Zv

OZm

Zdi

SOcgr

Zgr

PzZr

Sgr

Dpgr

OZnb

SOngd

Ops

Dfgr

Zpg

SOagr

Dfgrg

Zb

SOqgr

Dcgr

igd

DSw Zhg Zm

Pgr

Dchgr

OZsh

Zmgd

Pw

SOad

Ztgd

Opsa

Zmgr

DZl

Oa

Zssy

DSdi

Spqr

Dfgd

Dpgg

Sagr

mgr

Opc

Sacgr

SZtb

Dbi

Drgr

Zwgr

Zvf

Spsq

Dbmdg

Ssaqd

Sngr

Opv

Zw

SOcb

OZmg

Dwm

Opbg

Sts

OZf

Zgb

St

SObo

Drh

Sbs

DSna

OZt

Zrdi

PzZrb

Zdngr

Ebw

Pp

DSnl

Dbh

u

OZfm

grg

Dlf

DSnu

Dfgds

Pwv

Jd

SObgr

DSn

Deg

Opau

Ogl

Dl+Ops Sc

Dcygr

Dgr

Dpgb

Ddi

Tre

Spbc

OZma

Eh

Opvs

Sfs

Dmgr

Spbs

SOcsm

Prc

Eg

OZty

gr

SOvh

gd

Sf

OZtf

Ph

DSnr

Pcm

hg

Dhgr

Dlm

gb

Dlo

Sfss

Dchh

Ddn

Opa

Jsi

qd

OZmoa

Opu

Oau

Oaq

Spa

Dft

Ssqd

OZnb

SOagr

Sb Se

OZf

72°00' 71°00'

42°40'

42°20'

42°00'

Base geology from Zen and others (1983), digitized by Nicholson and others (2007), 

scale 1:250,000, NAD 1983, StatePlane Massachusetts Mainland FIPS 2001,

Lambert Conformal Conic projection

OZn

So

Sb

SOagr

Sacgr

SOad

SZtb

OZnb

Dcgr

St

OZm

Sagr

Sbs

Jd

DSdi

Ssaqd

Ph

OZsh

EXPLANATION

Town boundary

Clinton-Newbury fault

< 1

1 – < 5

5 – < 10

10 – < 20

20 – 1,540

Arsenic, in micrograms per liter—Black-border symbols

indicate concentrations greater than the U.S. Environmental

Protection Agency public drinking-water standard.

South

Groveland

Quadrangle

Ayer

Quadrangle

Hudson

Quadrangle

Ssqd

Primary study

area boundary

Secondary study

area boundary

0 20 MILES

0 10

10

20 KILOMETERS

Figure 5. Arsenic concentrations in east-central Massachusetts, 2009. Sampling coverage was increased in 

the areas of the insert maps where geology was mapped at the 1:24,000 scale. See figure 3 and appendix 1 for 

explanation of bedrock units. <, less than
14 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

U.S. Environmental Protection Agency

public drinking-water standard

11 Number of values 

EXPLANATION 

x

x

o

o

Upper adjacent

75th percentile

Median

25th percentile

Lower adjacent

Lower outside

Lower detached

Upper detached

Upper outside

x

o

o

o

o

o

o

x

o

x

x

x

o

o

o

o

o o

o

o

o

o

o

o

o

o 0.1

0.01

1

10

100

1,000

10,000

Arsenic, in micrograms per liter

9 8 7 9 9 7 10 12 15 8 8 22 7 3133 20 10 16 14 7 8 53 7 11 12 11 23 11

PhSe

Ops

Sbs

Spss

St

DSw

Spsq

OZf

Dl

Sp

SObo

SZtb

OZn

OZnb

OZm

SbSo

Dcgr

Dfgr

Sacgr

Sagr

Sgr

SOagr

Zpg

Zsg

Ssqd

Bedrock unit abbreviation

Metamorphic rock with Igneous rock

igneous intrusives

Metamorphic rock

Figure 6. Distribution of arsenic concentrations by bedrock unit, with seven or more samples, in the primary 

and secondary study areas, east-central Massachusetts, 2009. See figure 3 and appendix 1 for explanation of 

bedrock units.

Arsenic concentrations north and west of the ClintonNewbury fault are elevated (fig. 5). The fault marks a boundary 

between the Merrimack belt and Nashoba zone (fig. 3), 

and bedrock units do not extend across the fault boundary. 

The elevated arsenic concentrations extend approximately 

20 km west and northwest of the fault. Within the 20-km 

zone, elevated concentrations were measured across a variety 

of bedrock unit rock types. Beyond the 20-km distance, 

sometimes within a rock type that has elevated concentrations 

near the fault, concentrations decrease. Lower concentrations 

of arsenic were measured in the large bedrock unit (OZn) 

east of the Clinton-Newbury fault. However, some elevated 

arsenic concentrations occur east of the fault, particularly in the 

OZnb unit.

An elevated-concentration area was defined as being 

bounded on the east by the Clinton-Newbury fault and 

extending westward to include all the concentrations measured 

greater than 10 μg/L (fig. 7). MDEP data were combined with 

the USGS data to define the western part of the elevatedconcentration area. One-way ANOVA analysis was used to 

assess the relations between concentration and bedrock unit in 

the elevated-concentration area. Within the elevated-concentration area, there was no statistically significant difference 

at the 5-percent level between log-transformed concentration 

distributions, grouped by bedrock unit (fig. 8).
Arsenic and Uranium Concentrations and Correlations with Bedrock Units 15

Boundary of elevated arsenic

concentration area

Clinton-Newbury fault

EXPLANATION

10 – <20

Massachusetts Department of 

Environmental Protection sites

Arsenic, in micrograms per liter—Black-border symbols

indicate concentrations greater than the U.S. Environmental

Protection Agency public drinking-water standard.

U.S. Geological

Survey sites

5 – < 10

1 – < 5

< 1

20 – 1,540

10 – <20

5 – < 10

1 – < 5

< 1

20 – 1,540

72°00' 71°00'

42°40'

42°20'

Base geology from Zen and others (1983), digitized by Nicholson and others (2007), 

scale 1:250,000, NAD 1983, StatePlane Massachusetts Mainland FIPS 2001,

Lambert Conformal Conic projection 0 20 MILES

0 10

10

20 KILOMETERS

Primary study

Ayer and Hudson area boundary

Quadrangle boundaries South Groveland

Quadrangle boundary

Secondary

study area

boundary

Figure 7. Arsenic concentrations, including Massachusetts Department of Environmental Protection data, 

showing elevated concentrations west of the Clinton-Newbury fault, east-central Massachusetts. <, less than
16 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

11

x

x

o

o

Metamorphic rock Igneous rock

Number of values 

EXPLANATION 

Upper adjacent

75th percentile

Median

25th percentile

Lower adjacent

Lower outside

Lower detached

Upper detached

Upper outside

U.S. Environmental Protection Agency

public drinking-water standard

x

x

x

x

Arsenic, in micrograms per liter

0.1

1

10

100

1,000

10,000

Bedrock unit abbreviation

Dl

DSw

PhSb

Sbs

Se

So

SObo

Sp

St

Dcgr

Dfgr

DSdi

Sacgr

SagrSngr

5 8 9 16 12 8 14 7 14 15 7 8 6 53 11 6

Figure 8. Distribution of arsenic concentrations by rock type in the elevated-concentration area, where 

differences in concentrations by unit were not significant, east-central Massachusetts. See figure 3 and 

appendix 1 for explanation of bedrock units.

Two of the bedrock units (Sp and Dl) inside the 

elevated-concentration area also extend outside the elevatedconcentration area, where no concentrations exceeded the 

standard (fig. 9). Comparison of the data in the two units that 

cross the area boundary indicated that the difference across 

the elevated-concentration boundary, but within a bedrock 

unit, was statistically significant (fig. 10). These statistics 

indicate that the high-concentration area is within the 

Merrimack belt, but does not extend to the western boundary 

of the belt (fig. 9).

Three bedrock units with seven or more samples 

(Ops, Spss, and Spsq) were west or mostly west of the 

elevated-arsenic area. Concentrations in these bedrock units 

were significantly different from the grouped elevated arsenic 

area adjacent to the west. 

A different pattern is observed east of the fault. Most 

striking is the difference between the bedrock unit SZtb, 

aligned with the Clinton-Newbury fault, and the bedrock unit 

OZn, adjacent to the east (fig. 5). Because of extra sampling 

in the area of the remapped quadrangles, there is an excellent 
Arsenic and Uranium Concentrations and Correlations with Bedrock Units 17

Primary

study area

Secondary

study area

0 20 MILES

0 10

10

20 KILOMETERS

73°00' 72°30' 72°00' 71°30'

42°40'

42°20'

42°00'

Base geology from Zen and others (1983), digitized by Nicholson and others (2007), 

scale 1:250,000, NAD 1983, StatePlane Massachusetts Mainland FIPS 2001,

Lambert Conformal Conic projection

Clinton-Newbury fault

EXPLANATION

Arsenic, in micrograms per liter—Black-border symbols

indicate concentrations greater than the U.S. Environmental

Protection Agency public drinking-water standard.

U.S. Geological

Survey sites

10 – <20

5 – < 10

1 – < 5

< 1

20 – 1,540

10 – <20

5 – < 10

1 – < 5

< 1

20 – 354

Bedrock unit

Sp

Dl

Boundary of elevated arsenic concentration area

Massachusetts Department of 

Environmental Protection

Merrimack belt western boundary

Figure 9. Arsenic concentrations inside and outside the elevated-arsenic area in bedrock units Dl and Sp. 

Data from the U.S. Geological Survey and the Massachusetts Department of Environmental Protection. 

See figure 3 and appendix 1 for explanation of bedrock units. <, less than

visual indication of arsenic concentration association with 

geology (inset map, fig. 5). One-way ANOVA analysis shows 

significant concentration differences between lower-concentration (OZn, Zhg, Zpg, Zsg, and Zw) and higher-concentration 

(SZtb and OZnb) units. The amphibolite-bearing rocks, OZnb, 

have elevated arsenic. Although not used for statistics, the 

MDEP dataset includes elevated concentrations in the southern 

parts of the amphibolite unit (fig. 7), which appears to indicate 

that the association is rock specific, not region specific as was 

found in the elevated concentration area in the west. 

One-way ANOVA analysis of log-arsenic concentration 

in the rocks east of the Clinton-Newbury fault indicates that 

the arsenic concentrations in the OZnb unit are significantly 

higher than in the OZn unit (fig. 11). In this region east of the 

Clinton-Newbury fault, the mapped bedrock units indictate 

the distribution of arsenic concentrations. The OZnb unit 

extends well outside the primary study area and, as such, 

extends the area where elevated arsenic concentrations may 

be expected in Massachusetts from previous estimates (Ayotte 

and others, 2003). 
18 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

o

Dl 

Sp

Dl

Sp

0.1

10

1,000

Arsenic, in micrograms per liter 

Bedrock unit abbreviation

100

1

5 14 4 8

Elevated-arsenic area West of elevated-arsenic area 8 Number of values 

EXPLANATION 

o Upper detached

Upper adjacent

75th percentile

Median

25th percentile

Lower adjacent

Indicates differences

among bedrock units.

Data for bedrock units

that do not share a

letter have geometric

means that are

significantly different

A

A and B

A and B

BB

Figure 10. Distribution of arsenic concentrations inside and outside the elevatedarsenic area in bedrock units Dl and Sp, 

east-central Massachusetts. Data from the 

U.S. Geological Survey. See figure 3 and 

appendix 1 for explanation of bedrock units.

x

x

o

o

o

o

o

o

o

o

o

o

o

o

A to C

C

A

A to C

A and B

CC

0.1

0.5

1

5

50

10 32 20 12 35

Arsenic, in micrograms per liter

Bedrock unit abbreviation

10

100

11 23

15 Number of values 

EXPLANATION 

OZm

OZn

OZnb

SOagr

SZtb

Zpg

Zsg

x

o

o

Upper adjacent

75th percentile

Median

25th percentile

Lower adjacent

Lower detached

Upper detached

Upper outside

Indicates differences

among bedrock units.

Data for bedrock units

that do not share a

letter have geometric

means that are

significantly different

A and B

Figure 11. Distribution of arsenic concentrations by bedrock unit east of the Clinton-Newbury fault, east-central 

Massachusetts. See figure 3 and appendix 1 for explanation of bedrock units.
Arsenic and Uranium Concentrations and Correlations with Bedrock Units 19

fig 12

Pr

Sp

OZn

Zdgr

Sb

Dht

OZmo

Zsg

Dl

Zgg

So

PzZc

Spss

Se

Ssqd

Zdigb

Zv

OZm

Zdi

SOcgr

Zgr

PzZr

Sgr

Dpgr

OZnb

SOngd

Ops

Dfgr

Zpg

SOagr

Dfgrg

Zb

SOqgr

Dcgr

igd

DSw Zhg Zm

Pgr

Dchgr

OZsh

Zmgd

Pw

SOad

Ztgd

Opsa

Zmgr

DZl

Oa

Zssy

DSdi

Spqr

Dfgd

Dpgg

Sagr

mgr

Opc

Sacgr

SZtb

Dbi

Drgr

Zwgr

Zvf

Spsq

Dbmdg

Ssaqd

Sngr

Opv

Zw

SOcb

OZmg

Dwm

Opbg

Sts

OZf

Zgb

St

SObo

Drh

Sbs

DSna

OZt

Zrdi

PzZrb

Zdngr

Ebw

Pp

DSnl

Dbh

u

OZfm

grg

Dlf

DSnu

Dfgds

Pwv

Jd

SObgr

DSn

Deg

Opau

Ogl

Dl+Ops Sc

Dcygr

Dgr

Dpgb

Ddi

Tre

Spbc

OZma

Eh

Opvs

Sfs

Dmgr

Spbs

SOcsm

Prc

Eg

OZty

gr

SOvh

gd

Sf

OZtf

Ph

DSnr

Pcm

hg

Dhgr

Dlm

gb

Dlo

Sfss

Dchh

Ddn

Opa

Jsi

qd

OZmoa

Opu

Oau

Oaq

Spa

Dft

Ssqd

OZnb

SOagr

Sb Se

OZf

72°00' 71°00'

42°40'

42°20'

42°00'

OZn

So

Sb

SOagr

Sacgr

SOad

SZtb

OZnb

Dcgr

St

OZm

Sagr

Sbs

Jd

DSdi

Ssaqd

Ph

OZsh

Primary study

area boundary

Secondary 

study area

boundary

Base geology from Zen and others (1983), digitized by Nicholson and others (2007), 

scale 1:250,000, NAD 1983, StatePlane Massachusetts Mainland FIPS 2001,

Lambert Conformal Conic projection 0 20 MILES

0 10

10

20 KILOMETERS

EXPLANATION

Town boundary

Clinton-Newbury fault

< 1

1 – < 10

10 – < 20

20 – < 30

30 – 817

Uranium, in micrograms per liter—Black-border symbols

indicate concentrations greater than the U.S. Environmental

Protection Agency public drinking-water standard

South

Groveland

Quadrangle

Ayer

Quadrangle

Hudson

Quadrangle

Figure 12. Uranium concentrations in east-central Massachusetts, 2009. Sampling coverage was increased in 

the areas of the insert maps where geology was mapped at the 1:24,000 scale. See figure 3 and appendix 1 for 

explanation of bedrock units. <, less than

Uranium Concentrations

Uranium concentrations ranged from less than the 

analytical reporting limit, 0.02 μg/L, to 817 μg/L. The low 

reporting limit allows description of uranium concentration variability in virtually all ranges of occurrence. Of 344 

samples from the stratified random sampling, 12 samples 

(3.5 percent) exceeded the drinking-water standard of 30 μg/L. 

With the samples from the intensive sampling included, 

concentrations in 13 of the total of 478 samples (2.7 percent) 

were greater than the drinking-water standard. Elevated 

concentrations of uranium were widely distributed across 

the study area (fig. 12). As with arsenic, elevated uranium 

concentrations can be in close proximity to low concentrations 

in the same unit. Some units, however, had consistently low 

concentrations.
20 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

PhSe

Ops

Sbs

SpssSt

DSw

Spsq

OZf

Dl

Sp

SObo

SZtb

OZn

OZnb

OZm

SbSo

Dcgr

Dfgr

Sacgr

Sagr

Sgr

SOagr

Zpg

Zsg

Ssqd

0.01

0.1

1

10

100

1,000

Uranium, in micrograms per liter

Bedrock unit abbreviation

U.S. Environmental Protection Agency

public drinking-water standard

11

8 8 12 7 9 8 14 8 8 23 7 20 10 17 35 32 14 9 11 7 12 11 20 11 527 A to E A to F

F

A to FB to FB to FA to FD to FA to FB to FB to F

A to D

E and F

A to E

C to F

A to F

A to E

B to F

A

A and B

A to CA to C

A to FB to F

A to D

A

A to F

10

Metamorphic rock with Igneous rock

igneous intrusives

Metamorphic rock

Number of values 

EXPLANATION 

x

x

Upper adjacent

75th percentile

Median

25th percentile

Lower adjacent

Lower outside

Upper outside

Indicates differences

among bedrock units.

Data for bedrock units

that do not share a

letter have geometric

means that are

significantly different

A and B

x

x

x

x

Figure 13. Distribution of uranium concentrations by bedrock unit, with seven or more samples, in the 

primary and secondary study area, east-central Massachusetts, 2009. See figure 3 and appendix 1 for 

explanation of bedrock units.

Uranium Correlations with Bedrock Units

Variation of uranium concentration by bedrock unit is 

apparent in units sampled seven or more times, a threshold 

used to increase statistical significance (fig. 13). Median 

concentrations are generally greater in igneous rock than 

in metamorphic rock (fig. 13). Concentrations in metamorphic rock intruded by igneous rock were intermediate. 

Concentrations were lowest in the unintruded metamorphic 

rock. Uranium concentrations exceeded the 30 μg/L drinkingwater standard only in the igneous units.

The visual differences (fig. 13) were confirmed by 

one-way ANOVA analysis applied to the log-transformed 

uranium concentrations for bedrock units with seven or more 

samples, using rock type as a discrete independent variable. 

Significant differences were noted in concentrations among 

the rock types, indicating the association of rock type with 

distribution of uranium concentrations. Several bedrock units 

west of the Clinton-Newbury fault, such as Dcgr and Dl, were 

significantly different from each other. 

Bedrock units classified as metamorphic, but intruded 

by igneous rocks, occasionally might be expected to reflect 

the elevated igneous concentrations. Well boreholes might 

intersect igneous rock even though the unit was classified as 

metamorphic, although this investigation did not find standard 

exceedences in metamorphic rock intruded by igneous rock. 

Intruded rock, however, did include concentrations that were 

greater than in unintruded rock.

Detailed Geologic Quadrangle Mapping of 

Bedrock Units

Several of the 1:24,000 quadrangles within the study area 

were remapped recently (three are shown in fig. 14). Some 

of the contacts between bedrock units are changed on the 

new maps compared to the State map (Zen and others, 1983; 

Nicholson and others, 2007). Bedrock unit identifications of 

some of the polygons also have changed. Correlations between 

arsenic and uranium concentration and the remapped units 

may be stronger than that of the State map if the newly identified units more accurately represent rock boundaries and if the 

concentrations are controlled by bedrock unit type.
OZnb

Ssqd

SOagr

Sb

Se

OZf

Sap

Ssd

Oba Obb

Smb Sme

Obb

COf

Ssbh

Ssd

Ssbh

Oba

Obg

Sab

Obg

Sam

Obba

Obba

Ssbh

Obb

Obba

Obb

Obba

Ssbh

Obb

Sab

Sab

Obba

Obba

Ssbh

Ssb

Ssbh

Sap

Ssd

Obba

Ssd

Obb

Obb

Obb

Sab

Obba

Obba

Ssbh

Obba

Obb

Ssbh

Obb

Obba

Ssb

Obb

Obb

Ssbh

Obba

Obb

Obba

Sab

Sap

Ssd

Obba

Ssb

Obb

Obba

Obb

Ssd

Obb

Obba

COf

Ssd

COf

Ssd

Obba

Obb

Obb

Sab

Ssb

Obba

Ssb

Sap

Sap

Sb

So

Sacgr

OZn

SOad

SZtb

Dcgr

Sbs

St

Jd

DSdi

Ph

Sagr

Sb

Sdgc

So

Saygp

OZnu

OZtb

So

Dcgr

Dcgr

So Sb

Sbbks

So

Dcgr Dcgrm

Sdgc

Dcgrb

SaygpSayg

Phc

OZn

SOagr

OZnb

SZtb

St

So Sagr

Sacgr

Ssaqd

Ph

OZm

COnu

Dag

OSas

OSp

COtb

Sshd

OSq

COas

COgn

OShc

COna

COtb

OSaygp

COna

OSq

OScs

COna

COgnSDagf SDgd

COna

COna

OShc

COna

Dacg

Dp

CObs

COna

OSrs

COna

OSsg OSrs

Dp

Dacg

COnm

Dp

Dp

Dp

Dp

COnm

Dp

Dp

Dp

Dp

Dp

Dp Dp

Dacg

Dacg

Dp

COnm

Dp

COnm

Dp

Dp

COnm

Sb

So

OZn

Sacgr

SOad

SZtb

Dcgr

Sbs

St

Jd

DSdi

Ph

Sagr

Sb

Sdgc

So

Saygp

OZnu

OZtb

So

Dcgr

Dcgr

So Sb

Sbbks

So

Dcgr Dcgrm

Sdgc

Dcgrb

SaygpSayg

Phc

OZn

SOagr

OZnb

SZtb

St

So Sagr

Sacgr

Ssaqd

Ph

OZm

COnu

Dag

OSas

OSp

COtb

Sshd

OSq

COas

COgn

OShc

COna

COtb

OSaygp

COna

OSq

COna

OScs

SDagf COgn SDgd

COna

COna

OShc

COna

Dacg

Dp

COna

CObs

OSrs

COna

OSsg OSrs

Dp

Dacg

COnm

Dp

Dp

Dp

Dp

COnm

Dp

Dp

Dp

Dp

Dp

Dp

Dp

Dacg

Dacg

Dp

Dp

COnm

Dp

COnm

Dp

Dp

COnm

COnm

OZnb

Ssqd

SOagr

Sb

Se

OZf

Sap

Ssd

Oba Obb

Smb Sme

Obb

COf

Ssbh

Ssd

Ssbh

Oba

Obg

Sab

Obg

Sam

Obba

Obba

Ssbh

Obb

Obba

Obb

Obba

Ssbh

Obb

Sab

Sab

Obba

Obba

Ssbh

Ssb

Ssbh

Sap

Ssd

Obba

Ssd

Obb

Obb

Obb

Obba

Sab

Obba

Ssbh

Obba

Obb

Ssbh

Obb

Obba

Ssb

Obb

Obb

Ssbh

Obba

Obb

Obba

Sab

Sap

Ssd

Obba

Ssb

Obb

Obba

Obb

Ssd

Obb

Obba

COf

Ssd

COf

Ssd

Obba

Obb

Obb

Sab

Ssb

Obba

Ssb

Sap

Sap

E

< 11 – 5 – 10 20 < 11 – 10 20 30 

ArseUran

Se Stat

 bouQuad uni

Sme

Ayer Hudson South Groveland

Arsenic

Uranium

Figure 14. Details of change in geologic remapping of the Ayer, Hudson, and South Groveland 7.5-minute quadrangles compared tof Zen and others (1983). <, less than
22 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

This effort reflects an attempt to test if the analysis of 

arsenic and uranium concentrations might be scale-dependent, 

as the 1:250,000 statewide map and 1:24,000 quadrangles 

differ significantly in scale. In New Hampshire, statewide 

analysis of well yield found that detailed (1:24,000) geologic 

maps improved the results of a predictive well-yield probability model over a statewide (1:250,000) model (Moore and 

others, 2002).

Correlations were compared by considering adjusted 

R-squared values for multiple linear regression of log concentration on bedrock unit for each pair of maps, that is, the map of 

Zen and others (1983) published in digital form by Nicholson 

and others (2007) compared to (1) the Ayer quadrangle 

(Kopera, 2006), (2) the Hudson quadrangle (Kopera, 2005) and 

(3) the South Groveland quadrangle (Castle and others, 2005) 

(table 3). Changes in renaming bedrock units alone would not 

change the value of the adjusted R-squared. Only a regrouping 

of well sites could change the R-squared value. 

The adjusted R-squared value is a measure of the fraction 

of variance in the data that is explained by the regression 

variables. Results of the regressions indicate that no more 

variance of log-arsenic concentration is explained in the Ayer 

and Hudson quadrangles by the detailed (1:24,000) geologic 

mapping than by the statewide (1:250,000) mapping. For 

uranium, the adjusted R-squared value is about the same for 

the two mapping scales in the Ayer quadrangle but increases 

in the Hudson quadrangle with the 1:24,000 mapping. In the 

South Groveland quadrangle, more variance is explained 

with the new mapping than the old for both arsenic and 

uranium. One explanation for these results is the ClintonNewbury fault that cuts though each quadrangle. In the Ayer 

and Hudson quadrangles, about half of the wells were in 

the elevated-arsenic zone where correlation with individual 

bedrock units was lacking. In the South Groveland quadrangle, only four wells were in the high arsenic zone, and all 

of these were in the same bedrock unit. Thus, arsenic would 

not improve with remapping for Ayer and Hudson because of 

a general lack of correlation by bedrock unit in much of the 

quadrangles. Uranium, by contrast, improved in two of the 

quadrangles with remapping and stayed about the same in 

the third. Overall, these results suggest that detailed mapping 

improves the ability to explain variance in uranium concentrations by bedrock unit, but that when variability in arsenic 

concentrations occurs at the terrane-scale, detailed mapping is 

less useful.

Table 3. Constituent correlation with bedrock units in 

statewide scale (1:250,000) and quadrangle scale (1:24,000), 

east-central Massachusetts. 

[As, arsenic; U, uranium]

Geologic 

quadrangle Regression Adjusted R-squared P value

Ayer Log As, statewide scale 0.31 0.0001

Ayer Log As, quadrangle scale 0.15 0.0198

Ayer Log U, statewide scale 0.59 0.0000

Ayer Log U, quadrangle scale 0.53 0.0000

Hudson Log As, statewide scale 0.06 0.1952

Hudson Log As, quadrangle scale 0.04 0.2997

Hudson Log U, statewide scale 0.16 0.0225

Hudson Log U, quadrangle scale 0.32 0.0010

South Groveland Log As, statewide scale 0.03 0.3375

South Groveland Log As, quadrangle scale 0.22 0.0578

South Groveland Log U, statewide scale 0.05 0.2673

South Groveland Log U, quadrangle scale 0.17 0.1006

Water-Quality Correlations with Ancillary 

Constituents

Analysis of ancillary constituents, acid neutralizing 

capacity, iron, manganese, and conductance was used to assess 

geochemical associations of arsenic and uranium occurrences. 

This was done using two-parameter plots (fig. 15). The plot 

matrix shows virtually no correlations among constituents. 

Some constituents appear to be mutually exclusive, particularly arsenic and iron, uranium and iron, and arsenic and 

uranium (fig. 15). This is in contrast to the relation found in 

overburden samples, where arsenic and iron are commonly 

correlated (Stollenwerk and Colman, 2003). 

Peters (2008) attributes the difference in iron-arsenic 

association between overburden and bedrock as reflecting the 

lack of organic carbon likely present in bedrock units. Iron and 

arsenic associate in coatings deposited from oxic weathering 

of arsenic minerals, such as arsenopyrite. These coatings 

remain in place unless reducing conditions occur, such as 

associated with the presence of anthropogenic organic carbon 

(Stollenwerk and Colman, 2003; Peters, 2008). Iron concentrations were elevated in the water of some of the tested wells. 

The reducing conditions associated with these wells, however, 

were likely associated with sediments of wetlands or lakes that 

are providing recharge to the bedrock.

Bedrock Units, Geologic Terranes, and Geologic 

Sources of Arsenic and Uranium

The MDEP and the USGS data indicate that elevated 

arsenic in bedrock well water is associated primarily with two 

terranes in Massachusetts, the Merrimack belt and the Nashoba 

zone (figs. 1, 3, and 5). Within the terranes of elevated arsenic 

concentration, arsenic appeared to be correlated with bedrock 
450300150

100250400350200

50

0

0 1,000 2,000 3,000 0 100 200

Conductance, in 

microsiemens per centimeter

0 1,000 2,000 3,000

Conductance, in 

microsiemens per centimeter

Alkalinity, in milligrams 

calcium carbonate per liter

0 100 200

Alkalinity, in milligrams 

calcium carbonate per liter

Iron, in 

micrograms per liter

Arsenic, in 

micrograms per liter

Uranium, in 

micrograms per liter

Manganese, in 

micrograms per liter

m

0 50,000 100,000

Iron, in 

micrograms per liter

0 50,000 100,000

2

0 

Manganese, in 

micrograms per liter

0 1,000 2,000

Manganese, in 

micrograms per liter

0 1,000 2,000

Iron, in 

micrograms per liter

0 50,000 100,000

2,5002,0001,5001,000

500

0

300200100

0

Figure 15. Associations among constituents measured in bedrock wells in east-central Massachusetts, 2009.
24 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

units in some parts of the study area and not correlated in other 

parts (note the elevated-concentration area of fig. 7). Sources of 

the arsenic in the areas that correlated with bedrock units could 

be in the rock protolith; however, the arsenic source in areas 

without bedrock correlation could have resulted from relatively 

equal redistribution of arsenic by metamorphic and/or metasomatic fluids from an original rock source (Henke, 2009). 

Although associated with the Merrimack belt, the elevated 

arsenic did not extend to the western border of the belt (fig. 9). 

The processes responsible for distributing the arsenic that is 

present in well water did not operate throughout the terrane. 

In the Nashoba zone, where correlation between bedrock 

unit and arsenic concentrations was more prevalent, bedrock 

units with elevated arsenic extended to the Bloody Bluff 

fault, the eastern boundary of the zone. Two elevated arsenic 

concentrations were measured east of the Bloody Bluff fault 

in the Milford-Dedham zone, indicating that elevated arsenic 

concentrations are possible east of the Nashoba zone. Little 

previous data on arsenic in bedrock wells is available from this 

area where much of the water supply is public.

In the north, the elevated-arsenic area in Massachusetts 

abuts New Hampshire towns included in the private bedrockwell study by Montgomery and others (2003). In contrast to 

Massachusetts where units were grouped for concentrationprobability analysis, units were grouped by fraction of 

samples greater than 10 μg/L in the New Hampshire study. 

The different statistical approaches prevent exact comparisons 

of data between the two States. Clearly, however, both States 

have elevated arsenic concentrations in the border area.

The association of igneous rock with uranium results from 

its deposition during magma cooling (Keevil and others, 1944). 

Uranium is one of the last elements to come out of solution, 

and it associates with rock surfaces from which mobilization into well water can occur. A report on uranium potential 

in two-mica granites of New England indicates that certain 

mineralized granites in New Hampshire and Massachusetts 

contain secondary uranyl-phosphate minerals (Boudette, 1977). 

Mobilization of uranium can occur in oxic conditions that are 

common in New England bedrock aquifers.

Maps of Estimated Probability for 

Elevated Arsenic and Uranium in 

Groundwater

Arsenic

Determination of probability of wells yielding water with 

arsenic concentration greater than the USEPA public drinkingwater standard (10 μg/L) could help guide development 

of new supplies—domestic and public—and the testing of 

existing wells. Because of correlations of arsenic with bedrock 

unit and with groups of bedrock units described in a previous 

section on correlations, concentration distributions can be 

defined by bedrock unit. Cumulative distribution functions 

can be used to determine overstandard probabilities as well 

as probabilities of wells yielding water at levels of concentration greater than any given value (fig. 16). The distribution 

for each unit fits a log-normal distribution, and 95-percent 

confidence intervals based on the log-normal distribution can 

be computed (apps. 3 and 4). 

The confidence interval of probability estimates 

depends on the number of samples for the bedrock unit and 

the concentration for which the probability is of interest. 

Probability distributions based on randomly selected samples 

of a population become more accurate as the sample size 

gets larger. Therefore, confidence intervals are a function 

of the number of samples. Finally, the probabilities can 

Cumulative probability, in percent 

Arsenic, in micrograms per liter

EXPLANATION EXPLANATION Cumulative probability, in percent 

Arsenic, in micrograms per liter

0 5 10 15 20

100

80

60

40

20

0

0 20 40 60 80 100

100

80

60

40

20

0

95-percent confidence

bounds of fit

Log-normal fit

95-percent confidence

bounds of fit

Log-normal fit

Data for bedrock unit OZn Data for bedrock unit OZnb

Figure 16. Cumulative probabilities for arsenic for two bedrock units east of the Clinton-Newbury fault. 
Arsenic and Uranium Concentrations and Correlations with Bedrock Units 25

0 20 MILES

0 10

10

Base geology from Zen and others (1983), digitized by Nicholson and others (2007), 20 KILOMETERS

scale 1:250,000, NAD 1983, StatePlane Massachusetts Mainland FIPS 2001,

Lambert Conformal Conic projection

72°00' 71°00'

42°30'

42°00'

Primary study

area boundary

Secondary study

area boundary

Town boundary

< 0.5

0.5 – < 2

2 – < 5

5 – < 10

10 – 25

No data

EXPLANATION

Probability, in percent, of

exceeding arsenic standard

Figure 17. Probabilities of arsenic concentrations in bedrock well water being greater than 10 micrograms per liter, the 

U.S. Environmental Protection Agency drinking-water standard for public supplies, east-central Massachusetts. <, less than
26 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

be mapped so that areas with higher or lower probabilities 

of concentration than a given level (such as the USEPA 

drinking-water standard for public water supply) can be 

known (fig. 17). For example, the probability that a well 

in the OZn bedrock unit will contain water with an arsenic 

concentration greater than 10 μg/L (equal to 100 percent 

minus the cumulative probabililty) is low—0.79 percent with 

95-percent confidence interval of 0.05 to 6.6 percent (fig. 16 

and app. 3). The probability that a well will contain water 

with arsenic concentration greater than 10 μg/L for OZnb, an 

elevated-concentration unit, is 26 percent with a 95-percent 

confidence interval of 13 to 43 percent. 

Bedrock units in the elevated-concentration area (fig. 7) 

were grouped for computing cumulative probabilities. 

The probability of well water being greater than 10 μg/L for 

the elevated-concentration grouping of units was 23 percent, 

exceeded only by OZnb at 25 percent. 

Uranium

In this study, uranium is more generally correlated to 

bedrock unit than is arsenic, so uranium associations can be 

mapped exclusively by bedrock unit. Distributions of uranium 

concentration in a bedrock unit are log normal. Cumulative 

log-normal distributions indicate the probability of concentrations occurring for the whole range of concentrations, including 

the probability of exceeding 30 μg/L, the USEPA drinkingwater standard for public supplies. The 95-percent confidence 

intervals of the probability estimates can also be determined 

from the log-normal fits (fig. 18, apps. 5 and 6). The uncertainty of the predictions—that is, the size of the confidence 

interval—decreases at high and low ends of the concentration 

range (fig. 18). 

Example probabilities of encountering a concentration 

greater than 30 μg/L ( fig. 18) range from 0.0001 percent 

(95-percent confidence interval of 0.0 to 0.005 percent) for 

Ops, to 21 percent (95-percent confidence interval of 5.5 to 

50 percent) for Dcgr. Areas with granitic rock have higher 

probabilities (figs. 5 and 19).

Estimates of the Number of Wells that Exceed 

USEPA Drinking-Water Standards

Estimates of the number of wells affected can be determined 

by the product of the probability for well water to exceed 

the USEPA standard and the estimated number of wells per 

bedrock unit.

Estimates of private well distributions were made for the 

MDPH by Weston & Sampson Engineers, Inc., during 2005 

(fig. 20). Potential private wells were identified by crossreferencing addresses in property-tax-assessment databases 

0 20 40 60 80 100 120 140 160 180 200

Cumulative probability, in percent

Uranium, in micrograms per liter Uranium, in micrograms per liter

EXPLANATION EXPLANATION 

0 20 40 60 80 100

0

20

40

60

80

100

0

20

40

60

80

100

Data for bedrock unit Dfgr

Log-normal fit

95-percent confidence bounds of fit 95-percent confidence bounds of fit 

Log-normal fit 

Data for bedrock unit Sb

Cumulative probability, in percent

Figure 18. Cumulative log-normal distribution functions for uranium in an elevated-concentration bedrock unit, Dfgr, 

and a low-concentration bedrock unit, Sb, east-central Massachusetts.
Maps of Estimated Probability for Elevated Arsenic and Uranium in Groundwater 27

0 20 MILES

0 10

10

20 KILOMETERS

Primary study

area boundary

Secondary

study area

boundary

72°00' 71°00'

42°40'

42°20'

42°00'

Town boundary

EXPLANATION

Probability, in percent, of

exceeding uranium standard

< 0.5

0.5 – < 2

2 – < 5

5 – < 10

10 – 25

Base geology from Zen and others (1983), digitized by Nicholson and others (2007), 

scale 1:250,000, NAD 1983, StatePlane Massachusetts Mainland FIPS 2001,

Lambert Conformal Conic projection

Figure 19. Probabilities of uranium concentrations in bedrock well water being greater than 30 micrograms per liter, the U.S. 

Environmental Protection Agency drinking water standard for public supplies, east-central Massachusetts. <, less than

with those in water-billing databases. The addresses in the 

tax-assessment databases that did not have a match in the 

water-billing databases were classified as potential private 

wells. In communities not served by a public water supply, all 

addresses contained in the tax-assessment data were classified 

as potential private wells. For the purposes of the estimate, all 

the inferred private wells were assumed to be bedrock wells. 

All the potential private well addresses were geocoded using 

the GDT/TeleAtlas Batch Geocoding Service®. 

Not all towns in the study area were included in the 

MDPH inferred private-well investigation (fig. 20). The 1990 

census, which provided information about households per 

census track and percentage of households on public or private 

water, was used to supplement well estimates in locations not 

covered by MDPH (U.S. Census, 1992). The census areas in 

towns not covered by the MDPH study were intersected with 

the bedrock data using Geographic Information System (GIS) 

techniques to delineate parts of census tracts that were in each 
28 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

0 20 MILES

0 10

10

20 KILOMETERS

72°00' 71°00'

42°40'

42°20'

42°00'

Base geology from Zen and others (1983), digitized by Nicholson and others (2007), 

scale 1:250,000, NAD 1983, StatePlane Massachusetts Mainland FIPS 2001,

Lambert Conformal Conic projection, Census data from U.S. Census (1992)

Primary study

area boundary Secondary study

area boundary

EXPLANATION

Massachusetts Department of Public

Health inferred well location

Census tract

Figure 20. Inferred locations of private wells and census tracts for towns not included in the inferred private-well 

study, east-central Massachusetts.
Maps of Estimated Probability for Elevated Arsenic and Uranium in Groundwater 29

Table 4. Number of wells in each bedrock unit and estimates of number of wells exceeding the arsenic and uranium U.S. 

Environmental Protection Agency drinking-water standards for public supplies, east-central Massachusetts. 

[* , bedrock unit within the high-arsenic zone; —, no data; MDPH, Massachusetts Department of Public Health; μg/L, micrograms per liter; standard, 

U.S.Environmental Protection Agency public drinking-water standard]

Bedrock unit

Total number 

of MDPH 

wells

Total number 

of estimated 

census 

wells

Probability 

of arsenic 

concentrations 

greater than 10 μg/L, 

in percent

Probability 

of uranium 

concentrations 

greater than 30 μg/L, 

in percent

Estimated number 

of wells exceeding 

the 10 μg/L 

standard for 

arsenic

Estimated number 

of wells exceeding 

the 30 μg/L 

standard for 

uranium

Grouped elevatedarsenic units13,500 5,763 23.08 — 4,445 —

Dcgr* 418 1,275 — 21.01 — 356

Dfgr* 1,522 702 — 13.97 — 311

Dl 2,010 8,024 0.00 0.03 0 3

DSw* 382 629 — 0.13 — 1

Ops 770 7,707 0.10 0.00 8 0

OZf 0 507 7.64 0.01 39 0

OZm 735 679 10.83 4.64 153 66

OZn 7,007 5,621 0.79 0.89 100 113

OZnb 930 1,357 25.50 0.70 583 16

Ph* 60 0 — 11.99 — 7

Sacgr* 884 373 — 8.43 — 106

Sagr* 971 1,013 — 12.54 — 249

Sb* 2,315 4,594 — 0.69 — 47

Sbs* 67 133 — 0.00 — 0

Se* 305 492 — 0.00 — 0

Sgr 0 533 0.00 0.64 0 3

So* 1,374 2,406 — 1.55 — 59

SOagr 569 2,326 6.92 4.11 200 119

SObo* 0 236 — 12.42 — 29

Sp 2,862 10,343 0.00 4.61 0 609

Spsq 85 238 0.14 0.07 0 0

Spss 908 723 0.38 0.18 6 3

Ssqd 224 2,982 4.63 2.53 148 81

St* 245 150 — 0.76 — 3

SZtb 861 464 3.68 0.17 49 2

Zpg 2,197 1,361 0.02 6.94 1 247

Zsg 5,012 2,972 0.10 10.61 8 847

Totals 32,713 57,840 5,741 3,277
30 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

bedrock unit. The number of wells per census tract was then 

adjusted by the proportional area of the tract that was in the 

bedrock unit. Finally, all the wells in the parts of tracts in a 

bedrock unit were added to determine the number of wells in 

each unit. The number of wells estimated to exceed a standard 

was determined by multiplying the probability of exceeding 

a standard for that bedrock unit by the sum of the number of 

wells determined from the MDPH assessment and the census 

assessment (table 4).

Arsenic

For arsenic, no probability was given in table 4 for 

bedrock units that were within the elevated-arsenic area. 

Rather, the probabilities for the units in this area are covered 

by the grouped-units estimate (top of table 4). 

The number of wells with arsenic concentrations that 

exceeded the USEPA drinking-water standard was estimated 

to be 5,741. Because the study area covered most of the 

known elevated-concentration areas for the State, this estimate 

is likely appropriate for the entire State. Several small units 

within the study area did not have enough data for probability 

statistics to be computed; however, these would not greatly 

alter the total.

Uranium

For uranium, correlations were strictly with bedrock 

units rather than grouped units (table 4). The number of wells 

with uranium concentrations that exceeded the standard for 

uranium was estimated to be 3,277. Most of these wells are in 

igneous rock. Because units west of the Clinton-Newbury fault 

were not grouped on an areal basis for uranium, several more 

bedrock units were excluded from the calculation of probability statistics than for arsenic. 

Igneous bedrock units in Massachusetts are not confined 

to the primary and secondary study areas of this investigation. 

The statewide number of wells affected by uranium is likely 

larger than the number reported herein, based on the bedrock 

units in the study areas. 

Implications for New Supplies, 

Testing, and Treatment

Locating Future Bedrock Water Supplies

Few private well owners have options regarding choosing 

locations that have favorable bedrock. For private supply, the 

probability maps (figs. 17 and 19) can be used to guide wellwater testing. 

Although the data collected were from private wells, 

the data could be used to assess conditions likely in public as 

well as private bedrock water supplies. Commonly, there are 

several site options for locating public wells. Consideration of 

the bedrock unit when selecting sites for public supplies could 

result in substantially decreased probabilities of concentrations 

exceeding the drinking-water standard. Towns that straddle 

the Clinton-Newbury fault, such as Harvard and Westford, 

could make use of the result that there is a lower probability 

of elevated arsenic concentration in the rocks east of the fault 

than those to the west.

Directing Resources for Water Testing

The numbers of overstandard water supplies without 

treatment can be computed by using the fraction of households 

currently using water without treatment for arsenic (66 percent 

of 5,741 = 3,789) and uranium (93 percent of 3,277 = 3,047). 

If testing could be directed toward the elevated-concentration 

areas, these numbers of untreated supplies would presumably 

decrease. By testing all wells that are in bedrock units with 

probabilities of elevated arsenic concentration greater than 

10 percent, 90 percent of the wells exceeding the standard 

could be identified. Applied to data collected in this investigation, for example, all but two wells exceeding the standard 

(which are in SZtb with concentrations of 10 and 20 μg/L) 

would have been tested. This approach is likely to include 

testing of the highest concentration wells, because the elevated 

concentrations are associated with bedrock units that have 

the highest probabilities of overstandard concentrations. For 

example, of the two wells that were missed by this approach, 

one had a concentration at the standard and one had a concentration twice the standard; the highest concentration well 

tested in this study had a concentration 150 times the standard. 

Because health risk increases with increasing concentration, a testing routine that likely includes the highest 

concentrations is beneficial. The 10-percent probability 

testing algorithm would result in testing 26 percent of all the 

wells estimated to be in the study areas. As a fraction of wells 

statewide, the percentage of wells tested would, of course, be 

much smaller. 

For uranium, to determine 90 percent of wells greater 

than the standard, all units with overstandard probability of 

4 percent or greater would need to be analyzed. This would 

involve testing about 40 percent of the wells in the study area. 

Defining Natural Background Concentrations

A problem for site-contamination assessment in areas 

where arsenic occurs naturally is whether concentrations at a 

given site are caused by natural conditions or are the result of 

human-induced activity. In cases where there is a possibility 

that the bedrock has been contaminated with anthropogenic 

arsenic, the distribution frequencies of concentration for a 

given bedrock unit could be used to assess whether or not 

the distribution frequency of concentration at a site that is 

suspected of contamination is significantly different from 

natural conditions. 
References Cited 31

Summary

This investigation is the first regional-scale study of 

arsenic concentrations in water from private wells completed 

in bedrock throughout east-central Massachusetts, the region 

of elevated-arsenic concentrations in the State. Measurements 

of uranium concentrations also were included in the investigation, because uranium, similar to arsenic, likely has a bedrock 

source. Although private water supplies are not subject to new 

U.S. Environmental Protection Agency (USEPA) drinkingwater standards for public-water supplies, such as those established for arsenic and uranium in the last 7 years of 10 and 30 

micrograms per liter, respectively, the standards are thresholds 

whereby private well users can assess the need for water treatment. Concentration data are needed for arsenic and uranium 

concentrations to (1) assess the geographic distribution of 

elevated concentrations, (2) guide testing of existing supplies, 

and (3) develop new supplies. These needs were addressed 

by correlating concentrations of arsenic and uranium with 

bedrock units and applying the correlations to the mapped 

distributions of wells. For arsenic, the number of overstandard 

wells estimated by these methods in the study area would 

account for most of the overstandard wells in the State. For 

uranium, the number of overstandard wells estimated for the 

study area would be less than the total for the State, because 

bedrock units with elevated concentrations of uranium are also 

expected outside of the region of this study. 

Samples were collected by private well users that 

responded to sampling kits that were mailed to randomly 

selected well addresses. An instruction sheet and water-use 

questionnaire were included in the sampling kit. Of the 

wells randomly sampled, 13 percent had concentrations 

that exceeded the drinking-water standard for arsenic, 

and 3.5 percent exceeded the drinking-water standard 

for uranium. 

One-way ANOVA analysis of log-transformed concentration data indicated significant differences for arsenic and for 

uranium concentration populations grouped by bedrock unit in 

most of the study area. However, an area of elevated arsenic 

concentrations was identified west of the Clinton-Newbury 

fault, where there were no significant differences in arsenic 

concentrations among the bedrock units. Lack of correlation 

with individual bedrock units in this area could have resulted 

from relatively equal redistribution of arsenic by metamorphic 

and/or metasomatic fluids. 

Concentrations of arsenic and uranium fit log-normal 

distributions for populations separated by bedrock unit. For 

each bedrock unit, log-normal fits of the data were used 

to determine probabilities of concentrations exceeding the 

drinking-water standards. Overstandard probabilities were as 

great as 26 percent for arsenic in a unit containing amphibolite 

and 21 percent for uranium in a granitic unit.

Water-use data from the well users indicated that most 

of the overstandard wells were being used for drinking water 

without treatment—66 percent for arsenic and 93 percent 

for uranium. This data together with probability and 

well-distribution data were used to estimate the potential total 

number of wells in the study area used for drinking water 

without treatment: approximately 3,800 for arsenic and 3,000 

for uranium. 

Probability and well-distribution data were also used to 

determine the sampling effort required to locate 90 percent 

of the estimated overstandard wells. For arsenic, this could 

be achieved by sampling wells in those bedrock units with an 

overstandard probability of 10 percent or greater. This would 

involve sampling 26 percent of the total number of wells 

in the study area. For uranium, 90 percent of overstandard 

wells could be determined by sampling wells in bedrock 

units with an overstandard probability of 4 percent or greater. 

This would involve sampling 40 percent of all the wells in the 

study area. 

Increased sampling in the investigation was directed 

in the regions of three 1:24,000 quadrangles where recent 

detailed geologic mapping had been conducted. Improved 

correlations of arsenic and uranium with bedrock unit were 

measured for two of the three quadrangles compared to the 

correlations made with the statewide map. 

The correlations with bedrock are compatible with a 

natural bedrock source of the contaminants. By addressing 

the potential for contamination of bedrock wells in areas of 

increased contamination probability, well owners and resource 

managers can better assess risk.

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34 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 
Appendix 1. Abbreviations and Descriptions for Bedrock 

Units in and Adjacent to the Study Area
36 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 1. Abbreviations and descriptions for bedrock units in and adjacent to the study area. —Continued

[Fm, formation; Mbr, member; bedrock unit abbreviations and descriptions are from Zen and others, 1983]

Bedrock unit 

abbreviation Age Bedrock unit descriptions

Cbw Cambrian Braintree Argillite and Weymouth Fm—argillite, with some rare limestone

Cg Cambrian Green Lodge Fm of Rhodes and Graves (1931)—quartzite and slate

Ch Cambrian Hoppin Fm—quartzite, argillite, and minor limestone

cu Unknown age Cumberlandite—rock containing magnetite, ilmenite, olivine, labradorite, and spinel

Dcgr Devonian Chelmsford Granite—muscovite-biotite granite

Dchgr Devonian Coys Hill Porphyritic Granite Gneiss—microcline granite gneiss

Dchh Devonian Coys Hill Porphyritic Granite Gneiss— hornblende gneiss inclusions

Dcygr Devonian Cherry Hill Granite—alaskite granite containing ferro-hornblende

Ddi Devonian Hardwick Tonalite: Biotite-hornblende diorite and quartz-bearing diorite 

Ddn Devonian Hardwick Tonalite: Meladiorite and norite

Dfgd Devonian Fitchburg Complex—biotite granodiorite to tonalite gneiss

Dfgds Devonian Fitchburg Complex—biotite-muscovite granitic gneiss with mica schist and feldspathic 

granulite inclusions

Dfgr Devonian Fitchburg Complex—muscovite-biotite granite

Dfgrg Devonian Fitchburg Complex—biotite-muscovite granite to granodiorite gneiss

Dft Devonian Fitchburg Complex—biotite-hornblende tonalite inclusions

Dgd Devonian Granodiorite

Dgr Devonian Biotite-muscovite granite

Dhgr Devonian Hardwick Tonalite—porhyritic microcline-biotite granite gneiss

Dht Devonian Hardwick Tonalite—biotite tonalite to granodiorite gneiss

Dl Devonian Littleton Fm

Dl+Ops Devonian Littleton and Partridge Fms, interfolded

Dl+Ops Devonian Partridge Fm—interfolded Littleton and Partridge Fms

Dlf Devonian Littleton Fm—quartz-feldspar-garnet gneiss, probably felsic metavolcanic rock

Dlm Devonian Littleton Fm—calcitic marble

Dlo Devonian Littleton Fm—orthopyroxene-biotite gneiss, probably intermediate metavolcanic rock

Dmgr Devonian Muscovite-biotite granite

DOgr Devonian/Ordovician Alkalic granite in Franklin

Dpgr Devonian Peabody Granite—alkalic granite containing ferro-hornblende

Drgr Devonian Granite of Rattlesnake Hill pluton—biotite-granite and fine-grained riebeckite granite

Drh Devonian Hardwick Tonalite: Biotite-garnet-feldspar gneiss of Ragged Hill 

DSdi Devonian/Silurian Diorite and tonalite

DSn Devonian/Silurian Newbury Volcanic Complex—undivided sedimentray and volcanic rocks

DSna Devonian/Silurian Newbury Volcanic Complex—porphyritic andesite, includes tuffaceous mudstone

DSnl Devonian/Silurian Newbury Volcanic Complex—basalt, andesite, rhyolite, and tuff

DSnr Devonian/Silurian Newbury Volcanic Complex—micrographic rhyolite

DSnu Devonian/Silurian Newbury Volcanic Complex—calcareous mudstone, red mudstone, and siliceous siltstone

DSw Devonian/Silurian Worcester Fm—carbonaceous slate and phyllite and minor metagraywacke

Dwm Devonian Wenham Monzonite—monzonite containing ferro-hornblende

DZl Devonian Lynn Volcanic Complex—rhyolite, agglomerate, and tuff

fgr Unknown age Fine-grained granite and granite porphyry
Appendix 1 37

Appendix 1. Abbreviations and descriptions for bedrock units in and adjacent to the study area. —Continued

[Fm, formation; Mbr, member; bedrock unit abbreviations and descriptions are from Zen and others, 1983]

Bedrock unit 

abbreviation Age Bedrock unit descriptions

gb Precambrian to Paleozoic Hornblende-olivine gabbro

Cbw Cambrian Braintree Argillite and Weymouth Fm—argillite, with some rare limestone

Cg Cambrian Green Lodge Fm of Rhodes and Graves (1931)—quartzite and slate

Ch Cambrian Hoppin Fm—quartzite, argillite, and minor limestone

cu Unknown age Cumberlandite—rock containing magnetite, ilmenite, olivine, labradorite, and spinel

Dcgr Devonian Chelmsford Granite—muscovite-biotite granite

Dchgr Devonian Coys Hill Porphyritic Granite Gneiss—microcline granite gneiss

Dchh Devonian Coys Hill Porphyritic Granite Gneiss— hornblende gneiss inclusions

Dcygr Devonian Cherry Hill Granite—alaskite granite containing ferro-hornblende

Ddi Devonian Hardwick Tonalite: Biotite-hornblende diorite and quartz-bearing diorite 

Ddn Devonian Hardwick Tonalite: Meladiorite and norite

Dfgd Devonian Fitchburg Complex—biotite granodiorite to tonalite gneiss

Dfgds Devonian Fitchburg Complex—biotite-muscovite granitic gneiss with mica schist and feldspathic 

granulite inclusions

Dfgr Devonian Fitchburg Complex—muscovite-biotite granite

Dfgrg Devonian Fitchburg Complex—biotite-muscovite granite to granodiorite gneiss

Dft Devonian Fitchburg Complex—biotite-hornblende tonalite inclusions

Dgd Devonian Granodiorite

Dgr Devonian Biotite-muscovite granite

Dhgr Devonian Hardwick Tonalite—porhyritic microcline-biotite granite gneiss

Dht Devonian Hardwick Tonalite—biotite tonalite to granodiorite gneiss

Dl Devonian Littleton Fm

Dl+Ops Devonian Littleton and Partridge Fms, interfolded

Dl+Ops Devonian Partridge Fm—interfolded Littleton and Partridge Fms

Dlf Devonian Littleton Fm—quartz-feldspar-garnet gneiss, probably felsic metavolcanic rock

Dlm Devonian Littleton Fm—calcitic marble

Dlo Devonian Littleton Fm—orthopyroxene-biotite gneiss, probably intermediate metavolcanic rock

Dmgr Devonian Muscovite-biotite granite

DOgr Devonian/Ordovician Alkalic granite in Franklin

Dpgr Devonian Peabody Granite—alkalic granite containing ferro-hornblende

Drgr Devonian Granite of Rattlesnake Hill pluton—biotite-granite and fine-grained riebeckite granite

Drh Devonian Hardwick Tonalite: Biotite-garnet-feldspar gneiss of Ragged Hill 

DSdi Devonian/Silurian Diorite and tonalite

DSn Devonian/Silurian Newbury Volcanic Complex—undivided sedimentray and volcanic rocks

DSna Devonian/Silurian Newbury Volcanic Complex—porphyritic andesite, includes tuffaceous mudstone

DSnl Devonian/Silurian Newbury Volcanic Complex—basalt, andesite, rhyolite, and tuff

DSnr Devonian/Silurian Newbury Volcanic Complex—micrographic rhyolite

DSnu Devonian/Silurian Newbury Volcanic Complex—calcareous mudstone, red mudstone, and siliceous siltstone

DSw Devonian/Silurian Worcester Fm—carbonaceous slate and phyllite and minor metagraywacke

Dwm Devonian Wenham Monzonite—monzonite containing ferro-hornblende

DZl Devonian Lynn Volcanic Complex—rhyolite, agglomerate, and tuff
38 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 1. Abbreviations and descriptions for bedrock units in and adjacent to the study area. —Continued

[Fm, formation; Mbr, member; bedrock unit abbreviations and descriptions are from Zen and others, 1983]

Bedrock unit 

abbreviation Age Bedrock unit descriptions

fgr Unknown age Fine-grained granite and granite porphyry

gb Precambrian to Paleozoic Hornblende-olivine gabbro

gd Precambrian to Paleozoic Granodiorite

gr Precambrian to Paleozoic Granite

grg Devonian Biotite granitic gneiss

hg Precambrian to Paleozoic Hornblende-plagioclase gneiss

igd Precambrian to Paleozoic Granodiorite of the Indian Head pluton—biotite granodiorite and 

hornblende-biotite tonalite

Jd Jurassic Diabase dikes and sills

Jsi Jurassic Silicified fault-breccia or strongly silicified metamorphic rocks

K Cretaceous Cretaceous sediments—clay, silt, sand, and gravel, mostly non-marine and near-shore

mgr Precambrian to Silurian Muscovite granite

Ogl Ordovician Glastonbury Gneiss—granitic gneiss

Ongb Ordovician Nahant Gabbro and gabbro at Salem Neck—labradorite-pyroxene gabbro, hornblende 

gabbro, and hornblende diorite

Opa Ordovician Partridge Fm—amphibolite

Opau Ordovician Partridge Fm—sillimanite-feldspar augen gneiss

Opbg Ordovician Partridge Fm—biotite gneiss

Opc Ordovician Pauchaug Gneiss—granitic gneiss

Opf Ordovician Partridge Fm—felsic gneiss, metavolcanic, and minor amphibolite

Ops Ordovician Partridge Fm—sulfidic mica schist and subordinate amphibolite

Opsa Ordovician Partridge Fm—sulfidic mica schist and abundant amphibolite

Opsc Ordovician Partridge Fm—sulfidic schist and abundant calc-silicate

Opsg Ordovician Partridge Fm—felsic gneiss and schist

Opu Ordovician Partridge Fm—ultramafic lenses, commonly hornblendite 

Opv Ordovician Partridge Fm—mafic and felsic gneisses, metavolcanic, with calc-silicate granofels

Opvs Ordovician Partridge Fm—biotite gneiss, metavolcanic; minor amphibolite and sulfidic schist

OZf Neoproterozoic Fish Brook Gneiss—biotite-plagioclase quartz gneiss

OZm Neoproterozoic Marlboro Fm—amphibolite, biotite schist and gneiss, minor calc-silicate granofels and felsic 

granofels

OZma Neoproterozoic Massabesic Gneiss Complex—biotite feldspar paragneiss intruded by potassium-feldsparrich gneiss

OZmg Neoproterozoic Marlboro Fm—feldspathic gneiss

OZn Neoproterozoic Nashoba Fm—sillimanite schist and gneiss, partly sulfidc, amphibolite, biotite gneiss, calcsilicate gneiss, and marble

OZnb Neoproterozoic Nashoba Fm: Boxford Mbr—massive amphibolite, minor biotite gneiss

OZq Neoproterozoic Quinebaug Fm—amphibolite, biotite, and hornblende gneiss, felsic gneiss, and calc-silicate 

gneiss

OZsh Neoproterozoic Shawsheen Gneiss—sillimanite gneiss, sulfidic at base; minor amphibolite

OZt Neoproterozoic Tatnic Hill Fm—sulfidic sillimanite schist, sillimanite schist and gneiss, biotite gneiss; 

minor amphibolite, calc-silicate gneiss and marble

OZtf Neoproterozoic Tatnic Hill Fm: Fly Pond Mbr—calc-silicate gneiss and marble
Appendix 1 39

Appendix 1. Abbreviations and descriptions for bedrock units in and adjacent to the study area. —Continued

[Fm, formation; Mbr, member; bedrock unit abbreviations and descriptions are from Zen and others, 1983]

Bedrock unit 

abbreviation Age Bedrock unit descriptions

OZty Neoproterozoic Tatnic Hill Fm: Yantic Mbr—grey mica schist

Pcm Pennsylvanian Coal Mine Brook Fm—carbonaceous slate and garnet phyllite; lens of meta-anthracite; 

conglomerate and arkose

Pd Pennsylvanian Dighton Conglomerate—coarse conglomerate having sandy matrix; minor sandstone

Pgr Pennsylvanian Biotite granite, with magnetite-bearing pegmatite

Ph Pennsylvanian Harvard Conglomerate—conglomerate and chloritoid-hematite phyllite

Pp Pennsylvanian Pondville Conglomerate—quartz conglomerate having abundant sandy matrix; boulder 

conglomerate; arkose

Pr Pennsylvanian Rhode Island Fm—sandstone, graywacke, shale, and conglomerate; minor beds of metaantracite

Prc Pennsylvanian Rhode Island Fm—conglomerate, sandstone, and graywacke

Pw Pennsylvanian Wamsutta Fm—red to pink conglomerate, graywacke, sandstone, and shale

Pwv Pennsylvanian Wamsutta Fm—rhyolite and mafic volcanic rocks

PZb Unknown age Bellingham Conglomerate—red and gray metamorphosed conglomerate, sandstone, graywacke, and shale

PzZc Proterozoic Z to earliest 

Paleozoic

Cambridge Argillite—gray argillite and minor quartzite; rare sandstone and conglomerate

PzZr Proterozoic Z to earliest 

Paleozoic

Roxbury Conglomerate—conglomerate, sandstone, siltstone, argillite, and melaphyre

PzZrb Proterozoic Z to earliest 

Paleozoic

Roxbury Conglomerate—melaphyre

q Unknown age Massive quartz and silicified rock

qd Precambrian to 

Phanerozoic

Quartz diorite

Sacgr Silurian Ayer Granite—Clinton facies, porphyritic biotite granite

Sagr Silurian Ayer Granite—granite to tonalite

Sb Silurian Berwick Fm—metamorphosed calcareous sandstone, silstone, and minor muscovite schist (1 

polygon)

Sb Silurian Berwick Fm—metamorphosed calcareous sandstone, silstone, and minor muscovite schist

Sbs Silurian Berwick Fm—mica schist

Se Silurian Eliot Fm—phyllite and calcareous phyllite

Sfs Silurian Fitch Fm—sulfidic calc-silicate and minor sulfidic schist 

Sfss Silurian Fitch Fm—sulfidic mica schist

Sgr Silurian Rusty-weathering biotite granite to granodiorite

Sngr Silurian Newburyport Complex—porphyritic granite with microcline phenocrysts

So Silurian Oakdale Fm—metamorphosed pelitic and calcareous siltsone and muscovite schist

SOad Silurian Ayer Granite—Devens-Long Pond facies, porphyritic gneissic biotite granite and granodiorite

SOagr Silurian Andover Granite—muscovite-biotite granite

SObgr Silurian Blue Hill Granite Porphyry—microperthite-quartz porphyry

SObo Silurian Boylston Schist—carbonaceous phyllite and schist, locally sulfidic; quartzite; calc-silicate beds

SOcb Silurian Cape Ann Complex: Beverly Syenite

SOcgr Silurian Cape Ann Complex—alkalic granite to quartz syenite containing ferro-hornblende

SOcsm Silurian Cape Ann Complex: Squam Granite—monzodiorite

SOk Silurian Kittery Fm—quartzite, partly calcareous; phyllite, schist
40 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 1. Abbreviations and descriptions for bedrock units in and adjacent to the study area. —Continued

[Fm, formation; Mbr, member; bedrock unit abbreviations and descriptions are from Zen and others, 1983]

Bedrock unit 

abbreviation Age Bedrock unit descriptions

SOngd Silurian Newburyport Complex—tonalite and granodiorite

SOqgr Silurian Quincy Granite—alkalic granite containing riebeckite and aegirine

SOrh Silurian Reubens Hill Fm—amphibolite, hornblende-chlorite schist, and feldspathic schist; includes 

metamorphosed diorite

SOvh Silurian Vaughn Hills Quartzite—quartzite, phyllite, conglomerate, and chlorite schist

Sp Silurian Paxton Fm—biotite granofels, calc-silicate granofels, and sulfidic schist 

Spa Silurian Paxton Fm—amphibolite

Spbc Silurian Paxton Fm—diopside calc-silicate granofels

Spbs Silurian Paxton Fm: Bigelow Brook Mbr—biotite granofels, sulfidic schist, and minor calc-silicate 

granofels

Spqr Silurian Paxton Fm—rusty-weathering sulfidic quartzite and sulfidic schist

Spso Silurian Paxton Fm: Southbridge Mbr—biotite granofels and calc-silicate granofels

Spsq Silurian Paxton Fm—sulfidic magnesian biotite and magnesian cordierite schist and sillimanite 

quartzite

Spss Silurian Paxton Fm—sulfidic mica schist

Ssaqd Silurian Straw Hollow Diorite and Assabet Quartz Diorite, undifferentiated—biotite-hornblende 

diorite and quartz diorite

Ssqd Silurian Sharpners Pond Diorite—biotite-hornblende tonalite and diorite

St Silurian Tower Hill Quartzite—quartzite and phyllite

Sts Silurian Tower Hill Quartzite—gray phyllite

SZtb Silurian Tadmuck Brook Schist—andalusite phyllite and sillimanite schist, partly sulfidic; local 

quartzite

T Tertiary Tertiary sediments—unconsolidated sand, silt, and clay in discontinuous patches

TRe Triassic Red arkosic conglomerate, sandstone, and siltstone

u Precambrian to 

Phanerozoic

Serpentinite

Zagr Neoproterozoic Alaskite—mafic-poor gneissic granite, commonly containing muscovite

Zb Proterozoic Z Blackstone Group—undivided, quartzite, schist, phyllite, marble, and metavolcanic rocks

Zbq Proterozoic Z Blackstone Group: Quinnville Quartzite

Zbs Proterozoic Z Blackstone Group—mica schist and phyllite

Zbv Proterozoic Z Blackstone Group—greenstone and amphibolite

Zdgr Proterozoic Z Dedham Granite—granite; includes dioritic rock

Zdi Proterozoic Z Diorite—hornblende diorite metamorhosed in part to amphibolite and hornblende gneiss

Zdigb Proterozoic Z Diorite and gabbro—complex of diorite and gabbro, sub. metavolcanic rocks and intrusive 

granite and granodiorite

Zdngr Proterozoic Z Dedham Granite—granite to granodiorite

Zegr Proterozoic Z Esmond Granite—biotite granite

Zfgr Proterozoic Z Granite of the Fall River pluton—biotite granite, in part mafic poor

Zfm Proterozoic Z Felsic and mafic volcanic rocks

Zgb Proterozoic Z Gabbro—hornblende gabbro and hornblende-pyroxene gabbro metamorphosed in part to 

hornblende gneiss and amphibolite

Zgg Proterozoic Z Granite, gneiss, and schist, undivided—plutonic and metamorphic rocks

Zgmgd Proterozoic Z Grant Mills Granodiorite—porphyritic granodiorite
Appendix 1 41

Appendix 1. Abbreviations and descriptions for bedrock units in and adjacent to the study area. —Continued

[Fm, formation; Mbr, member; bedrock unit abbreviations and descriptions are from Zen and others, 1983]

Bedrock unit 

abbreviation Age Bedrock unit descriptions

Zgn Proterozoic Z Biotite gneiss near New Bedford—feldspathic gneiss

Zgr Proterozoic Z Biotite granite

Zgs Proterozoic Z Gneiss and schist near New Bedford—hornblende and biotite schist and gneiss, amphibolite

Zhg Proterozoic Z Hope Valley Alaskite Gneiss—mafic-poor gneissic granite, locally containing muscovite

Zm Proterozoic Z Mattapan Volcanic Complex—rhyolite, melaphyre, agglomerate, and tuff

Zmgd Proterozoic Z Milford Granite—seriate to subporphyritic granite to granodiorite, locally gneissic

Zmgr Proterozoic Z Milford Granite—biotite granite, locally gneissic

Zp Proterozoic Z Plainfield Fm—quartzite, pelitic schist, minor calc-silicate rock and amphibolite

Zpg Proterozoic Z Ponaganset Gneiss—gneissic biotite granite containing megacrysts of microcline

Zpgr Proterozoic Z Porphyritic granite—seriate to porphyritic biotite granite with epidote and sphene and mafic 

inclusions

Zrdi Proterozoic Z Diorite at Rowley—hornblende diorite

Zsg Proterozoic Z Scituate Granite Gneiss—gneissic granite containing biotite

Zssy Proterozoic Z Sharon Syenite—syenite containing microperthite, oligoclase, and clinopyroxene, mixed 

with ferro-gabbro

Ztgd Proterozoic Z Topsfield Granodiorite—porphyritic granodiorite 

Zv Proterozoic Z Metamorphosed mafic to felsic flow, and volcaniclastic and hypabyssal intrusive rocks

Zvf Proterozoic Z Metamorphosed felsic metavolcanic rocks

Zw Proterozoic Z Westboro Fm—quartzite, schist, calc-silicate quartzite, and amphibolite

Zwgr Proterozoic Z Westwood Granite
42 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 
Appendix 2. Letter to Potential Participants in the Study
44 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 2. Letter to potential participants in the study. Appendix 2: Letter to Potential Participants in the study

OMB Control Number 1028-0086

USGS Study on Arsenic and Uranium in Bedrock Wells of East Central Massachusetts

Dear Resident Well User:

The U.S. Geological Survey (USGS) and the Massachusetts Department of Environmental Protection (MDEP) 

are conducting a study of drinking water to assess the extent of possible elevated concentrations of naturally 

occurring arsenic and uranium in bedrock aquifers that provide drinking water in east central Massachusetts. The 

well at your address has been chosen by a random selection process to be included in the study. 

The study, conducted by John Colman, U.S. Geological Survey (508 490 5027), will indicate relationships 

between arsenic and uranium concentrations and type of bedrock in which a well is drilled. This information will 

help guide future water-supply development, well-water testing, and estimates of total numbers of wells affected.

Your participation is completely voluntary, and results from your well will be kept completely confidential (by 

Exemption 9, well data is not subject to the Freedom of Information Act) and will only be used for the purpose of 

this study. 

We will report results to you with information about health effects of drinking water greater than standards and 

ways to decrease concentrations. If you have any questions, please do not hesitate to contact the project leader 

John Colman at: (508) 490 5027. 

Questionnaires will be mailed to a small number of the selected well addresses by the Massachusetts 

Department of Public Health (MDPH). The MDPH questionnaire offers a second program of biomonitoring for 

some participants concerned about uranium and arsenic effects on health. Participation in the MDPH program is 

also voluntary and is not required for well testing by USGS.

In Parts 1 and 3 of the survey we want to know a little about your water and where it comes from. In Part 2, there 

are instructions about how to collect a water sample. When you are done, please use the enclosed business reply

envelope to mail your survey and water samples back to the USGS. Please mail in the bottles and survey 

soon, if possible within 2 weeks. If it goes longer, however, we are still interested.

____________________________________________________________________________________

PART 1 - Water Sources and Supplies

The majority of residential water supply wells in east-central Massachusetts are private wells that tap ground 

water aquifers in fractured bedrock formations. In the first part of this study, we would like to ask you a few 

questions about your water source and supply. 

1. Is your home supplied with water from a private (bedrock) well? 

 Yes (go to question 2)

 No. My house supply is town water or another source other than bedrock well. 

Please STOP here. You do not have to mail back bottles or a water sample. 
Appendix 2 45

Appendix 2. Letter to potential participants in the study.—Continued

2. Is your well water treated? 

 Yes 

What is the treatment? ______________________________

 No

3. How many people are in your household? (This question is to determine the amount of water use in your 

household).

______ People live in this household .

4. Do you use your well water for drinking water and/or cooking? 

 Yes

 No, because of water quality issues (Select all that apply):

 Arsenic  Uranium

 Iron  Sediment

 Manganese  Taste

 Other___________________________________________________________

Part 2 - Water Sampling Instructions

Although collecting a water sample is a relatively simple task, there are 

several steps that must be taken to ensure accurate results. Please follow the 

instructions in steps 1-6 below to complete the next section of the survey. 

Sampling Objective

The objective is to get a water sample that represents the water in the bedrock aquifer as 

closely as possible, so please select a tap that does not have treatment. Both bottles should be 

filled from the same faucet, one that does not have a water treatment system. Sample bottle 

screw threads and cap should not be contaminated with dirt from hands or the tap.

Once the bottles are filled, please mail the samples and questionnaire in the enclosed, prepaid business reply 

envelope.
46 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 2. Letter to potential participants in the study.—Continued

Instructions 

1. Collect your water sample in the sample containers provided by the USGS. Samples collected in any 

other container will not meet lab standards and cannot be processed.

2. Choose a location to sample your water. If you do not have any water treatment devices, such as a 

water softener or a reverse osmosis filter, take the sample from a cold water tap where you get your 

drinking water. If you do have treatment devices on your water system, (other than a whole-house filter for 

sediment) please locate a faucet which is attached to the water line before the treatment system. 

3. Please avoid contamination of your samples, and do not touch the inside of the bottle or cap.

4. Turn on the cold water and let it run for 1 minute to flush the water out of the pipes. Turn the faucet 

down to a pencil size stream of water and fill the sample container.

5. Place the bottles and your completed survey in the enclosed postage-paid, business-reply envelope.

6. Mail the envelope to the USGS.

PART 3 - Location and Time of Water Sample

Please tell us where and when you collected the water for this sample.

 Basement Faucet

 Outside Spigot

 Bathroom Faucet

 Kitchen Faucet

 Other __________________________________

Date and time of sampling_____________________________________

We would like to conduct follow-up sampling with a visit to a small number of participants. Would you be willing to 

participate in the follow-up visit? 

 Yes, I would like to participate in a follow-up visit.

Please contact me by phone: _____________________________________

Or by email: ____________________________________________________

 No, I would not like to participate in a follow-up visit.

We would like to thank you for taking the time to participate in this important study.

PAPERWORK REDUCTION ACT STATEMENT: The Paperwork Reduction Act of 1995 (44 U.S.C. 3501 et. seq.) requires us to inform you 

that this information is being collected to inform a study on arsenic and uranium in bedrock wells of east central Massachusetts. The

estimated burden for this collection of information is estimated to average 20 minutes per response, including the time for reviewing 

instructions, answering questions, collecting water samples. The response to this request is voluntary. An agency may not conduct or 

sponsor, and a person is not required to respond to, a collection of information unless it displays a currently valid OMB Control Number. 

Comments regarding the burden estimate or any other aspect of this collection of information should be directed to: John Colman at (508) 490 

5027.
 

Appendix 3. Probability of Arsenic Exceeding a Given 

Concentration by Bedrock Unit
48 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 3. Probability of arsenic exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a common 

scale was used in the distribution fitting]

Arsenic, 

in 

micrograms 

per liter

Grouped bedrock units with 

elevated arsenic concentration

Bedrock unit abbreviation

Ops* OZf

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

1 0.66442 0.60023 0.72414 0.03526 0.00377 0.17241 0.55522 0.27338 0.81066

2 0.52993 0.46620 0.59290 0.01398 0.00108 0.09179 0.36942 0.15070 0.64306

3 0.44855 0.38670 0.51167 0.00764 0.00049 0.06006 0.27105 0.09073 0.54658

4 0.39190 0.33202 0.45446 0.00484 0.00027 0.04334 0.21023 0.05795 0.48441

5 0.34942 0.29143 0.41117 0.00334 0.00017 0.03316 0.16912 0.03875 0.44042

6 0.31604 0.25983 0.37687 0.00244 0.00011 0.02639 0.13965 0.02687 0.40719

7 0.28893 0.23440 0.34879 0.00186 0.00008 0.02161 0.11763 0.01919 0.38091

8 0.26637 0.21342 0.32525 0.00146 0.00006 0.01809 0.10064 0.01406 0.35941

9 0.24723 0.19578 0.30515 0.00117 0.00004 0.01540 0.08721 0.01051 0.34138

10 0.23076 0.18073 0.28772 0.00096 0.00003 0.01329 0.07637 0.00801 0.32594

11 0.21641 0.16771 0.27242 0.00080 0.00003 0.01161 0.06748 0.00619 0.31252

12 0.20376 0.15633 0.25886 0.00068 0.00002 0.01024 0.06008 0.00486 0.30069

13 0.19253 0.14630 0.24673 0.00058 0.00002 0.00910 0.05384 0.00386 0.29017

14 0.18247 0.13739 0.23581 0.00050 0.00001 0.00815 0.04854 0.00310 0.28071

15 0.17341 0.12942 0.22590 0.00043 0.00001 0.00735 0.04399 0.00251 0.27214

16 0.16520 0.12225 0.21687 0.00038 0.00001 0.00666 0.04005 0.00205 0.26434

17 0.15772 0.11576 0.20860 0.00034 0.00001 0.00607 0.03661 0.00169 0.25718

18 0.15088 0.10986 0.20098 0.00030 0.00001 0.00555 0.03360 0.00140 0.25058

19 0.14459 0.10448 0.19395 0.00027 0.00001 0.00510 0.03094 0.00117 0.24447

20 0.13878 0.09954 0.18742 0.00024 0.00001 0.00470 0.02857 0.00099 0.23879

21 0.13341 0.09501 0.18135 0.00022 0.00001 0.00435 0.02647 0.00084 0.23349

22 0.12843 0.09082 0.17568 0.00020 0.00000 0.00403 0.02459 0.00071 0.22853

23 0.12379 0.08694 0.17037 0.00018 0.00000 0.00375 0.02289 0.00061 0.22387

24 0.11945 0.08334 0.16540 0.00016 0.00000 0.00350 0.02136 0.00052 0.21949

25 0.11540 0.08000 0.16072 0.00015 0.00000 0.00327 0.01998 0.00045 0.21535

26 0.11160 0.07687 0.15631 0.00014 0.00000 0.00307 0.01872 0.00039 0.21143

27 0.10802 0.07396 0.15215 0.00013 0.00000 0.00288 0.01758 0.00034 0.20772

28 0.10466 0.07123 0.14821 0.00012 0.00000 0.00271 0.01653 0.00030 0.20419

29 0.10149 0.06866 0.14448 0.00011 0.00000 0.00256 0.01557 0.00026 0.20083

30 0.09849 0.06625 0.14093 0.00010 0.00000 0.00241 0.01469 0.00023 0.19763

31 0.09565 0.06398 0.13756 0.00009 0.00000 0.00228 0.01388 0.00020 0.19458

32 0.09296 0.06184 0.13436 0.00009 0.00000 0.00216 0.01313 0.00018 0.19166

33 0.09040 0.05982 0.13130 0.00008 0.00000 0.00205 0.01244 0.00016 0.18886

34 0.08798 0.05791 0.12839 0.00008 0.00000 0.00195 0.01180 0.00014 0.18618

35 0.08567 0.05609 0.12560 0.00007 0.00000 0.00185 0.01120 0.00012 0.18361
Appendix 3 49

Appendix 3. Probability of arsenic exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a common 

scale was used in the distribution fitting]

Arsenic, 

in 

micrograms 

per liter

Grouped bedrock units with 

elevated arsenic concentration

Bedrock unit abbreviation

Ops* OZf

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

36 0.08346 0.05438 0.12293 0.00007 0.00000 0.00176 0.01065 0.00011 0.18113

37 0.08136 0.05274 0.12038 0.00006 0.00000 0.00168 0.01014 0.00010 0.17875

38 0.07936 0.05119 0.11793 0.00006 0.00000 0.00160 0.00966 0.00009 0.17646

39 0.07744 0.04972 0.11558 0.00006 0.00000 0.00153 0.00921 0.00008 0.17425

40 0.07561 0.04831 0.11332 0.00005 0.00000 0.00146 0.00879 0.00007 0.17212

41 0.07385 0.04697 0.11115 0.00005 0.00000 0.00140 0.00840 0.00006 0.17006

42 0.07216 0.04569 0.10906 0.00005 0.00000 0.00134 0.00803 0.00006 0.16807

43 0.07055 0.04446 0.10705 0.00004 0.00000 0.00129 0.00768 0.00005 0.16615

44 0.06900 0.04329 0.10512 0.00004 0.00000 0.00123 0.00736 0.00005 0.16428

45 0.06750 0.04217 0.10325 0.00004 0.00000 0.00119 0.00705 0.00004 0.16248

46 0.06607 0.04110 0.10144 0.00004 0.00000 0.00114 0.00676 0.00004 0.16073

47 0.06469 0.04007 0.09970 0.00004 0.00000 0.00110 0.00649 0.00004 0.15903

48 0.06336 0.03908 0.09802 0.00003 0.00000 0.00105 0.00623 0.00003 0.15738

49 0.06208 0.03813 0.09639 0.00003 0.00000 0.00102 0.00599 0.00003 0.15578

50 0.06084 0.03722 0.09481 0.00003 0.00000 0.00098 0.00576 0.00003 0.15423

55 0.05526 0.03316 0.08765 0.00002 0.00000 0.00082 0.00478 0.00002 0.14706

60 0.05054 0.02978 0.08147 0.00002 0.00000 0.00070 0.00402 0.00001 0.14075

65 0.04647 0.02692 0.07609 0.00002 0.00000 0.00060 0.00341 0.00001 0.13514

70 0.04295 0.02447 0.07136 0.00001 0.00000 0.00052 0.00293 0.00001 0.13011

75 0.03987 0.02237 0.06716 0.00001 0.00000 0.00046 0.00253 0.00000 0.12556

80 0.03715 0.02054 0.06341 0.00001 0.00000 0.00040 0.00221 0.00000 0.12143

85 0.03474 0.01894 0.06005 0.00001 0.00000 0.00036 0.00194 0.00000 0.11764

90 0.03258 0.01752 0.05700 0.00001 0.00000 0.00032 0.00171 0.00000 0.11416

95 0.03065 0.01627 0.05424 0.00001 0.00000 0.00029 0.00152 0.00000 0.11094

100 0.02890 0.01515 0.05172 0.00001 0.00000 0.00026 0.00136 0.00000 0.10796

110 0.02587 0.01325 0.04729 0.00000 0.00000 0.00021 0.00109 0.00000 0.10259

120 0.02334 0.01170 0.04351 0.00000 0.00000 0.00018 0.00090 0.00000 0.09788

130 0.02120 0.01041 0.04026 0.00000 0.00000 0.00015 0.00074 0.00000 0.09370

140 0.01937 0.00932 0.03744 0.00000 0.00000 0.00013 0.00062 0.00000 0.08997

150 0.01779 0.00841 0.03495 0.00000 0.00000 0.00011 0.00053 0.00000 0.08660

160 0.01641 0.00762 0.03275 0.00000 0.00000 0.00010 0.00045 0.00000 0.08354

170 0.01520 0.00694 0.03079 0.00000 0.00000 0.00009 0.00039 0.00000 0.08075

180 0.01413 0.00635 0.02904 0.00000 0.00000 0.00008 0.00034 0.00000 0.07819

190 0.01318 0.00583 0.02746 0.00000 0.00000 0.00007 0.00030 0.00000 0.07582

200 0.01233 0.00538 0.02602 0.00000 0.00000 0.00006 0.00026 0.00000 0.07364
50 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 3. Probability of arsenic exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a common 

scale was used in the distribution fitting]

Arsenic, 

in 

micrograms 

per liter

Grouped bedrock units with 

elevated arsenic concentration

Bedrock unit abbreviation

Ops* OZf

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

210 0.01157 0.00497 0.02472 0.00000 0.00000 0.00005 0.00023 0.00000 0.07161

220 0.01087 0.00461 0.02352 0.00000 0.00000 0.00005 0.00020 0.00000 0.06971

230 0.01025 0.00429 0.02243 0.00000 0.00000 0.00004 0.00018 0.00000 0.06794

240 0.00968 0.00400 0.02142 0.00000 0.00000 0.00004 0.00016 0.00000 0.06628

250 0.00916 0.00374 0.02050 0.00000 0.00000 0.00004 0.00015 0.00000 0.06472

260 0.00868 0.00350 0.01964 0.00000 0.00000 0.00003 0.00013 0.00000 0.06325

270 0.00824 0.00329 0.01884 0.00000 0.00000 0.00003 0.00012 0.00000 0.06186

280 0.00784 0.00309 0.01810 0.00000 0.00000 0.00003 0.00011 0.00000 0.06055

290 0.00747 0.00291 0.01740 0.00000 0.00000 0.00003 0.00010 0.00000 0.05930

300 0.00712 0.00275 0.01676 0.00000 0.00000 0.00002 0.00009 0.00000 0.05811
Appendix 3 51

Appendix 3. Probability of arsenic exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a common 

scale was used in the distribution fitting]

Arsenic, 

in micrograms 

per liter

Bedrock unit abbreviation

OZm OZn OZnb

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

1 0.23792 0.07581 0.50313 0.16282 0.07832 0.29137 0.63210 0.44055 0.79514

2 0.19207 0.05460 0.44482 0.07879 0.02495 0.19331 0.51498 0.33884 0.68819

3 0.16795 0.04320 0.41687 0.04795 0.01088 0.15020 0.44518 0.27992 0.62072

4 0.15207 0.03587 0.39961 0.03262 0.00562 0.12468 0.39654 0.23959 0.57260

5 0.14047 0.03069 0.38756 0.02373 0.00322 0.10742 0.35986 0.20970 0.53578

6 0.13144 0.02681 0.37852 0.01807 0.00199 0.09480 0.33080 0.18642 0.50628

7 0.12413 0.02380 0.37140 0.01422 0.00130 0.08510 0.30699 0.16769 0.48187

8 0.11803 0.02137 0.36559 0.01148 0.00089 0.07737 0.28700 0.15224 0.46118

9 0.11283 0.01938 0.36074 0.00946 0.00063 0.07103 0.26990 0.13926 0.44331

10 0.10832 0.01771 0.35659 0.00792 0.00046 0.06573 0.25505 0.12819 0.42764

11 0.10435 0.01630 0.35299 0.00672 0.00034 0.06122 0.24199 0.11862 0.41375

12 0.10082 0.01508 0.34983 0.00577 0.00026 0.05733 0.23039 0.11026 0.40129

13 0.09765 0.01402 0.34701 0.00501 0.00020 0.05393 0.22000 0.10291 0.39003

14 0.09478 0.01309 0.34449 0.00438 0.00015 0.05093 0.21063 0.09638 0.37979

15 0.09217 0.01227 0.34221 0.00386 0.00012 0.04827 0.20211 0.09055 0.37040

16 0.08977 0.01154 0.34013 0.00342 0.00010 0.04589 0.19434 0.08530 0.36175

17 0.08756 0.01088 0.33823 0.00305 0.00008 0.04374 0.18720 0.08057 0.35374

18 0.08552 0.01029 0.33647 0.00274 0.00007 0.04179 0.18063 0.07627 0.34630

19 0.08361 0.00975 0.33485 0.00247 0.00005 0.04001 0.17454 0.07235 0.33935

20 0.08184 0.00926 0.33335 0.00224 0.00005 0.03839 0.16889 0.06877 0.33285

21 0.08018 0.00882 0.33194 0.00203 0.00004 0.03689 0.16363 0.06547 0.32674

22 0.07862 0.00841 0.33062 0.00185 0.00003 0.03551 0.15871 0.06244 0.32098

23 0.07715 0.00803 0.32939 0.00170 0.00003 0.03423 0.15410 0.05964 0.31555

24 0.07576 0.00768 0.32823 0.00156 0.00002 0.03305 0.14977 0.05704 0.31040

25 0.07445 0.00736 0.32713 0.00143 0.00002 0.03194 0.14569 0.05463 0.30552

26 0.07320 0.00706 0.32609 0.00132 0.00002 0.03091 0.14185 0.05238 0.30088

27 0.07202 0.00679 0.32511 0.00123 0.00001 0.02995 0.13821 0.05028 0.29646

28 0.07089 0.00653 0.32417 0.00114 0.00001 0.02904 0.13477 0.04832 0.29224

29 0.06982 0.00629 0.32328 0.00106 0.00001 0.02819 0.13151 0.04648 0.28821

30 0.06880 0.00606 0.32243 0.00099 0.00001 0.02739 0.12841 0.04476 0.28435

31 0.06782 0.00585 0.32162 0.00092 0.00001 0.02663 0.12545 0.04314 0.28065

32 0.06688 0.00565 0.32084 0.00086 0.00001 0.02591 0.12264 0.04161 0.27711

33 0.06598 0.00546 0.32010 0.00081 0.00001 0.02523 0.11996 0.04017 0.27370

34 0.06511 0.00528 0.31939 0.00076 0.00001 0.02459 0.11740 0.03881 0.27042

35 0.06428 0.00511 0.31870 0.00071 0.00001 0.02398 0.11494 0.03752 0.26726
52 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 3. Probability of arsenic exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a common 

scale was used in the distribution fitting]

Arsenic, 

in micrograms 

per liter

Bedrock unit abbreviation

OZm OZn OZnb

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

36 0.06348 0.00495 0.31804 0.00067 0.00000 0.02339 0.11260 0.03631 0.26422

37 0.06271 0.00480 0.31741 0.00063 0.00000 0.02284 0.11035 0.03515 0.26128

38 0.06197 0.00466 0.31680 0.00060 0.00000 0.02231 0.10819 0.03405 0.25844

39 0.06125 0.00452 0.31621 0.00056 0.00000 0.02181 0.10612 0.03301 0.25570

40 0.06056 0.00439 0.31564 0.00053 0.00000 0.02132 0.10412 0.03202 0.25305

41 0.05989 0.00427 0.31509 0.00050 0.00000 0.02086 0.10220 0.03108 0.25048

42 0.05924 0.00415 0.31455 0.00048 0.00000 0.02042 0.10036 0.03018 0.24799

43 0.05861 0.00404 0.31404 0.00045 0.00000 0.02000 0.09858 0.02932 0.24558

44 0.05801 0.00393 0.31354 0.00043 0.00000 0.01959 0.09686 0.02850 0.24324

45 0.05742 0.00383 0.31305 0.00041 0.00000 0.01920 0.09521 0.02771 0.24097

46 0.05685 0.00374 0.31258 0.00039 0.00000 0.01882 0.09361 0.02696 0.23876

47 0.05629 0.00364 0.31213 0.00037 0.00000 0.01846 0.09206 0.02624 0.23661

48 0.05575 0.00355 0.31168 0.00035 0.00000 0.01811 0.09057 0.02556 0.23452

49 0.05523 0.00347 0.31125 0.00034 0.00000 0.01778 0.08912 0.02490 0.23249

50 0.05472 0.00338 0.31083 0.00032 0.00000 0.01745 0.08772 0.02426 0.23051

55 0.05236 0.00302 0.30889 0.00026 0.00000 0.01600 0.08133 0.02145 0.22133

60 0.05028 0.00271 0.30718 0.00021 0.00000 0.01476 0.07581 0.01912 0.21319

65 0.04843 0.00246 0.30564 0.00018 0.00000 0.01370 0.07099 0.01717 0.20589

70 0.04676 0.00224 0.30426 0.00015 0.00000 0.01277 0.06674 0.01551 0.19930

75 0.04525 0.00205 0.30300 0.00012 0.00000 0.01196 0.06297 0.01409 0.19331

80 0.04387 0.00189 0.30185 0.00011 0.00000 0.01124 0.05959 0.01286 0.18782

85 0.04261 0.00175 0.30079 0.00009 0.00000 0.01060 0.05654 0.01178 0.18277

90 0.04145 0.00162 0.29981 0.00008 0.00000 0.01003 0.05378 0.01084 0.17810

95 0.04037 0.00151 0.29890 0.00007 0.00000 0.00951 0.05128 0.01001 0.17376

100 0.03937 0.00141 0.29805 0.00006 0.00000 0.00905 0.04898 0.00928 0.16972

110 0.03757 0.00124 0.29650 0.00005 0.00000 0.00823 0.04494 0.00803 0.16240

120 0.03598 0.00111 0.29514 0.00004 0.00000 0.00754 0.04149 0.00702 0.15593

130 0.03457 0.00099 0.29391 0.00003 0.00000 0.00696 0.03851 0.00620 0.15015

140 0.03330 0.00089 0.29280 0.00003 0.00000 0.00645 0.03590 0.00551 0.14494

150 0.03215 0.00081 0.29179 0.00002 0.00000 0.00601 0.03361 0.00493 0.14022

160 0.03111 0.00074 0.29086 0.00002 0.00000 0.00562 0.03158 0.00443 0.13591

170 0.03016 0.00068 0.29000 0.00002 0.00000 0.00527 0.02976 0.00401 0.13195

180 0.02928 0.00063 0.28921 0.00001 0.00000 0.00497 0.02813 0.00364 0.12830

190 0.02848 0.00058 0.28847 0.00001 0.00000 0.00469 0.02665 0.00332 0.12492

200 0.02773 0.00054 0.28778 0.00001 0.00000 0.00444 0.02531 0.00304 0.12178
Appendix 3 53

Appendix 3. Probability of arsenic exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a common 

scale was used in the distribution fitting]

Arsenic, 

in micrograms 

per liter

Bedrock unit abbreviation

OZm OZn OZnb

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

210 0.02703 0.00050 0.28713 0.00001 0.00000 0.00422 0.02409 0.00280 0.11885

220 0.02638 0.00047 0.28652 0.00001 0.00000 0.00401 0.02297 0.00258 0.11610

230 0.02577 0.00044 0.28595 0.00001 0.00000 0.00382 0.02195 0.00238 0.11353

240 0.02519 0.00041 0.28541 0.00001 0.00000 0.00365 0.02100 0.00221 0.11110

250 0.02465 0.00038 0.28489 0.00001 0.00000 0.00349 0.02012 0.00206 0.10881

260 0.02414 0.00036 0.28440 0.00001 0.00000 0.00335 0.01931 0.00192 0.10665

270 0.02366 0.00034 0.28393 0.00000 0.00000 0.00321 0.01856 0.00179 0.10460

280 0.02320 0.00032 0.28349 0.00000 0.00000 0.00308 0.01786 0.00167 0.10266

290 0.02277 0.00031 0.28307 0.00000 0.00000 0.00297 0.01720 0.00157 0.10080

300 0.02236 0.00029 0.28266 0.00000 0.00000 0.00286 0.01658 0.00147 0.09904
54 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 3. Probability of arsenic exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Arsenic, 

in micrograms 

per liter

Bedrock unit abbreviation

Sgr SOagr Spsq

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

1 0.43165 0.15898 0.74354 0.32722 0.14632 0.56242 0.06350 0.01045 0.22900

2 0.06143 0.01062 0.21710 0.22397 0.08084 0.45292 0.02471 0.00212 0.14221

3 0.00952 0.00061 0.07257 0.17337 0.05237 0.39760 0.01316 0.00066 0.10868

4 0.00179 0.00004 0.02970 0.14228 0.03691 0.36223 0.00811 0.00026 0.09011

5 0.00040 0.00000 0.01393 0.12094 0.02746 0.33686 0.00546 0.00012 0.07803

6 0.00010 0.00000 0.00719 0.10525 0.02121 0.31738 0.00390 0.00006 0.06940

7 0.00003 0.00000 0.00399 0.09318 0.01686 0.30173 0.00291 0.00003 0.06287

8 0.00001 0.00000 0.00234 0.08358 0.01370 0.28876 0.00224 0.00002 0.05771

9 0.00000 0.00000 0.00143 0.07575 0.01134 0.27773 0.00177 0.00001 0.05351

10 0.00000 0.00000 0.00091 0.06923 0.00952 0.26820 0.00142 0.00001 0.05001

11 0.00000 0.00000 0.00060 0.06371 0.00809 0.25983 0.00117 0.00001 0.04704

12 0.00000 0.00000 0.00040 0.05898 0.00695 0.25239 0.00097 0.00000 0.04447

13 0.00000 0.00000 0.00028 0.05487 0.00602 0.24571 0.00082 0.00000 0.04223

14 0.00000 0.00000 0.00020 0.05127 0.00527 0.23967 0.00069 0.00000 0.04026

15 0.00000 0.00000 0.00014 0.04809 0.00463 0.23416 0.00060 0.00000 0.03850

16 0.00000 0.00000 0.00010 0.04526 0.00410 0.22911 0.00052 0.00000 0.03692

17 0.00000 0.00000 0.00008 0.04273 0.00366 0.22445 0.00045 0.00000 0.03549

18 0.00000 0.00000 0.00006 0.04045 0.00327 0.22013 0.00040 0.00000 0.03420

19 0.00000 0.00000 0.00004 0.03838 0.00294 0.21611 0.00035 0.00000 0.03301

20 0.00000 0.00000 0.00003 0.03650 0.00266 0.21236 0.00031 0.00000 0.03192

21 0.00000 0.00000 0.00003 0.03478 0.00241 0.20884 0.00028 0.00000 0.03092

22 0.00000 0.00000 0.00002 0.03321 0.00219 0.20553 0.00025 0.00000 0.02999

23 0.00000 0.00000 0.00002 0.03176 0.00200 0.20241 0.00022 0.00000 0.02912

24 0.00000 0.00000 0.00001 0.03042 0.00183 0.19946 0.00020 0.00000 0.02832

25 0.00000 0.00000 0.00001 0.02918 0.00168 0.19667 0.00018 0.00000 0.02756

26 0.00000 0.00000 0.00001 0.02803 0.00155 0.19401 0.00017 0.00000 0.02686

27 0.00000 0.00000 0.00001 0.02695 0.00143 0.19149 0.00015 0.00000 0.02620

28 0.00000 0.00000 0.00001 0.02595 0.00132 0.18908 0.00014 0.00000 0.02557

29 0.00000 0.00000 0.00000 0.02502 0.00123 0.18678 0.00013 0.00000 0.02498

30 0.00000 0.00000 0.00000 0.02414 0.00114 0.18458 0.00012 0.00000 0.02443

31 0.00000 0.00000 0.00000 0.02332 0.00106 0.18247 0.00011 0.00000 0.02390

32 0.00000 0.00000 0.00000 0.02254 0.00099 0.18045 0.00010 0.00000 0.02340

33 0.00000 0.00000 0.00000 0.02181 0.00092 0.17851 0.00009 0.00000 0.02292

34 0.00000 0.00000 0.00000 0.02112 0.00086 0.17665 0.00009 0.00000 0.02247

35 0.00000 0.00000 0.00000 0.02047 0.00081 0.17485 0.00008 0.00000 0.02204
Appendix 3 55

Appendix 3. Probability of arsenic exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Arsenic, 

in micrograms 

per liter

Bedrock unit abbreviation

Sgr SOagr Spsq

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

36 0.00000 0.00000 0.00000 0.01986 0.00076 0.17312 0.00007 0.00000 0.02162

37 0.00000 0.00000 0.00000 0.01927 0.00071 0.17145 0.00007 0.00000 0.02123

38 0.00000 0.00000 0.00000 0.01872 0.00067 0.16984 0.00006 0.00000 0.02085

39 0.00000 0.00000 0.00000 0.01819 0.00063 0.16828 0.00006 0.00000 0.02049

40 0.00000 0.00000 0.00000 0.01769 0.00060 0.16678 0.00006 0.00000 0.02014

41 0.00000 0.00000 0.00000 0.01721 0.00056 0.16532 0.00005 0.00000 0.01981

42 0.00000 0.00000 0.00000 0.01675 0.00053 0.16390 0.00005 0.00000 0.01949

43 0.00000 0.00000 0.00000 0.01632 0.00050 0.16253 0.00005 0.00000 0.01918

44 0.00000 0.00000 0.00000 0.01590 0.00048 0.16120 0.00004 0.00000 0.01888

45 0.00000 0.00000 0.00000 0.01551 0.00045 0.15991 0.00004 0.00000 0.01860

46 0.00000 0.00000 0.00000 0.01512 0.00043 0.15866 0.00004 0.00000 0.01832

47 0.00000 0.00000 0.00000 0.01476 0.00041 0.15744 0.00004 0.00000 0.01806

48 0.00000 0.00000 0.00000 0.01441 0.00039 0.15625 0.00003 0.00000 0.01780

49 0.00000 0.00000 0.00000 0.01408 0.00037 0.15509 0.00003 0.00000 0.01755

50 0.00000 0.00000 0.00000 0.01375 0.00035 0.15397 0.00003 0.00000 0.01731

55 0.00000 0.00000 0.00000 0.01232 0.00028 0.14875 0.00002 0.00000 0.01622

60 0.00000 0.00000 0.00000 0.01112 0.00022 0.14412 0.00002 0.00000 0.01527

65 0.00000 0.00000 0.00000 0.01011 0.00018 0.13996 0.00002 0.00000 0.01445

70 0.00000 0.00000 0.00000 0.00925 0.00015 0.13619 0.00001 0.00000 0.01373

75 0.00000 0.00000 0.00000 0.00851 0.00013 0.13277 0.00001 0.00000 0.01308

80 0.00000 0.00000 0.00000 0.00786 0.00011 0.12962 0.00001 0.00000 0.01251

85 0.00000 0.00000 0.00000 0.00729 0.00009 0.12673 0.00001 0.00000 0.01198

90 0.00000 0.00000 0.00000 0.00679 0.00008 0.12405 0.00001 0.00000 0.01151

95 0.00000 0.00000 0.00000 0.00634 0.00007 0.12155 0.00001 0.00000 0.01108

100 0.00000 0.00000 0.00000 0.00594 0.00006 0.11922 0.00000 0.00000 0.01068

110 0.00000 0.00000 0.00000 0.00526 0.00005 0.11500 0.00000 0.00000 0.00998

120 0.00000 0.00000 0.00000 0.00470 0.00004 0.11124 0.00000 0.00000 0.00938

130 0.00000 0.00000 0.00000 0.00423 0.00003 0.10788 0.00000 0.00000 0.00886

140 0.00000 0.00000 0.00000 0.00383 0.00002 0.10484 0.00000 0.00000 0.00839

150 0.00000 0.00000 0.00000 0.00349 0.00002 0.10207 0.00000 0.00000 0.00798

160 0.00000 0.00000 0.00000 0.00320 0.00002 0.09954 0.00000 0.00000 0.00762

170 0.00000 0.00000 0.00000 0.00295 0.00001 0.09721 0.00000 0.00000 0.00729

180 0.00000 0.00000 0.00000 0.00272 0.00001 0.09505 0.00000 0.00000 0.00699

190 0.00000 0.00000 0.00000 0.00253 0.00001 0.09305 0.00000 0.00000 0.00671

200 0.00000 0.00000 0.00000 0.00235 0.00001 0.09118 0.00000 0.00000 0.00646
56 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 3. Probability of arsenic exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Arsenic, 

in micrograms 

per liter

Bedrock unit abbreviation

Sgr SOagr Spsq

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

210 0.00000 0.00000 0.00000 0.00220 0.00001 0.08942 0.00000 0.00000 0.00623

220 0.00000 0.00000 0.00000 0.00206 0.00001 0.08778 0.00000 0.00000 0.00602

230 0.00000 0.00000 0.00000 0.00193 0.00001 0.08624 0.00000 0.00000 0.00583

240 0.00000 0.00000 0.00000 0.00182 0.00000 0.08478 0.00000 0.00000 0.00564

250 0.00000 0.00000 0.00000 0.00171 0.00000 0.08339 0.00000 0.00000 0.00547

260 0.00000 0.00000 0.00000 0.00162 0.00000 0.08208 0.00000 0.00000 0.00531

270 0.00000 0.00000 0.00000 0.00153 0.00000 0.08084 0.00000 0.00000 0.00517

280 0.00000 0.00000 0.00000 0.00145 0.00000 0.07966 0.00000 0.00000 0.00503

290 0.00000 0.00000 0.00000 0.00138 0.00000 0.07853 0.00000 0.00000 0.00489

300 0.00000 0.00000 0.00000 0.00131 0.00000 0.07745 0.00000 0.00000 0.00477
Appendix 3 57

Appendix 3. Probability of arsenic exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Arsenic, 

in micrograms 

per liter

Bedrock unit abbreviation

Spss Ssqd SZtb

Probability of 

concentration 

being greater 

than concentration listed

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

1 0.23273 0.06670 0.51638 0.64322 0.38238 0.84930 0.44216 0.31151 0.57949

2 0.09457 0.01492 0.32491 0.40139 0.19993 0.63395 0.26095 0.15832 0.38996

3 0.04903 0.00450 0.24303 0.27074 0.10603 0.51066 0.17621 0.09343 0.29462

4 0.02895 0.00165 0.19660 0.19308 0.05819 0.43523 0.12812 0.06020 0.23651

5 0.01857 0.00069 0.16620 0.14340 0.03328 0.38371 0.09772 0.04117 0.19710

6 0.01262 0.00032 0.14451 0.10983 0.01980 0.34569 0.07710 0.02941 0.16851

7 0.00896 0.00016 0.12816 0.08619 0.01221 0.31611 0.06240 0.02172 0.14678

8 0.00658 0.00008 0.11533 0.06898 0.00776 0.29222 0.05152 0.01648 0.12970

9 0.00496 0.00005 0.10495 0.05611 0.00507 0.27240 0.04323 0.01277 0.11591

10 0.00382 0.00003 0.09636 0.04628 0.00339 0.25560 0.03676 0.01009 0.10455

11 0.00300 0.00002 0.08913 0.03863 0.00232 0.24112 0.03161 0.00809 0.09504

12 0.00239 0.00001 0.08294 0.03257 0.00162 0.22848 0.02744 0.00657 0.08696

13 0.00194 0.00001 0.07758 0.02771 0.00115 0.21731 0.02403 0.00540 0.08001

14 0.00159 0.00000 0.07289 0.02377 0.00082 0.20735 0.02119 0.00449 0.07397

15 0.00131 0.00000 0.06874 0.02053 0.00060 0.19840 0.01880 0.00376 0.06869

16 0.00110 0.00000 0.06505 0.01785 0.00044 0.19031 0.01679 0.00318 0.06403

17 0.00092 0.00000 0.06174 0.01561 0.00033 0.18294 0.01506 0.00271 0.05988

18 0.00078 0.00000 0.05875 0.01372 0.00025 0.17620 0.01358 0.00232 0.05618

19 0.00067 0.00000 0.05604 0.01212 0.00019 0.17000 0.01229 0.00200 0.05284

20 0.00058 0.00000 0.05357 0.01076 0.00015 0.16427 0.01117 0.00174 0.04984

21 0.00050 0.00000 0.05131 0.00958 0.00011 0.15897 0.01019 0.00151 0.04711

22 0.00043 0.00000 0.04923 0.00857 0.00009 0.15403 0.00932 0.00133 0.04462

23 0.00038 0.00000 0.04731 0.00769 0.00007 0.14943 0.00856 0.00117 0.04235

24 0.00033 0.00000 0.04554 0.00693 0.00006 0.14512 0.00787 0.00103 0.04026

25 0.00029 0.00000 0.04389 0.00625 0.00004 0.14108 0.00727 0.00091 0.03834

26 0.00026 0.00000 0.04236 0.00567 0.00004 0.13728 0.00672 0.00081 0.03657

27 0.00023 0.00000 0.04093 0.00515 0.00003 0.13370 0.00623 0.00072 0.03493

28 0.00021 0.00000 0.03959 0.00468 0.00002 0.13032 0.00579 0.00065 0.03341

29 0.00018 0.00000 0.03833 0.00428 0.00002 0.12713 0.00539 0.00058 0.03200

30 0.00016 0.00000 0.03715 0.00391 0.00002 0.12409 0.00503 0.00052 0.03068

31 0.00015 0.00000 0.03604 0.00358 0.00001 0.12122 0.00470 0.00047 0.02945

32 0.00013 0.00000 0.03499 0.00329 0.00001 0.11848 0.00440 0.00043 0.02830

33 0.00012 0.00000 0.03400 0.00303 0.00001 0.11588 0.00412 0.00039 0.02722

34 0.00011 0.00000 0.03306 0.00279 0.00001 0.11339 0.00387 0.00035 0.02620

35 0.00010 0.00000 0.03217 0.00258 0.00001 0.11102 0.00364 0.00032 0.02525
58 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 3. Probability of arsenic exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Arsenic, 

in micrograms 

per liter

Bedrock unit abbreviation

Spss Ssqd SZtb

Probability of 

concentration 

being greater 

than concentration listed

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

36 0.00009 0.00000 0.03133 0.00239 0.00001 0.10875 0.00342 0.00029 0.02435

37 0.00008 0.00000 0.03053 0.00221 0.00000 0.10658 0.00323 0.00027 0.02351

38 0.00008 0.00000 0.02977 0.00205 0.00000 0.10450 0.00305 0.00025 0.02271

39 0.00007 0.00000 0.02904 0.00191 0.00000 0.10251 0.00288 0.00023 0.02195

40 0.00006 0.00000 0.02834 0.00177 0.00000 0.10059 0.00272 0.00021 0.02123

41 0.00006 0.00000 0.02768 0.00165 0.00000 0.09875 0.00258 0.00019 0.02055

42 0.00005 0.00000 0.02705 0.00154 0.00000 0.09698 0.00244 0.00018 0.01991

43 0.00005 0.00000 0.02644 0.00144 0.00000 0.09527 0.00232 0.00016 0.01930

44 0.00005 0.00000 0.02586 0.00135 0.00000 0.09363 0.00220 0.00015 0.01871

45 0.00004 0.00000 0.02530 0.00126 0.00000 0.09205 0.00210 0.00014 0.01816

46 0.00004 0.00000 0.02477 0.00118 0.00000 0.09052 0.00199 0.00013 0.01763

47 0.00004 0.00000 0.02426 0.00111 0.00000 0.08905 0.00190 0.00012 0.01712

48 0.00003 0.00000 0.02376 0.00104 0.00000 0.08762 0.00181 0.00011 0.01664

49 0.00003 0.00000 0.02329 0.00098 0.00000 0.08624 0.00173 0.00010 0.01618

50 0.00003 0.00000 0.02283 0.00092 0.00000 0.08491 0.00165 0.00010 0.01574

55 0.00002 0.00000 0.02078 0.00069 0.00000 0.07884 0.00132 0.00007 0.01380

60 0.00002 0.00000 0.01905 0.00053 0.00000 0.07360 0.00107 0.00005 0.01222

65 0.00001 0.00000 0.01757 0.00041 0.00000 0.06904 0.00089 0.00004 0.01090

70 0.00001 0.00000 0.01630 0.00032 0.00000 0.06502 0.00074 0.00003 0.00980

75 0.00001 0.00000 0.01519 0.00026 0.00000 0.06145 0.00062 0.00002 0.00886

80 0.00001 0.00000 0.01421 0.00021 0.00000 0.05826 0.00053 0.00002 0.00805

85 0.00000 0.00000 0.01334 0.00017 0.00000 0.05539 0.00045 0.00001 0.00736

90 0.00000 0.00000 0.01256 0.00014 0.00000 0.05279 0.00039 0.00001 0.00675

95 0.00000 0.00000 0.01186 0.00011 0.00000 0.05042 0.00034 0.00001 0.00622

100 0.00000 0.00000 0.01124 0.00010 0.00000 0.04826 0.00030 0.00001 0.00575

110 0.00000 0.00000 0.01015 0.00007 0.00000 0.04444 0.00023 0.00001 0.00496

120 0.00000 0.00000 0.00923 0.00005 0.00000 0.04118 0.00018 0.00000 0.00432

130 0.00000 0.00000 0.00846 0.00004 0.00000 0.03836 0.00015 0.00000 0.00380

140 0.00000 0.00000 0.00780 0.00003 0.00000 0.03589 0.00012 0.00000 0.00337

150 0.00000 0.00000 0.00722 0.00002 0.00000 0.03372 0.00010 0.00000 0.00301

160 0.00000 0.00000 0.00672 0.00002 0.00000 0.03178 0.00008 0.00000 0.00271

170 0.00000 0.00000 0.00628 0.00001 0.00000 0.03005 0.00007 0.00000 0.00245

180 0.00000 0.00000 0.00588 0.00001 0.00000 0.02850 0.00006 0.00000 0.00222

190 0.00000 0.00000 0.00553 0.00001 0.00000 0.02709 0.00005 0.00000 0.00203

200 0.00000 0.00000 0.00522 0.00001 0.00000 0.02581 0.00004 0.00000 0.00186
Appendix 3 59

Appendix 3. Probability of arsenic exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Arsenic, 

in micrograms 

per liter

Bedrock unit abbreviation

Spss Ssqd SZtb

Probability of 

concentration 

being greater 

than concentration listed

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

210 0.00000 0.00000 0.00493 0.00001 0.00000 0.02464 0.00004 0.00000 0.00171

220 0.00000 0.00000 0.00467 0.00001 0.00000 0.02356 0.00003 0.00000 0.00158

230 0.00000 0.00000 0.00444 0.00000 0.00000 0.02257 0.00003 0.00000 0.00146

240 0.00000 0.00000 0.00422 0.00000 0.00000 0.02166 0.00003 0.00000 0.00135

250 0.00000 0.00000 0.00402 0.00000 0.00000 0.02082 0.00002 0.00000 0.00126

260 0.00000 0.00000 0.00384 0.00000 0.00000 0.02003 0.00002 0.00000 0.00118

270 0.00000 0.00000 0.00367 0.00000 0.00000 0.01930 0.00002 0.00000 0.00110

280 0.00000 0.00000 0.00352 0.00000 0.00000 0.01862 0.00002 0.00000 0.00103

290 0.00000 0.00000 0.00337 0.00000 0.00000 0.01798 0.00001 0.00000 0.00097

300 0.00000 0.00000 0.00324 0.00000 0.00000 0.01738 0.00001 0.00000 0.00091
60 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 3. Probability of arsenic exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinkingwater standard for public supplies. Multiply probability values by 100 to obtain percent probability; *, fewer than 

five analyses were above the analytical reporting limit and the option to assume a common scale was used in the 

distribution fitting]

Arsenic, in 

micrograms 

per liter

Bedrock unit abbreviation

Zpg* Zsg

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

1 0.01393 0.00098 0.09648 0.04051 0.00712 0.14958

2 0.00446 0.00022 0.04351 0.01576 0.00089 0.12002

3 0.00213 0.00008 0.02561 0.00848 0.00020 0.10841

4 0.00122 0.00004 0.01708 0.00529 0.00006 0.10152

5 0.00078 0.00002 0.01227 0.00361 0.00002 0.09673

6 0.00053 0.00001 0.00926 0.00261 0.00001 0.09310

7 0.00038 0.00001 0.00724 0.00197 0.00000 0.09020

8 0.00028 0.00001 0.00582 0.00153 0.00000 0.08780

9 0.00022 0.00000 0.00478 0.00122 0.00000 0.08577

10 0.00017 0.00000 0.00400 0.00099 0.00000 0.08400

11 0.00014 0.00000 0.00339 0.00082 0.00000 0.08245

12 0.00011 0.00000 0.00291 0.00069 0.00000 0.08107

13 0.00009 0.00000 0.00252 0.00059 0.00000 0.07982

14 0.00008 0.00000 0.00220 0.00050 0.00000 0.07869

15 0.00007 0.00000 0.00194 0.00044 0.00000 0.07766

16 0.00006 0.00000 0.00172 0.00038 0.00000 0.07670

17 0.00005 0.00000 0.00154 0.00033 0.00000 0.07582

18 0.00004 0.00000 0.00138 0.00030 0.00000 0.07500

19 0.00004 0.00000 0.00125 0.00026 0.00000 0.07424

20 0.00003 0.00000 0.00113 0.00023 0.00000 0.07352

21 0.00003 0.00000 0.00103 0.00021 0.00000 0.07285

22 0.00003 0.00000 0.00094 0.00019 0.00000 0.07221

23 0.00002 0.00000 0.00086 0.00017 0.00000 0.07161

24 0.00002 0.00000 0.00079 0.00016 0.00000 0.07104

25 0.00002 0.00000 0.00073 0.00014 0.00000 0.07050

26 0.00002 0.00000 0.00068 0.00013 0.00000 0.06998

27 0.00001 0.00000 0.00063 0.00012 0.00000 0.06949

28 0.00001 0.00000 0.00058 0.00011 0.00000 0.06901

29 0.00001 0.00000 0.00054 0.00010 0.00000 0.06856

30 0.00001 0.00000 0.00051 0.00009 0.00000 0.06813

31 0.00001 0.00000 0.00047 0.00009 0.00000 0.06771

32 0.00001 0.00000 0.00044 0.00008 0.00000 0.06731

33 0.00001 0.00000 0.00042 0.00008 0.00000 0.06693

34 0.00001 0.00000 0.00039 0.00007 0.00000 0.06656

35 0.00001 0.00000 0.00037 0.00007 0.00000 0.06620
Appendix 3 61

Appendix 3. Probability of arsenic exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinkingwater standard for public supplies. Multiply probability values by 100 to obtain percent probability; *, fewer than 

five analyses were above the analytical reporting limit and the option to assume a common scale was used in the 

distribution fitting]

Arsenic, in 

micrograms 

per liter

Bedrock unit abbreviation

Zpg* Zsg

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

36 0.00001 0.00000 0.00035 0.00006 0.00000 0.06585

37 0.00001 0.00000 0.00033 0.00006 0.00000 0.06551

38 0.00001 0.00000 0.00031 0.00005 0.00000 0.06519

39 0.00001 0.00000 0.00029 0.00005 0.00000 0.06488

40 0.00001 0.00000 0.00028 0.00005 0.00000 0.06457

41 0.00000 0.00000 0.00026 0.00004 0.00000 0.06427

42 0.00000 0.00000 0.00025 0.00004 0.00000 0.06399

43 0.00000 0.00000 0.00024 0.00004 0.00000 0.06371

44 0.00000 0.00000 0.00023 0.00004 0.00000 0.06344

45 0.00000 0.00000 0.00022 0.00004 0.00000 0.06317

46 0.00000 0.00000 0.00021 0.00003 0.00000 0.06291

47 0.00000 0.00000 0.00020 0.00003 0.00000 0.06266

48 0.00000 0.00000 0.00019 0.00003 0.00000 0.06242

49 0.00000 0.00000 0.00018 0.00003 0.00000 0.06218

50 0.00000 0.00000 0.00017 0.00003 0.00000 0.06195

55 0.00000 0.00000 0.00014 0.00002 0.00000 0.06086

60 0.00000 0.00000 0.00011 0.00002 0.00000 0.05988

65 0.00000 0.00000 0.00010 0.00001 0.00000 0.05900

70 0.00000 0.00000 0.00008 0.00001 0.00000 0.05820

75 0.00000 0.00000 0.00007 0.00001 0.00000 0.05746

80 0.00000 0.00000 0.00006 0.00001 0.00000 0.05677

85 0.00000 0.00000 0.00005 0.00001 0.00000 0.05614

90 0.00000 0.00000 0.00005 0.00001 0.00000 0.05554

95 0.00000 0.00000 0.00004 0.00001 0.00000 0.05499

100 0.00000 0.00000 0.00004 0.00000 0.00000 0.05447

110 0.00000 0.00000 0.00003 0.00000 0.00000 0.05351

120 0.00000 0.00000 0.00002 0.00000 0.00000 0.05265

130 0.00000 0.00000 0.00002 0.00000 0.00000 0.05187

140 0.00000 0.00000 0.00002 0.00000 0.00000 0.05116

150 0.00000 0.00000 0.00001 0.00000 0.00000 0.05051

160 0.00000 0.00000 0.00001 0.00000 0.00000 0.04990

170 0.00000 0.00000 0.00001 0.00000 0.00000 0.04934

180 0.00000 0.00000 0.00001 0.00000 0.00000 0.04882

190 0.00000 0.00000 0.00001 0.00000 0.00000 0.04833

200 0.00000 0.00000 0.00001 0.00000 0.00000 0.04787
62 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 3. Probability of arsenic exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinkingwater standard for public supplies. Multiply probability values by 100 to obtain percent probability; *, fewer than 

five analyses were above the analytical reporting limit and the option to assume a common scale was used in the 

distribution fitting]

Arsenic, in 

micrograms 

per liter

Bedrock unit abbreviation

Zpg* Zsg

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

210 0.00000 0.00000 0.00001 0.00000 0.00000 0.04743

220 0.00000 0.00000 0.00000 0.00000 0.00000 0.04702

230 0.00000 0.00000 0.00000 0.00000 0.00000 0.04663

240 0.00000 0.00000 0.00000 0.00000 0.00000 0.04626

250 0.00000 0.00000 0.00000 0.00000 0.00000 0.04591

260 0.00000 0.00000 0.00000 0.00000 0.00000 0.04557

270 0.00000 0.00000 0.00000 0.00000 0.00000 0.04525

280 0.00000 0.00000 0.00000 0.00000 0.00000 0.04494

290 0.00000 0.00000 0.00000 0.00000 0.00000 0.04464

300 0.00000 0.00000 0.00000 0.00000 0.00000 0.04436
 

Appendix 4. Arsenic Log-Normal Fit Statistics by 

Bedrock Unit
64 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 4. Arsenic log-normal fit statistics by bedrock unit.

[CI, confidence interval; %, percent; *, fewer than five analyses were above the analytical reporting limit and the Minitab option to assume a common scale was 

used in the distribution fitting]

Grouped bedrock units with 

elevated-arsenic concentration

Bedrock unit abbreviation

Ops*

Censoring information Count Censoring information Count

Uncensored value 142 Uncensored value 2

Left censored value 13 Left censored value 8

Parameter estimates Parameter estimates

Parameter Estimate Standard 

error

95% normal CI

Parameter Estimate Standard 

error

95% normal CI

Lower Upper Lower Upper

Location 0.842088 0.160891 0.526746 1.15743 Location -3.21928 0.787011 -4.7618 -1.67677

Scale 1.98346 0.122107 1.75801 2.23782 Scale 1.78003 0.0901298 1.61186 1.96574

Log-likelihood -484.214 Log-likelihood -4.305

Goodness-of-fit Goodness-of-fit

Anderson-Darling (adjusted) 0.431 Anderson-Darling (adjusted) 2.245

Correlation coefficient 0.999 Correlation coefficient 1

Characteristics of distribution Characteristics of distribution

Descriptor Estimate Standard

error

95% normal CI

Descriptor Estimate Standard

error

95% normal CI

Lower Upper Lower Upper

Mean 16.5957 4.65715 9.57473 28.7649 Mean 0.194946 0.152905 0.041906 0.906885

Standard 

deviation 117.486 59.1549 43.7925 315.189 Standard deviation 0.93028 0.759049 0.18797 4.60404

Median 2.32121 0.373462 1.69341 3.18174 Median 0.0399836 0.0314676 0.0085502 0.186977

First quartile 

(Q1) 0.609123 0.113368 0.422943 0.877259 First quartile (Q1) 0.0120355 0.0095863 0.0025262 0.0573391

Third quartile 

(Q3) 8.84551 1.54983 6.27455 12.4699 Third quartile 

(Q3) 0.132832 0.103893 0.0286776 0.615262

Interquartile 

range (IQR) 8.23639 1.48626 5.78278 11.7311 Interquartile range (IQR) 0.120796 0.0944301 0.0261001 0.559067
Appendix 4 65

Appendix 4. Arsenic log-normal fit statistics by bedrock unit.—Continued

[CI, confidence interval; %, percent; *, fewer than five analyses were above the analytical reporting limit and the Minitab option to assume a common scale was 

used in the distribution fitting]

Bedrock unit abbreviation

OZf OZm

Censoring information Count Censoring information Count

Uncensored value 7 Uncensored value 4

Left censored value 1 Left censored value 6

Distribution Log normal Distribution Log normal

Parameter estimates Parameter estimates

Parameter Estimate Standard 

error

95% normal CI

Parameter Estimate Standard 

error

95% normal CI

Lower Upper Lower Upper

Location 0.203812 0.537881 -0.850415 1.25804 Location -3.14197 2.2943 -7.63872 1.35477

Scale 1.46776 0.444717 0.810489 2.65803 Scale 4.40671 2.19624 1.65915 11.7042

Log-likelihood -19.146 Log-likelihood -20.355

Goodness-of-fit Goodness-of-fit

Anderson-Darling (adjusted) 3.106 Anderson-Darling (adjusted) 2.122

Correlation coefficient 0.922 Correlation coefficient 0.956

Characteristics of distribution Characteristics of distribution

Descriptor Estimate Standard

error

95% normal CI

Descriptor Estimate Standard

error

95% normal CI

Lower Upper Lower Upper

Mean 3.60011 2.6815 0.836197 15.4997 Mean 711.633 5.84 × 103 0.0000725 6.99 × 109

Standard 

deviation 9.93912 13.636 0.675371 146.269 Standard deviation 1.17 × 107 2.09 × 108 0 1.68 × 1022

Median 1.22607 0.659479 0.427238 3.51852 Median 0.0431974 0.0991078 0.0004814 3.87586

First quartile 

(Q1) 0.455585 0.306663 0.121789 1.70424 First quartile (Q1) 0.0022111 0.0077461 0.0000023 2.1211

Third quartile 

(Q3) 3.29959 1.82372 1.11684 9.7483 Third quartile (Q3) 0.843922 1.3722 0.0348552 20.4332

Interquartile 

range (IQR) 2.84401 1.67949 0.89385 9.04891 Interquartile range (IQR) 0.841711 1.36804 0.0348095 20.353
66 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 4. Arsenic log-normal fit statistics by bedrock unit.—Continued

[CI, confidence interval; %, percent; *, fewer than five analyses were above the analytical reporting limit and the Minitab option to assume a common scale was 

used in the distribution fitting]

Bedrock unit abbreviation

OZn OZnb

Censoring information Count Censoring information Count

Uncensored value 19 Uncensored value 17

Left censored value 12 Left censored value 3

Distribution Log normal Distribution Log normal

Parameter estimates Parameter estimates

Parameter Estimate Standard 

error

95% normal CI

Parameter Estimate Standard 

error

95% normal CI

Lower Upper Lower Upper

Location -1.58309 0.352176 -2.27334 -0.892837 Location 0.779948 0.531552 -0.261874 1.82177

Scale 1.6106 0.349339 1.05283 2.46384 Scale 2.31159 0.437248 1.59552 3.34903

Log-likelihood -33.677 Log-likelihood -67.412

Goodness-of-fit Goodness-of-fit

Anderson-Darling (adjusted) 3.307 Anderson-Darling (adjusted) 1.281

Correlation coefficient 0.981 Correlation coefficient 0.98

Characteristics of distribution Characteristics of distribution

Descriptor Estimate Standard

error

95% normal CI

Descriptor Estimate Standard

error

95% normal CI

Lower Upper Lower Upper

Mean 0.751202 0.37721 0.280759 2.00993 Mean 31.5531 33.5261 3.93202 253.203

Standard 

deviation 2.64349 2.77567 0.337609 20.6986 Standard deviation 455.321 914.887 8.87111 2.34 × 104

Median 0.20534 0.0723157 0.102968 0.409492 Median 2.18136 1.1595 0.769608 6.18279

First quartile 

(Q1) 0.0692924 0.035228 0.0255822 0.187687 First quartile (Q1) 0.458775 0.297545 0.128689 1.63553

Third quartile 

(Q3) 0.608499 0.193027 0.326771 1.13312 Third quartile (Q3) 10.3718 5.85262 3.43193 31.3452

Interquartile 

range (IQR) 0.539207 0.180896 0.279377 1.04069 Interquartile range (IQR) 9.91304 5.69917 3.21246 30.5898
Appendix 4 67

Appendix 4. Arsenic log-normal fit statistics by bedrock unit.—Continued

[CI, confidence interval; %, percent; *, fewer than five analyses were above the analytical reporting limit and the Minitab option to assume a common scale was 

used in the distribution fitting]

Bedrock unit abbreviation

Sgr SOagr

Censoring information Count Censoring information Count

Uncensored value 7 Uncensored value 7

Left censored value 0 Left censored value 5

Distribution Log normal Distribution Log normal

Parameter estimates Parameter estimates

Parameter Estimate Standard 

error

95% normal CI

Parameter Estimate Standard 

error

95% normal CI

Lower Upper Lower Upper

Location -0.0870687 0.221555 -0.521308 0.347171 Location -0.996819 0.724544 -2.4169 0.423261

Scale 0.505699 0.101615 0.341076 0.749778 Scale 2.22697 0.632122 1.27674 3.88443

Log-likelihood -9.715 Log-likelihood -24.772

Goodness-of-fit Goodness-of-fit

Anderson-Darling (adjusted) 3.111 Anderson-Darling (adjusted) 1.726

Correlation coefficient 0.954 Correlation coefficient 0.947

Characteristics of distribution Characteristics of distribution

Descriptor Estimate Standard

error

95% normal CI

Descriptor Estimate Standard

error

95% normal CI

Lower Upper Lower Upper

Mean 1.04164 0.20888 0.703116 1.54315 Mean 4.40564 5.98493 0.307381 63.1452

Standard 

deviation 0.562298 0.142746 0.341884 0.924815 Standard deviation 52.4085 140.438 0.274442 1.00 × 104

Median 0.916614 0.20308 0.593743 1.41506 Median 0.369052 0.267394 0.0891978 1.52693

First quartile 

(Q1) 0.651709 0.171367 0.389252 1.09113 First quartile (Q1) 0.0821762 0.078262 0.0127084 0.531378

Third quartile 

(Q3) 1.2892 0.252714 0.877936 1.89311 Third quartile (Q3) 1.6574 1.17954 0.410814 6.68669

Interquartile 

range (IQR) 0.637489 0.136533 0.418955 0.970013 Interquartile range (IQR) 1.57523 1.14191 0.380445 6.5222
68 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 4. Arsenic log-normal fit statistics by bedrock unit.—Continued

[CI, confidence interval; %, percent; *, fewer than five analyses were above the analytical reporting limit and the Minitab option to assume a common scale was 

used in the distribution fitting]

Bedrock unit abbreviation

Spsq* Spss

Censoring information Count Censoring information Count

Uncensored value 4 Uncensored value 5

Left censored value 5 Left censored value 2

Distribution Log normal Distribution Log normal

Parameter estimates Parameter estimates

Parameter Estimate Standard 

error

95% normal CI

Parameter Estimate Standard 

error

95% normal CI

Lower Upper Lower Upper

Location -2.41045 0.846842 -4.07023 -0.750667 Location -0.867381 0.508521 -1.86406 0.129302

Scale 1.57953 0.495804 0.853772 2.92223 Scale 1.18838 0.332903 0.686285 2.0578

Log-likelihood -10.109 Log-likelihood -10.976

Goodness-of-fit Goodness-of-fit

Anderson-Darling (adjusted) 2.121 Anderson-Darling (adjusted) 2.799

Correlation coefficient 0.966 Correlation coefficient 0.982

Characteristics of distribution Characteristics of distribution

Descriptor Estimate Standard

error

95% normal CI

Descriptor Estimate Standard

error

95% normal CI

Lower Upper Lower Upper

Mean 0.312551 0.199818 0.0892766 1.09422 Mean 0.851069 0.428686 0.317112 2.28411

Standard 

deviation 1.04229 1.26353 0.0968518 11.2168 Standard deviation 1.4997 1.27936 0.281753 7.98256

Median 0.0897751 0.0760253 0.0170735 0.472051 Median 0.42005 0.213604 0.155041 1.13803

First quartile 

(Q1) 0.0309363 0.0342062 0.0035424 0.270172 First quartile (Q1) 0.188449 0.119276 0.0545049 0.651556

Third quartile 

(Q3) 0.260522 0.171901 0.0714813 0.9495 Third quartile (Q3) 0.936287 0.436567 0.375418 2.33509

Interquartile 

range (IQR) 0.229585 0.144786 0.0667025 0.790216 Interquartile range (IQR) 0.747838 0.362431 0.289256 1.93345
Appendix 4 69

Appendix 4. Arsenic log-normal fit statistics by bedrock unit.—Continued

[CI, confidence interval; %, percent; *, fewer than five analyses were above the analytical reporting limit and the Minitab option to assume a common scale was 

used in the distribution fitting]

Bedrock unit abbreviation

Ssqd SZtb

Censoring information Count Censoring information Count

Uncensored value 11 Uncensored value 29

Left censored value 0 Left censored value 4

Distribution Log normal Distribution Log normal

Parameter estimates Parameter estimates

Parameter Estimate Standard 

error

95% normal CI

Parameter Estimate Standard 

error

95% normal CI

Lower Upper Lower Upper

Location 0.412493 0.343881 -0.261502 1.08649 Location -0.203752 0.250689 -0.695093 0.287588

Scale 1.1237 0.320478 0.642518 1.96522 Scale 1.40051 0.187371 1.07747 1.8204

Log-likelihood -21.008 Log-likelihood -62.075

Goodness-of-fit Goodness-of-fit

Anderson-Darling (adjusted) 2.392 Anderson-Darling (adjusted) 0.892

Correlation coefficient 0.951 Correlation coefficient 0.992

Characteristics of distribution Characteristics of distribution

Descriptor Estimate Standard

error

95% normal CI

Descriptor Estimate Standard

error

95% normal CI

Lower Upper Lower Upper

Mean 2.8401 1.28763 1.16794 6.90631 Mean 2.17486 0.715688 1.1411 4.14514

Standard 

deviation 4.52184 3.94286 0.818658 24.9763 Standard deviation 5.3757 3.10934 1.7302 16.7023

Median 1.51058 0.51946 0.769894 2.96385 Median 0.815664 0.204478 0.499028 1.33321

First quartile 

(Q1) 0.707917 0.308919 0.30098 1.66505 First quartile (Q1) 0.317149 0.0951949 0.176104 0.571161

Third quartile 

(Q3) 3.22333 1.20405 1.55005 6.70291 Third quartile (Q3) 2.09778 0.545174 1.26051 3.49117

Interquartile 

range (IQR) 2.51541 1.10396 1.06423 5.94541 Interquartile range (IQR) 1.78063 0.49387 1.03392 3.06662
70 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 4. Arsenic log-normal fit statistics by bedrock unit.—Continued

[CI, confidence interval; %, percent; *, fewer than five analyses were above the analytical reporting limit and the Minitab option to assume a common scale was 

used in the distribution fitting]

Bedrock unit abbreviation

Zpg* Zsg

Censoring information Count Censoring information Count

Uncensored value 2 Uncensored value 7

Left censored value 9 Left censored value 16

Distribution Log normal Distribution Log normal

Parameter estimates Parameter estimates

Parameter Estimate Standard 

error

95% normal CI

Parameter Estimate Standard 

error

95% normal CI

Lower Upper Lower Upper

Location -3.66411 0.771435 -5.17609 -2.15212 Location -2.98176 0.999948 -4.94162 -1.0219

Scale 1.66617 0.100537 1.48032 1.87534 Scale 1.70893 0.748103 0.724607 4.03039

Log-likelihood -3.006 Log-likelihood -14.871

Goodness-of-fit Goodness-of-fit

Anderson-Darling (adjusted) 2.214 Anderson-Darling (adjusted) 2.733

Correlation coefficient 1 Correlation coefficient 0.982

Characteristics of distribution Characteristics of distribution

Descriptor Estimate Standard

error

95% normal CI

Descriptor Estimate Standard

error

95% normal CI

Lower Upper Lower Upper

Mean 0.102689 0.0779394 0.0231993 0.454541 Mean 0.218376 0.130661 0.0675934 0.705514

Standard 

deviation 0.398461 0.313134 0.0854009 1.85913 Standard deviation 0.914828 1.64495 0.0269649 31.037

Median 0.0256271 0.0197696 0.0056501 0.116237 Median 0.0507034 0.0507008 0.007143 0.35991

First quartile 

(Q1) 0.0083298 0.0065524 0.0017826 0.0389236 First quartile (Q1) 0.016012 0.0234942 0.0009026 0.284057

Third quartile 

(Q3) 0.0788433 0.0600783 0.0177073 0.351056 Third quartile (Q3) 0.160557 0.0958063 0.049855 0.517073

Interquartile 

range (IQR) 0.0705135 0.0536348 0.0158789 0.313129 Interquartile range (IQR) 0.144545 0.0768037 0.0510177 0.409532
Appendix 5. Probability of Uranium Exceeding a Given 

Concentration by Bedrock Unit
72 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 5. Probability of uranium exceeding a given concentration by bedrock unit. —Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

Dcgr Dfgr Dl

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

1 0.95614 0.51366 0.99964 0.64549 0.32667 0.88405 0.15706 0.03907 0.40068

2 0.88401 0.43605 0.99464 0.53055 0.24734 0.79848 0.06707 0.00759 0.28505

3 0.81477 0.38671 0.98120 0.46145 0.20378 0.73716 0.03710 0.00226 0.23244

4 0.75269 0.34946 0.96018 0.41300 0.17473 0.69003 0.02333 0.00085 0.20043

5 0.69779 0.31902 0.93403 0.37627 0.15347 0.65213 0.01588 0.00037 0.17825

6 0.64925 0.29304 0.90509 0.34705 0.13703 0.62065 0.01140 0.00018 0.16167

7 0.60617 0.27025 0.87509 0.32303 0.12384 0.59389 0.00852 0.00010 0.14867

8 0.56776 0.24991 0.84521 0.30281 0.11296 0.57073 0.00656 0.00005 0.13812

9 0.53332 0.23154 0.81621 0.28545 0.10381 0.55040 0.00517 0.00003 0.12932

10 0.50229 0.21481 0.78853 0.27033 0.09599 0.53235 0.00416 0.00002 0.12185

11 0.47420 0.19950 0.76239 0.25702 0.08921 0.51615 0.00340 0.00001 0.11540

12 0.44867 0.18543 0.73789 0.24516 0.08328 0.50151 0.00282 0.00001 0.10976

13 0.42537 0.17247 0.71502 0.23452 0.07804 0.48817 0.00237 0.00001 0.10476

14 0.40402 0.16051 0.69373 0.22490 0.07337 0.47595 0.00201 0.00000 0.10031

15 0.38440 0.14947 0.67395 0.21615 0.06918 0.46470 0.00172 0.00000 0.09631

16 0.36631 0.13925 0.65557 0.20815 0.06541 0.45429 0.00148 0.00000 0.09268

17 0.34958 0.12980 0.63849 0.20079 0.06199 0.44461 0.00129 0.00000 0.08937

18 0.33407 0.12106 0.62261 0.19400 0.05887 0.43558 0.00112 0.00000 0.08635

19 0.31966 0.11296 0.60782 0.18771 0.05602 0.42713 0.00099 0.00000 0.08356

20 0.30623 0.10545 0.59404 0.18186 0.05341 0.41920 0.00087 0.00000 0.08099

21 0.29369 0.09850 0.58116 0.17640 0.05100 0.41173 0.00078 0.00000 0.07860

22 0.28197 0.09206 0.56912 0.17129 0.04877 0.40469 0.00069 0.00000 0.07638

23 0.27098 0.08609 0.55784 0.16650 0.04670 0.39802 0.00062 0.00000 0.07431

24 0.26066 0.08055 0.54726 0.16199 0.04478 0.39170 0.00056 0.00000 0.07236

25 0.25095 0.07541 0.53731 0.15775 0.04299 0.38569 0.00050 0.00000 0.07054

26 0.24181 0.07064 0.52794 0.15374 0.04132 0.37997 0.00046 0.00000 0.06882

27 0.23319 0.06621 0.51910 0.14994 0.03976 0.37453 0.00042 0.00000 0.06721

28 0.22505 0.06209 0.51074 0.14635 0.03830 0.36932 0.00038 0.00000 0.06568

29 0.21735 0.05827 0.50284 0.14293 0.03692 0.36435 0.00035 0.00000 0.06423

30 0.21005 0.05471 0.49534 0.13968 0.03562 0.35958 0.00032 0.00000 0.06285

31 0.20313 0.05140 0.48822 0.13659 0.03440 0.35501 0.00029 0.00000 0.06155

32 0.19657 0.04832 0.48146 0.13364 0.03325 0.35062 0.00027 0.00000 0.06031

33 0.19033 0.04545 0.47502 0.13082 0.03216 0.34640 0.00025 0.00000 0.05912

34 0.18439 0.04277 0.46887 0.12813 0.03113 0.34234 0.00023 0.00000 0.05799

35 0.17874 0.04028 0.46301 0.12555 0.03015 0.33843 0.00021 0.00000 0.05691
Appendix 5 73

Appendix 5. Probability of uranium exceeding a given concentration by bedrock unit. —Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

Dcgr Dfgr Dl

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

36 0.17335 0.03795 0.45740 0.12308 0.02922 0.33466 0.00020 0.00000 0.05588

37 0.16821 0.03577 0.45204 0.12071 0.02834 0.33103 0.00018 0.00000 0.05489

38 0.16331 0.03374 0.44690 0.11843 0.02750 0.32751 0.00017 0.00000 0.05394

39 0.15862 0.03185 0.44196 0.11624 0.02670 0.32411 0.00016 0.00000 0.05302

40 0.15413 0.03007 0.43723 0.11414 0.02593 0.32082 0.00015 0.00000 0.05215

41 0.14984 0.02841 0.43267 0.11211 0.02521 0.31764 0.00014 0.00000 0.05130

42 0.14573 0.02686 0.42829 0.11016 0.02451 0.31455 0.00013 0.00000 0.05049

43 0.14179 0.02540 0.42407 0.10828 0.02385 0.31156 0.00012 0.00000 0.04971

44 0.13801 0.02404 0.42001 0.10646 0.02321 0.30866 0.00011 0.00000 0.04896

45 0.13438 0.02275 0.41608 0.10470 0.02260 0.30584 0.00011 0.00000 0.04823

46 0.13090 0.02155 0.41229 0.10301 0.02202 0.30310 0.00010 0.00000 0.04752

47 0.12755 0.02043 0.40863 0.10137 0.02146 0.30044 0.00009 0.00000 0.04684

48 0.12433 0.01937 0.40508 0.09978 0.02093 0.29785 0.00009 0.00000 0.04619

49 0.12123 0.01837 0.40165 0.09824 0.02041 0.29533 0.00008 0.00000 0.04555

50 0.11825 0.01743 0.39833 0.09676 0.01992 0.29287 0.00008 0.00000 0.04493

55 0.10488 0.01351 0.38316 0.08995 0.01770 0.28149 0.00006 0.00000 0.04212

60 0.09366 0.01058 0.36997 0.08406 0.01586 0.27140 0.00005 0.00000 0.03968

65 0.08415 0.00836 0.35838 0.07890 0.01430 0.26236 0.00004 0.00000 0.03754

70 0.07600 0.00667 0.34806 0.07434 0.01297 0.25420 0.00003 0.00000 0.03565

75 0.06897 0.00537 0.33880 0.07028 0.01183 0.24678 0.00002 0.00000 0.03397

80 0.06286 0.00435 0.33042 0.06664 0.01083 0.23999 0.00002 0.00000 0.03245

85 0.05751 0.00355 0.32278 0.06335 0.00996 0.23375 0.00002 0.00000 0.03108

90 0.05281 0.00292 0.31578 0.06037 0.00919 0.22798 0.00001 0.00000 0.02983

95 0.04864 0.00241 0.30932 0.05765 0.00851 0.22263 0.00001 0.00000 0.02869

100 0.04493 0.00201 0.30335 0.05516 0.00790 0.21764 0.00001 0.00000 0.02765

110 0.03865 0.00141 0.29260 0.05076 0.00687 0.20862 0.00001 0.00000 0.02579

120 0.03356 0.00101 0.28316 0.04699 0.00603 0.20064 0.00001 0.00000 0.02419

130 0.02938 0.00073 0.27479 0.04373 0.00534 0.19352 0.00000 0.00000 0.02279

140 0.02590 0.00054 0.26728 0.04087 0.00476 0.18712 0.00000 0.00000 0.02156

150 0.02298 0.00040 0.26048 0.03835 0.00427 0.18131 0.00000 0.00000 0.02047

160 0.02050 0.00031 0.25429 0.03610 0.00385 0.17601 0.00000 0.00000 0.01949

170 0.01839 0.00024 0.24862 0.03409 0.00349 0.17115 0.00000 0.00000 0.01860

180 0.01656 0.00018 0.24339 0.03229 0.00318 0.16666 0.00000 0.00000 0.01780

190 0.01498 0.00014 0.23855 0.03065 0.00290 0.16251 0.00000 0.00000 0.01708

200 0.01361 0.00011 0.23404 0.02916 0.00266 0.15865 0.00000 0.00000 0.01641
74 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 5. Probability of uranium exceeding a given concentration by bedrock unit. —Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

Dcgr Dfgr Dl

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

210 0.01240 0.00009 0.22983 0.02780 0.00245 0.15505 0.00000 0.00000 0.01579

220 0.01134 0.00007 0.22589 0.02655 0.00226 0.15168 0.00000 0.00000 0.01523

230 0.01040 0.00006 0.22219 0.02541 0.00210 0.14852 0.00000 0.00000 0.01470

240 0.00956 0.00005 0.21869 0.02435 0.00195 0.14554 0.00000 0.00000 0.01422

250 0.00881 0.00004 0.21539 0.02337 0.00181 0.14273 0.00000 0.00000 0.01376

260 0.00815 0.00003 0.21227 0.02245 0.00169 0.14007 0.00000 0.00000 0.01334

270 0.00755 0.00003 0.20930 0.02161 0.00158 0.13755 0.00000 0.00000 0.01294

280 0.00700 0.00002 0.20648 0.02082 0.00148 0.13516 0.00000 0.00000 0.01257

290 0.00651 0.00002 0.20379 0.02007 0.00139 0.13289 0.00000 0.00000 0.01222

300 0.00607 0.00002 0.20122 0.01938 0.00130 0.13073 0.00000 0.00000 0.01189
Appendix 5 75

Appendix 5. Probability of uranium exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

DSw Ops* OZf

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

1 0.27948 0.09368 0.55948 0.0035097 0.0002758 0.0263434 0.22587 0.07024 0.48763

2 0.14055 0.02225 0.44187 0.0009592 0.0000546 0.0097475 0.08718 0.01214 0.32133

3 0.08590 0.00696 0.39223 0.0004182 0.0000196 0.005111 0.04339 0.00294 0.25130

4 0.05806 0.00263 0.36239 0.0002247 0.0000091 0.0031409 0.02476 0.00089 0.21056

5 0.04181 0.00114 0.34152 0.0001362 0.0000049 0.0021176 0.01542 0.00032 0.18314

6 0.03145 0.00054 0.32567 0.0000894 0.0000029 0.0015181 0.01021 0.00013 0.16310

7 0.02444 0.00028 0.31299 0.0000621 0.0000019 0.0011371 0.00708 0.00006 0.14764

8 0.01948 0.00015 0.30248 0.000045 0.0000013 0.0008804 0.00509 0.00003 0.13527

9 0.01584 0.00009 0.29355 0.0000337 0.0000009 0.0006995 0.00376 0.00001 0.12510

10 0.01309 0.00005 0.28580 0.000026 0.0000007 0.0005675 0.00285 0.00001 0.11655

11 0.01097 0.00003 0.27898 0.0000204 0.0000005 0.0004683 0.00220 0.00000 0.10924

12 0.00930 0.00002 0.27290 0.0000163 0.0000004 0.0003921 0.00173 0.00000 0.10290

13 0.00797 0.00001 0.26742 0.0000133 0.0000003 0.0003324 0.00138 0.00000 0.09735

14 0.00689 0.00001 0.26245 0.000011 0.0000002 0.0002847 0.00111 0.00000 0.09243

15 0.00600 0.00001 0.25790 0.0000091 0.0000002 0.0002462 0.00091 0.00000 0.08804

16 0.00526 0.00000 0.25372 0.0000077 0.0000001 0.0002146 0.00075 0.00000 0.08409

17 0.00464 0.00000 0.24984 0.0000066 0.0000001 0.0001884 0.00062 0.00000 0.08052

18 0.00412 0.00000 0.24624 0.0000056 0.0000001 0.0001665 0.00052 0.00000 0.07727

19 0.00368 0.00000 0.24288 0.0000049 0.0000001 0.000148 0.00044 0.00000 0.07429

20 0.00329 0.00000 0.23973 0.0000042 0.0000001 0.0001322 0.00038 0.00000 0.07156

21 0.00296 0.00000 0.23676 0.0000037 0.0000001 0.0001187 0.00032 0.00000 0.06904

22 0.00268 0.00000 0.23397 0.0000033 0.0000001 0.000107 0.00028 0.00000 0.06670

23 0.00243 0.00000 0.23132 0.0000029 0.0000000 0.0000969 0.00024 0.00000 0.06453

24 0.00221 0.00000 0.22882 0.0000026 0.0000000 0.0000881 0.00021 0.00000 0.06251

25 0.00202 0.00000 0.22643 0.0000023 0.0000000 0.0000803 0.00018 0.00000 0.06062

26 0.00184 0.00000 0.22417 0.000002 0.0000000 0.0000734 0.00016 0.00000 0.05885

27 0.00169 0.00000 0.22200 0.0000018 0.0000000 0.0000674 0.00014 0.00000 0.05719

28 0.00156 0.00000 0.21993 0.0000017 0.0000000 0.000062 0.00012 0.00000 0.05563

29 0.00143 0.00000 0.21795 0.0000015 0.0000000 0.0000572 0.00011 0.00000 0.05416

30 0.00133 0.00000 0.21606 0.0000014 0.0000000 0.0000528 0.00010 0.00000 0.05276

31 0.00123 0.00000 0.21423 0.0000012 0.0000000 0.000049 0.00009 0.00000 0.05145

32 0.00114 0.00000 0.21248 0.0000011 0.0000000 0.0000455 0.00008 0.00000 0.05020

33 0.00106 0.00000 0.21079 0.000001 0.0000000 0.0000423 0.00007 0.00000 0.04901

34 0.00099 0.00000 0.20917 0.0000009 0.0000000 0.0000394 0.00006 0.00000 0.04788

35 0.00092 0.00000 0.20760 0.0000009 0.0000000 0.0000368 0.00006 0.00000 0.04681
76 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 5. Probability of uranium exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

DSw Ops* OZf

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

36 0.00086 0.00000 0.20608 0.0000008 0.0000001 0.0000344 0.00005 0.00000 0.04578

37 0.00080 0.00000 0.20462 0.0000007 0.0000001 0.0000323 0.00005 0.00000 0.04480

38 0.00075 0.00000 0.20320 0.0000007 0.0000000 0.0000303 0.00004 0.00000 0.04387

39 0.00071 0.00000 0.20183 0.0000006 0.0000000 0.0000285 0.00004 0.00000 0.04297

40 0.00066 0.00000 0.20050 0.0000006 0.0000000 0.0000268 0.00004 0.00000 0.04211

41 0.00062 0.00000 0.19921 0.0000005 0.0000000 0.0000252 0.00003 0.00000 0.04129

42 0.00059 0.00000 0.19796 0.0000005 0.0000000 0.0000238 0.00003 0.00000 0.04050

43 0.00055 0.00000 0.19674 0.0000005 0.0000000 0.0000225 0.00003 0.00000 0.03974

44 0.00052 0.00000 0.19555 0.0000004 0.0000000 0.0000213 0.00003 0.00000 0.03901

45 0.00049 0.00000 0.19440 0.0000004 0.0000000 0.0000201 0.00002 0.00000 0.03831

46 0.00047 0.00000 0.19328 0.0000004 0.0000001 0.0000191 0.00002 0.00000 0.03764

47 0.00044 0.00000 0.19219 0.0000004 0.0000001 0.0000181 0.00002 0.00000 0.03699

48 0.00042 0.00000 0.19113 0.0000003 0.0000000 0.0000172 0.00002 0.00000 0.03636

49 0.00040 0.00000 0.19009 0.0000003 0.0000000 0.0000163 0.00002 0.00000 0.03575

50 0.00038 0.00000 0.18908 0.0000003 0.0000000 0.0000155 0.00002 0.00000 0.03516

55 0.00029 0.00000 0.18436 0.0000002 0.0000000 0.0000123 0.00001 0.00000 0.03251

60 0.00023 0.00000 0.18014 0.0000002 0.0000000 0.0000099 0.00001 0.00000 0.03024

65 0.00019 0.00000 0.17633 0.0000001 0.0000000 0.000008 0.00001 0.00000 0.02827

70 0.00015 0.00000 0.17286 0.0000001 0.0000000 0.0000067 0.00000 0.00000 0.02654

75 0.00013 0.00000 0.16967 0.0000001 0.0000000 0.0000056 0.00000 0.00000 0.02502

80 0.00011 0.00000 0.16673 0.0000001 0.0000001 0.0000047 0.00000 0.00000 0.02367

85 0.00009 0.00000 0.16401 0.0000001 0.0000001 0.000004 0.00000 0.00000 0.02245

90 0.00008 0.00000 0.16148 0.0000000 0.0000000 0.0000035 0.00000 0.00000 0.02136

95 0.00007 0.00000 0.15911 0.0000000 0.0000000 0.000003 0.00000 0.00000 0.02036

100 0.00006 0.00000 0.15689 0.0000000 0.0000000 0.0000026 0.00000 0.00000 0.01946

110 0.00004 0.00000 0.15282 0.0000000 0.0000000 0.000002 0.00000 0.00000 0.01787

120 0.00003 0.00000 0.14918 0.0000000 0.0000000 0.0000016 0.00000 0.00000 0.01652

130 0.00003 0.00000 0.14590 0.0000000 0.0000000 0.0000013 0.00000 0.00000 0.01536

140 0.00002 0.00000 0.14290 0.0000000 0.0000000 0.000001 0.00000 0.00000 0.01434

150 0.00002 0.00000 0.14016 0.0000000 0.0000000 0.0000009 0.00000 0.00000 0.01346

160 0.00001 0.00000 0.13763 0.0000001 0.0000001 0.0000007 0.00000 0.00000 0.01267

170 0.00001 0.00000 0.13529 0.0000001 0.0000001 0.0000006 0.00000 0.00000 0.01197

180 0.00001 0.00000 0.13311 0.0000000 0.0000000 0.0000005 0.00000 0.00000 0.01133

190 0.00001 0.00000 0.13107 0.0000000 0.0000000 0.0000004 0.00000 0.00000 0.01077

200 0.00001 0.00000 0.12916 0.0000000 0.0000000 0.0000004 0.00000 0.00000 0.01025
Appendix 5 77

Appendix 5. Probability of uranium exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

DSw Ops* OZf

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

210 0.00001 0.00000 0.12737 0.0000000 0.0000000 0.0000003 0.00000 0.00000 0.00978

220 0.00001 0.00000 0.12567 0.0000000 0.0000000 0.0000003 0.00000 0.00000 0.00935

230 0.00000 0.00000 0.12407 0.0000000 0.0000000 0.0000003 0.00000 0.00000 0.00895

240 0.00000 0.00000 0.12255 0.0000000 0.0000000 0.0000002 0.00000 0.00000 0.00859

250 0.00000 0.00000 0.12111 0.0000000 0.0000000 0.0000002 0.00000 0.00000 0.00825

260 0.00000 0.00000 0.11973 0.0000001 0.0000001 0.0000002 0.00000 0.00000 0.00794

270 0.00000 0.00000 0.11842 0.0000001 0.0000001 0.0000002 0.00000 0.00000 0.00764

280 0.00000 0.00000 0.11717 0.0000000 0.0000000 0.0000001 0.00000 0.00000 0.00737

290 0.00000 0.00000 0.11597 0.0000000 0.0000000 0.0000001 0.00000 0.00000 0.00712

300 0.00000 0.00000 0.11482 0.0000000 0.0000000 0.0000001 0.00000 0.00000 0.00688
78 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 5. Probability of uranium exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

OZm OZn OZnb

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

1 0.39299 0.18635 0.63622 0.50445 0.36570 0.64266 0.20132 0.09010 0.36931

2 0.28816 0.11589 0.53119 0.31779 0.20138 0.45578 0.12168 0.04290 0.26921

3 0.23368 0.08203 0.47528 0.22434 0.12633 0.35520 0.08700 0.02593 0.21925

4 0.19878 0.06210 0.43859 0.16880 0.08553 0.29148 0.06729 0.01758 0.18780

5 0.17401 0.04905 0.41184 0.13241 0.06099 0.24710 0.05453 0.01276 0.16567

6 0.15529 0.03993 0.39107 0.10700 0.04518 0.21425 0.04559 0.00970 0.14902

7 0.14054 0.03324 0.37425 0.08842 0.03446 0.18887 0.03899 0.00763 0.13592

8 0.12856 0.02816 0.36021 0.07437 0.02691 0.16864 0.03392 0.00616 0.12529

9 0.11860 0.02420 0.34821 0.06346 0.02142 0.15212 0.02991 0.00507 0.11643

10 0.11016 0.02104 0.33778 0.05479 0.01732 0.13836 0.02667 0.00424 0.10892

11 0.10291 0.01847 0.32859 0.04778 0.01420 0.12673 0.02399 0.00360 0.10245

12 0.09659 0.01635 0.32039 0.04202 0.01179 0.11676 0.02175 0.00309 0.09681

13 0.09104 0.01458 0.31301 0.03724 0.00988 0.10813 0.01984 0.00268 0.09183

14 0.08611 0.01308 0.30630 0.03321 0.00836 0.10058 0.01821 0.00235 0.08740

15 0.08171 0.01180 0.30018 0.02979 0.00713 0.09392 0.01679 0.00207 0.08343

16 0.07774 0.01070 0.29454 0.02687 0.00613 0.08800 0.01555 0.00183 0.07985

17 0.07415 0.00975 0.28933 0.02434 0.00530 0.08272 0.01446 0.00164 0.07660

18 0.07088 0.00892 0.28449 0.02214 0.00461 0.07797 0.01349 0.00147 0.07362

19 0.06790 0.00819 0.27998 0.02022 0.00403 0.07367 0.01263 0.00132 0.07090

20 0.06515 0.00754 0.27575 0.01853 0.00354 0.06978 0.01185 0.00120 0.06839

21 0.06262 0.00697 0.27178 0.01703 0.00313 0.06622 0.01115 0.00109 0.06607

22 0.06028 0.00646 0.26805 0.01571 0.00277 0.06297 0.01052 0.00100 0.06392

23 0.05811 0.00600 0.26451 0.01452 0.00247 0.05999 0.00995 0.00091 0.06191

24 0.05609 0.00559 0.26117 0.01346 0.00221 0.05724 0.00942 0.00084 0.06004

25 0.05421 0.00522 0.25800 0.01250 0.00198 0.05470 0.00894 0.00077 0.05829

26 0.05244 0.00488 0.25498 0.01164 0.00178 0.05234 0.00850 0.00071 0.05665

27 0.05079 0.00457 0.25210 0.01086 0.00160 0.05016 0.00809 0.00066 0.05510

28 0.04923 0.00429 0.24935 0.01015 0.00145 0.04812 0.00772 0.00061 0.05364

29 0.04777 0.00404 0.24673 0.00951 0.00132 0.04623 0.00737 0.00057 0.05227

30 0.04639 0.00380 0.24421 0.00892 0.00120 0.04445 0.00705 0.00053 0.05097

31 0.04508 0.00359 0.24180 0.00838 0.00109 0.04279 0.00675 0.00050 0.04973

32 0.04385 0.00339 0.23948 0.00789 0.00100 0.04123 0.00647 0.00046 0.04856

33 0.04268 0.00321 0.23726 0.00743 0.00091 0.03976 0.00621 0.00043 0.04745

34 0.04157 0.00304 0.23511 0.00702 0.00084 0.03838 0.00596 0.00041 0.04639

35 0.04051 0.00288 0.23304 0.00663 0.00077 0.03708 0.00573 0.00038 0.04538
Appendix 5 79

Appendix 5. Probability of uranium exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

OZm OZn OZnb

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

36 0.03950 0.00274 0.23105 0.00627 0.00071 0.03584 0.00552 0.00036 0.04442

37 0.03855 0.00260 0.22912 0.00594 0.00065 0.03468 0.00532 0.00034 0.04350

38 0.03763 0.00248 0.22726 0.00563 0.00060 0.03358 0.00513 0.00032 0.04262

39 0.03676 0.00236 0.22546 0.00535 0.00056 0.03253 0.00495 0.00030 0.04177

40 0.03592 0.00225 0.22372 0.00508 0.00052 0.03154 0.00478 0.00029 0.04096

41 0.03512 0.00215 0.22202 0.00483 0.00048 0.03060 0.00462 0.00027 0.04019

42 0.03435 0.00205 0.22038 0.00460 0.00045 0.02970 0.00446 0.00026 0.03944

43 0.03362 0.00196 0.21879 0.00439 0.00041 0.02885 0.00432 0.00024 0.03872

44 0.03291 0.00188 0.21725 0.00418 0.00039 0.02803 0.00418 0.00023 0.03803

45 0.03223 0.00180 0.21574 0.00399 0.00036 0.02725 0.00405 0.00022 0.03737

46 0.03158 0.00173 0.21428 0.00382 0.00034 0.02651 0.00393 0.00021 0.03673

47 0.03095 0.00166 0.21286 0.00365 0.00031 0.02580 0.00381 0.00020 0.03611

48 0.03035 0.00159 0.21148 0.00349 0.00029 0.02512 0.00370 0.00019 0.03551

49 0.02977 0.00153 0.21013 0.00334 0.00028 0.02447 0.00359 0.00018 0.03494

50 0.02921 0.00147 0.20881 0.00320 0.00026 0.02385 0.00349 0.00017 0.03438

55 0.02667 0.00121 0.20270 0.00261 0.00019 0.02109 0.00304 0.00014 0.03185

60 0.02453 0.00102 0.19725 0.00216 0.00014 0.01881 0.00268 0.00012 0.02968

65 0.02268 0.00086 0.19234 0.00181 0.00011 0.01691 0.00238 0.00010 0.02780

70 0.02108 0.00074 0.18788 0.00153 0.00009 0.01530 0.00213 0.00008 0.02615

75 0.01967 0.00064 0.18381 0.00131 0.00007 0.01392 0.00192 0.00007 0.02469

80 0.01843 0.00056 0.18006 0.00112 0.00005 0.01273 0.00174 0.00006 0.02338

85 0.01732 0.00049 0.17660 0.00098 0.00004 0.01169 0.00159 0.00005 0.02221

90 0.01633 0.00043 0.17338 0.00085 0.00004 0.01078 0.00145 0.00004 0.02115

95 0.01544 0.00038 0.17039 0.00075 0.00003 0.00998 0.00134 0.00004 0.02019

100 0.01464 0.00034 0.16758 0.00066 0.00002 0.00927 0.00123 0.00003 0.01932

110 0.01323 0.00028 0.16247 0.00052 0.00002 0.00807 0.00106 0.00003 0.01778

120 0.01206 0.00023 0.15791 0.00042 0.00001 0.00709 0.00092 0.00002 0.01647

130 0.01105 0.00019 0.15381 0.00034 0.00001 0.00629 0.00081 0.00002 0.01533

140 0.01019 0.00016 0.15009 0.00028 0.00001 0.00562 0.00072 0.00001 0.01435

150 0.00944 0.00013 0.14669 0.00024 0.00001 0.00505 0.00064 0.00001 0.01348

160 0.00878 0.00011 0.14357 0.00020 0.00000 0.00457 0.00058 0.00001 0.01271

170 0.00820 0.00010 0.14068 0.00017 0.00000 0.00415 0.00052 0.00001 0.01202

180 0.00769 0.00009 0.13800 0.00015 0.00000 0.00380 0.00047 0.00001 0.01140

190 0.00723 0.00008 0.13551 0.00013 0.00000 0.00348 0.00043 0.00001 0.01084

200 0.00681 0.00007 0.13318 0.00011 0.00000 0.00320 0.00039 0.00001 0.01033
80 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 5. Probability of uranium exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

OZm OZn OZnb

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

210 0.00644 0.00006 0.13099 0.00010 0.00000 0.00296 0.00036 0.00000 0.00987

220 0.00610 0.00005 0.12893 0.00008 0.00000 0.00274 0.00033 0.00000 0.00944

230 0.00579 0.00005 0.12698 0.00007 0.00000 0.00255 0.00031 0.00000 0.00905

240 0.00550 0.00004 0.12514 0.00007 0.00000 0.00238 0.00029 0.00000 0.00869

250 0.00524 0.00004 0.12340 0.00006 0.00000 0.00222 0.00027 0.00000 0.00836

260 0.00500 0.00003 0.12174 0.00005 0.00000 0.00208 0.00025 0.00000 0.00805

270 0.00478 0.00003 0.12016 0.00005 0.00000 0.00195 0.00023 0.00000 0.00776

280 0.00457 0.00003 0.11866 0.00004 0.00000 0.00183 0.00022 0.00000 0.00749

290 0.00438 0.00003 0.11722 0.00004 0.00000 0.00173 0.00021 0.00000 0.00724

300 0.00421 0.00002 0.11585 0.00003 0.00000 0.00163 0.00019 0.00000 0.00700
Appendix 5 81

Appendix 5. Probability of uranium exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

Ph Sacgr Sagr

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

1 0.47220 0.23247 0.72282 0.69951 0.59142 0.79240 0.57749 0.33202 0.79539

2 0.38398 0.16877 0.64392 0.55401 0.44593 0.65820 0.46876 0.24920 0.69856

3 0.33475 0.13536 0.59782 0.46387 0.35942 0.57089 0.40572 0.20238 0.63909

4 0.30141 0.11388 0.56571 0.40076 0.30036 0.50822 0.36234 0.17092 0.59719

5 0.27663 0.09862 0.54129 0.35345 0.25703 0.46036 0.32983 0.14795 0.56534

6 0.25715 0.08711 0.52173 0.31637 0.22376 0.42223 0.30418 0.13029 0.53991

7 0.24126 0.07806 0.50549 0.28639 0.19737 0.39093 0.28322 0.11624 0.51890

8 0.22794 0.07073 0.49165 0.26155 0.17592 0.36463 0.26564 0.10476 0.50111

9 0.21654 0.06466 0.47963 0.24061 0.15816 0.34213 0.25060 0.09519 0.48574

10 0.20662 0.05954 0.46903 0.22267 0.14321 0.32261 0.23755 0.08710 0.47226

11 0.19789 0.05515 0.45957 0.20712 0.13048 0.30546 0.22606 0.08015 0.46030

12 0.19012 0.05135 0.45104 0.19351 0.11951 0.29025 0.21586 0.07413 0.44956

13 0.18314 0.04803 0.44328 0.18147 0.10997 0.27664 0.20672 0.06885 0.43985

14 0.17682 0.04509 0.43618 0.17076 0.10162 0.26438 0.19846 0.06420 0.43099

15 0.17106 0.04248 0.42963 0.16116 0.09424 0.25325 0.19095 0.06006 0.42286

16 0.16578 0.04013 0.42357 0.15251 0.08768 0.24311 0.18409 0.05637 0.41537

17 0.16092 0.03802 0.41792 0.14466 0.08183 0.23382 0.17778 0.05304 0.40841

18 0.15643 0.03611 0.41265 0.13752 0.07657 0.22526 0.17196 0.05003 0.40194

19 0.15225 0.03437 0.40770 0.13099 0.07183 0.21735 0.16657 0.04730 0.39589

20 0.14836 0.03277 0.40305 0.12499 0.06754 0.21001 0.16156 0.04481 0.39021

21 0.14472 0.03131 0.39866 0.11947 0.06363 0.20319 0.15689 0.04254 0.38487

22 0.14130 0.02996 0.39450 0.11437 0.06007 0.19682 0.15251 0.04045 0.37983

23 0.13809 0.02872 0.39055 0.10964 0.05681 0.19085 0.14841 0.03852 0.37507

24 0.13507 0.02757 0.38680 0.10524 0.05381 0.18526 0.14455 0.03675 0.37054

25 0.13221 0.02649 0.38323 0.10115 0.05106 0.18000 0.14092 0.03510 0.36625

26 0.12950 0.02549 0.37981 0.09733 0.04851 0.17504 0.13748 0.03357 0.36215

27 0.12693 0.02456 0.37655 0.09375 0.04616 0.17036 0.13423 0.03215 0.35825

28 0.12448 0.02369 0.37343 0.09039 0.04397 0.16593 0.13115 0.03082 0.35452

29 0.12216 0.02287 0.37043 0.08724 0.04195 0.16174 0.12822 0.02958 0.35095

30 0.11994 0.02210 0.36755 0.08428 0.04006 0.15776 0.12543 0.02842 0.34752

31 0.11782 0.02137 0.36477 0.08148 0.03829 0.15397 0.12278 0.02734 0.34423

32 0.11580 0.02069 0.36211 0.07884 0.03665 0.15036 0.12025 0.02631 0.34107

33 0.11386 0.02004 0.35953 0.07634 0.03511 0.14693 0.11783 0.02535 0.33803

34 0.11200 0.01943 0.35705 0.07398 0.03366 0.14365 0.11552 0.02445 0.33510

35 0.11021 0.01886 0.35465 0.07174 0.03230 0.14052 0.11330 0.02359 0.33228
82 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 5. Probability of uranium exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

Ph Sacgr Sagr

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

36 0.10850 0.01831 0.35233 0.06961 0.03103 0.13752 0.11118 0.02278 0.32955

37 0.10685 0.01779 0.35008 0.06758 0.02983 0.13465 0.10914 0.02202 0.32691

38 0.10526 0.01729 0.34790 0.06566 0.02869 0.13189 0.10719 0.02129 0.32436

39 0.10373 0.01682 0.34579 0.06383 0.02762 0.12925 0.10530 0.02061 0.32189

40 0.10226 0.01637 0.34374 0.06208 0.02661 0.12672 0.10349 0.01995 0.31950

41 0.10083 0.01594 0.34175 0.06041 0.02566 0.12428 0.10175 0.01933 0.31718

42 0.09946 0.01553 0.33981 0.05881 0.02475 0.12193 0.10007 0.01874 0.31493

43 0.09813 0.01514 0.33793 0.05729 0.02389 0.11967 0.09844 0.01818 0.31274

44 0.09684 0.01476 0.33610 0.05583 0.02308 0.11749 0.09688 0.01765 0.31061

45 0.09559 0.01440 0.33432 0.05443 0.02230 0.11539 0.09536 0.01713 0.30855

46 0.09438 0.01406 0.33258 0.05309 0.02156 0.11337 0.09390 0.01665 0.30654

47 0.09321 0.01373 0.33089 0.05180 0.02086 0.11141 0.09248 0.01618 0.30458

48 0.09208 0.01341 0.32924 0.05056 0.02020 0.10952 0.09111 0.01573 0.30267

49 0.09098 0.01311 0.32762 0.04938 0.01956 0.10769 0.08979 0.01531 0.30081

50 0.08991 0.01281 0.32605 0.04823 0.01895 0.10592 0.08850 0.01490 0.29900

55 0.08498 0.01150 0.31870 0.04313 0.01630 0.09786 0.08261 0.01309 0.29056

60 0.08067 0.01041 0.31210 0.03886 0.01415 0.09092 0.07750 0.01160 0.28303

65 0.07685 0.00948 0.30611 0.03524 0.01240 0.08488 0.07301 0.01035 0.27623

70 0.07343 0.00868 0.30064 0.03215 0.01094 0.07957 0.06904 0.00930 0.27004

75 0.07036 0.00799 0.29562 0.02947 0.00972 0.07486 0.06549 0.00841 0.26438

80 0.06757 0.00739 0.29097 0.02713 0.00869 0.07066 0.06230 0.00764 0.25918

85 0.06504 0.00686 0.28666 0.02508 0.00781 0.06688 0.05942 0.00698 0.25435

90 0.06271 0.00639 0.28263 0.02327 0.00705 0.06347 0.05679 0.00639 0.24987

95 0.06058 0.00597 0.27887 0.02165 0.00639 0.06037 0.05440 0.00588 0.24569

100 0.05860 0.00560 0.27532 0.02021 0.00582 0.05754 0.05220 0.00543 0.24177

110 0.05506 0.00496 0.26883 0.01775 0.00487 0.05257 0.04830 0.00467 0.23462

120 0.05199 0.00443 0.26301 0.01573 0.00413 0.04834 0.04495 0.00406 0.22824

130 0.04928 0.00398 0.25773 0.01405 0.00354 0.04471 0.04203 0.00356 0.22249

140 0.04687 0.00361 0.25292 0.01263 0.00306 0.04154 0.03947 0.00315 0.21726

150 0.04471 0.00329 0.24850 0.01143 0.00266 0.03876 0.03721 0.00280 0.21248

160 0.04277 0.00301 0.24441 0.01039 0.00234 0.03630 0.03518 0.00251 0.20809

170 0.04101 0.00277 0.24062 0.00949 0.00207 0.03411 0.03336 0.00226 0.20402

180 0.03940 0.00256 0.23709 0.00871 0.00183 0.03215 0.03172 0.00204 0.20025

190 0.03793 0.00237 0.23378 0.00802 0.00164 0.03038 0.03023 0.00186 0.19672

200 0.03657 0.00221 0.23068 0.00741 0.00147 0.02878 0.02887 0.00169 0.19343
Appendix 5 83

Appendix 5. Probability of uranium exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

Ph Sacgr Sagr

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

210 0.03532 0.00206 0.22775 0.00687 0.00132 0.02732 0.02762 0.00155 0.19033

220 0.03416 0.00192 0.22499 0.00639 0.00120 0.02599 0.02647 0.00143 0.18741

230 0.03308 0.00180 0.22237 0.00596 0.00109 0.02477 0.02541 0.00131 0.18466

240 0.03207 0.00170 0.21989 0.00557 0.00099 0.02365 0.02443 0.00122 0.18205

250 0.03113 0.00160 0.21753 0.00522 0.00090 0.02262 0.02352 0.00113 0.17958

260 0.03024 0.00151 0.21527 0.00490 0.00083 0.02166 0.02268 0.00105 0.17723

270 0.02941 0.00143 0.21312 0.00460 0.00076 0.02077 0.02188 0.00097 0.17499

280 0.02863 0.00135 0.21107 0.00434 0.00070 0.01994 0.02114 0.00091 0.17285

290 0.02789 0.00128 0.20910 0.00410 0.00065 0.01917 0.02045 0.00085 0.17080

300 0.02719 0.00122 0.20721 0.00387 0.00060 0.01845 0.01980 0.00080 0.16885
84 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 5. Probability of uranium exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

Sb Sbs Se

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

1 0.44502 0.26442 0.63806 0.28874 0.12867 0.50739 0.35132 0.14117 0.62230

2 0.27017 0.13088 0.45922 0.09640 0.02179 0.27875 0.09921 0.01598 0.33459

3 0.18684 0.07521 0.36649 0.04108 0.00484 0.18692 0.03476 0.00195 0.22850

4 0.13866 0.04725 0.30833 0.02030 0.00133 0.13758 0.01425 0.00029 0.17273

5 0.10768 0.03156 0.26777 0.01108 0.00043 0.10695 0.00654 0.00005 0.13793

6 0.08634 0.02205 0.23754 0.00651 0.00016 0.08622 0.00327 0.00001 0.11407

7 0.07090 0.01596 0.21397 0.00403 0.00006 0.07136 0.00175 0.00000 0.09668

8 0.05933 0.01188 0.19497 0.00261 0.00003 0.06025 0.00099 0.00000 0.08345

9 0.05040 0.00904 0.17928 0.00175 0.00001 0.05168 0.00058 0.00000 0.07308

10 0.04335 0.00702 0.16607 0.00121 0.00001 0.04490 0.00036 0.00000 0.06473

11 0.03768 0.00554 0.15476 0.00086 0.00000 0.03943 0.00022 0.00000 0.05789

12 0.03305 0.00443 0.14495 0.00062 0.00000 0.03494 0.00015 0.00000 0.05218

13 0.02921 0.00359 0.13636 0.00046 0.00000 0.03120 0.00010 0.00000 0.04735

14 0.02600 0.00294 0.12876 0.00034 0.00000 0.02804 0.00007 0.00000 0.04323

15 0.02328 0.00243 0.12199 0.00026 0.00000 0.02536 0.00005 0.00000 0.03967

16 0.02095 0.00203 0.11590 0.00020 0.00000 0.02305 0.00003 0.00000 0.03656

17 0.01895 0.00171 0.11041 0.00016 0.00000 0.02105 0.00002 0.00000 0.03384

18 0.01721 0.00145 0.10542 0.00012 0.00000 0.01930 0.00002 0.00000 0.03144

19 0.01570 0.00123 0.10086 0.00010 0.00000 0.01777 0.00001 0.00000 0.02930

20 0.01437 0.00106 0.09668 0.00008 0.00000 0.01641 0.00001 0.00000 0.02738

21 0.01319 0.00091 0.09284 0.00006 0.00000 0.01520 0.00001 0.00000 0.02566

22 0.01215 0.00079 0.08929 0.00005 0.00000 0.01413 0.00001 0.00000 0.02411

23 0.01122 0.00069 0.08600 0.00004 0.00000 0.01316 0.00000 0.00000 0.02271

24 0.01039 0.00060 0.08294 0.00004 0.00000 0.01229 0.00000 0.00000 0.02143

25 0.00965 0.00053 0.08009 0.00003 0.00000 0.01150 0.00000 0.00000 0.02026

26 0.00898 0.00047 0.07742 0.00003 0.00000 0.01079 0.00000 0.00000 0.01919

27 0.00837 0.00041 0.07493 0.00002 0.00000 0.01014 0.00000 0.00000 0.01821

28 0.00782 0.00037 0.07258 0.00002 0.00000 0.00955 0.00000 0.00000 0.01730

29 0.00732 0.00033 0.07038 0.00002 0.00000 0.00901 0.00000 0.00000 0.01647

30 0.00686 0.00029 0.06830 0.00001 0.00000 0.00851 0.00000 0.00000 0.01570

31 0.00644 0.00026 0.06634 0.00001 0.00000 0.00805 0.00000 0.00000 0.01498

32 0.00606 0.00023 0.06448 0.00001 0.00000 0.00763 0.00000 0.00000 0.01431

33 0.00571 0.00021 0.06273 0.00001 0.00000 0.00724 0.00000 0.00000 0.01369

34 0.00539 0.00019 0.06106 0.00001 0.00000 0.00687 0.00000 0.00000 0.01311

35 0.00509 0.00017 0.05947 0.00001 0.00000 0.00654 0.00000 0.00000 0.01257
Appendix 5 85

Appendix 5. Probability of uranium exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

Sb Sbs Se

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

36 0.00481 0.00016 0.05797 0.00001 0.00000 0.00623 0.00000 0.00000 0.01206

37 0.00456 0.00014 0.05653 0.00001 0.00000 0.00594 0.00000 0.00000 0.01158

38 0.00432 0.00013 0.05516 0.00000 0.00000 0.00566 0.00000 0.00000 0.01113

39 0.00410 0.00012 0.05386 0.00000 0.00000 0.00541 0.00000 0.00000 0.01071

40 0.00389 0.00011 0.05261 0.00000 0.00000 0.00517 0.00000 0.00000 0.01032

41 0.00370 0.00010 0.05141 0.00000 0.00000 0.00495 0.00000 0.00000 0.00994

42 0.00352 0.00009 0.05027 0.00000 0.00000 0.00474 0.00000 0.00000 0.00959

43 0.00336 0.00008 0.04917 0.00000 0.00000 0.00455 0.00000 0.00000 0.00925

44 0.00320 0.00008 0.04812 0.00000 0.00000 0.00436 0.00000 0.00000 0.00893

45 0.00306 0.00007 0.04711 0.00000 0.00000 0.00419 0.00000 0.00000 0.00863

46 0.00292 0.00006 0.04614 0.00000 0.00000 0.00403 0.00000 0.00000 0.00835

47 0.00279 0.00006 0.04520 0.00000 0.00000 0.00387 0.00000 0.00000 0.00808

48 0.00267 0.00006 0.04430 0.00000 0.00000 0.00372 0.00000 0.00000 0.00782

49 0.00256 0.00005 0.04344 0.00000 0.00000 0.00359 0.00000 0.00000 0.00758

50 0.00245 0.00005 0.04260 0.00000 0.00000 0.00346 0.00000 0.00000 0.00734

55 0.00200 0.00003 0.03884 0.00000 0.00000 0.00289 0.00000 0.00000 0.00632

60 0.00165 0.00002 0.03566 0.00000 0.00000 0.00246 0.00000 0.00000 0.00551

65 0.00138 0.00002 0.03292 0.00000 0.00000 0.00211 0.00000 0.00000 0.00484

70 0.00117 0.00001 0.03056 0.00000 0.00000 0.00182 0.00000 0.00000 0.00429

75 0.00100 0.00001 0.02848 0.00000 0.00000 0.00159 0.00000 0.00000 0.00383

80 0.00086 0.00001 0.02665 0.00000 0.00000 0.00140 0.00000 0.00000 0.00344

85 0.00075 0.00001 0.02503 0.00000 0.00000 0.00124 0.00000 0.00000 0.00310

90 0.00065 0.00000 0.02357 0.00000 0.00000 0.00110 0.00000 0.00000 0.00282

95 0.00057 0.00000 0.02226 0.00000 0.00000 0.00099 0.00000 0.00000 0.00257

100 0.00051 0.00000 0.02108 0.00000 0.00000 0.00089 0.00000 0.00000 0.00235

110 0.00040 0.00000 0.01902 0.00000 0.00000 0.00073 0.00000 0.00000 0.00199

120 0.00032 0.00000 0.01730 0.00000 0.00000 0.00061 0.00000 0.00000 0.00171

130 0.00026 0.00000 0.01584 0.00000 0.00000 0.00051 0.00000 0.00000 0.00148

140 0.00022 0.00000 0.01458 0.00000 0.00000 0.00044 0.00000 0.00000 0.00129

150 0.00018 0.00000 0.01349 0.00000 0.00000 0.00037 0.00000 0.00000 0.00114

160 0.00015 0.00000 0.01254 0.00000 0.00000 0.00032 0.00000 0.00000 0.00101

170 0.00013 0.00000 0.01169 0.00000 0.00000 0.00028 0.00000 0.00000 0.00090

180 0.00011 0.00000 0.01095 0.00000 0.00000 0.00025 0.00000 0.00000 0.00081

190 0.00010 0.00000 0.01028 0.00000 0.00000 0.00022 0.00000 0.00000 0.00073

200 0.00008 0.00000 0.00968 0.00000 0.00000 0.00020 0.00000 0.00000 0.00066
86 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 5. Probability of uranium exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

Sb Sbs Se

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

210 0.00007 0.00000 0.00913 0.00000 0.00000 0.00018 0.00000 0.00000 0.00060

220 0.00007 0.00000 0.00864 0.00000 0.00000 0.00016 0.00000 0.00000 0.00055

230 0.00006 0.00000 0.00819 0.00000 0.00000 0.00014 0.00000 0.00000 0.00051

240 0.00005 0.00000 0.00778 0.00000 0.00000 0.00013 0.00000 0.00000 0.00046

250 0.00005 0.00000 0.00741 0.00000 0.00000 0.00012 0.00000 0.00000 0.00043

260 0.00004 0.00000 0.00706 0.00000 0.00000 0.00011 0.00000 0.00000 0.00040

270 0.00004 0.00000 0.00675 0.00000 0.00000 0.00010 0.00000 0.00000 0.00037

280 0.00003 0.00000 0.00645 0.00000 0.00000 0.00009 0.00000 0.00000 0.00034

290 0.00003 0.00000 0.00618 0.00000 0.00000 0.00008 0.00000 0.00000 0.00032

300 0.00003 0.00000 0.00592 0.00000 0.00000 0.00008 0.00000 0.00000 0.00030
Appendix 5 87

Appendix 5. Probability of uranium exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

Sgr So SOagr

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

1 0.31386 0.10546 0.61071 0.32432 0.15913 0.53458 0.27049 0.11302 0.49520

2 0.18569 0.03382 0.51582 0.21113 0.08202 0.41552 0.20019 0.06910 0.42098

3 0.12859 0.01344 0.47890 0.15735 0.05103 0.35351 0.16471 0.04947 0.38190

4 0.09632 0.00620 0.45806 0.12521 0.03497 0.31333 0.14218 0.03819 0.35605

5 0.07572 0.00318 0.44411 0.10365 0.02546 0.28437 0.12621 0.03085 0.33704

6 0.06153 0.00176 0.43385 0.08815 0.01934 0.26212 0.11412 0.02570 0.32214

7 0.05124 0.00104 0.42584 0.07645 0.01515 0.24429 0.10457 0.02190 0.30999

8 0.04347 0.00064 0.41932 0.06730 0.01216 0.22956 0.09677 0.01898 0.29977

9 0.03744 0.00041 0.41385 0.05996 0.00995 0.21711 0.09025 0.01667 0.29099

10 0.03264 0.00027 0.40917 0.05393 0.00827 0.20639 0.08470 0.01481 0.28333

11 0.02874 0.00019 0.40509 0.04891 0.00697 0.19703 0.07991 0.01327 0.27653

12 0.02553 0.00013 0.40147 0.04465 0.00594 0.18876 0.07571 0.01199 0.27045

13 0.02285 0.00009 0.39824 0.04100 0.00511 0.18139 0.07200 0.01090 0.26496

14 0.02058 0.00007 0.39532 0.03785 0.00444 0.17475 0.06870 0.00997 0.25995

15 0.01864 0.00005 0.39266 0.03509 0.00388 0.16874 0.06572 0.00916 0.25536

16 0.01698 0.00004 0.39022 0.03266 0.00342 0.16326 0.06303 0.00846 0.25112

17 0.01553 0.00003 0.38797 0.03051 0.00303 0.15823 0.06058 0.00784 0.24720

18 0.01426 0.00002 0.38588 0.02859 0.00269 0.15360 0.05834 0.00729 0.24354

19 0.01314 0.00002 0.38394 0.02686 0.00241 0.14931 0.05629 0.00680 0.24013

20 0.01215 0.00001 0.38212 0.02531 0.00217 0.14533 0.05439 0.00637 0.23692

21 0.01127 0.00001 0.38041 0.02390 0.00196 0.14162 0.05263 0.00597 0.23391

22 0.01048 0.00001 0.37880 0.02262 0.00177 0.13815 0.05099 0.00562 0.23106

23 0.00978 0.00001 0.37728 0.02145 0.00161 0.13489 0.04947 0.00530 0.22837

24 0.00914 0.00001 0.37584 0.02038 0.00147 0.13183 0.04804 0.00500 0.22581

25 0.00856 0.00000 0.37447 0.01940 0.00134 0.12894 0.04671 0.00474 0.22338

26 0.00804 0.00000 0.37317 0.01849 0.00123 0.12622 0.04545 0.00449 0.22107

27 0.00756 0.00000 0.37193 0.01765 0.00113 0.12363 0.04427 0.00427 0.21886

28 0.00713 0.00000 0.37074 0.01687 0.00105 0.12119 0.04316 0.00406 0.21675

29 0.00673 0.00000 0.36960 0.01615 0.00097 0.11886 0.04210 0.00387 0.21473

30 0.00636 0.00000 0.36851 0.01548 0.00089 0.11664 0.04110 0.00369 0.21279

31 0.00602 0.00000 0.36747 0.01485 0.00083 0.11453 0.04015 0.00352 0.21093

32 0.00571 0.00000 0.36646 0.01427 0.00077 0.11252 0.03925 0.00337 0.20914

33 0.00542 0.00000 0.36549 0.01372 0.00072 0.11059 0.03840 0.00323 0.20742

34 0.00515 0.00000 0.36456 0.01320 0.00067 0.10874 0.03758 0.00309 0.20576

35 0.00491 0.00000 0.36366 0.01272 0.00063 0.10698 0.03680 0.00297 0.20415
88 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 5. Probability of uranium exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

Sgr So SOagr

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

36 0.00467 0.00000 0.36278 0.01226 0.00059 0.10528 0.03605 0.00285 0.20261

37 0.00446 0.00000 0.36194 0.01183 0.00055 0.10365 0.03534 0.00274 0.20111

38 0.00426 0.00000 0.36113 0.01143 0.00052 0.10208 0.03466 0.00264 0.19966

39 0.00407 0.00000 0.36034 0.01104 0.00048 0.10057 0.03400 0.00254 0.19826

40 0.00389 0.00000 0.35957 0.01068 0.00046 0.09912 0.03338 0.00245 0.19690

41 0.00373 0.00000 0.35882 0.01034 0.00043 0.09772 0.03277 0.00236 0.19559

42 0.00357 0.00000 0.35810 0.01001 0.00041 0.09637 0.03219 0.00228 0.19431

43 0.00343 0.00000 0.35740 0.00970 0.00038 0.09506 0.03163 0.00220 0.19306

44 0.00329 0.00000 0.35672 0.00941 0.00036 0.09380 0.03110 0.00213 0.19186

45 0.00316 0.00000 0.35605 0.00913 0.00034 0.09257 0.03058 0.00206 0.19068

46 0.00304 0.00000 0.35540 0.00886 0.00032 0.09139 0.03008 0.00199 0.18954

47 0.00292 0.00000 0.35477 0.00860 0.00031 0.09025 0.02960 0.00193 0.18842

48 0.00281 0.00000 0.35415 0.00836 0.00029 0.08914 0.02913 0.00187 0.18734

49 0.00271 0.00000 0.35355 0.00813 0.00028 0.08806 0.02868 0.00181 0.18628

50 0.00261 0.00000 0.35296 0.00791 0.00026 0.08702 0.02824 0.00176 0.18525

55 0.00219 0.00000 0.35022 0.00693 0.00021 0.08222 0.02626 0.00152 0.18044

60 0.00186 0.00000 0.34776 0.00613 0.00017 0.07803 0.02455 0.00133 0.17614

65 0.00160 0.00000 0.34552 0.00547 0.00013 0.07433 0.02307 0.00117 0.17226

70 0.00139 0.00000 0.34347 0.00492 0.00011 0.07102 0.02176 0.00104 0.16872

75 0.00121 0.00000 0.34159 0.00445 0.00009 0.06806 0.02060 0.00093 0.16549

80 0.00107 0.00000 0.33984 0.00404 0.00008 0.06538 0.01956 0.00084 0.16250

85 0.00095 0.00000 0.33822 0.00370 0.00007 0.06294 0.01862 0.00076 0.15974

90 0.00085 0.00000 0.33670 0.00339 0.00006 0.06071 0.01778 0.00069 0.15717

95 0.00076 0.00000 0.33527 0.00313 0.00005 0.05866 0.01701 0.00063 0.15477

100 0.00068 0.00000 0.33393 0.00289 0.00004 0.05676 0.01630 0.00058 0.15252

110 0.00056 0.00000 0.33146 0.00249 0.00003 0.05338 0.01506 0.00050 0.14840

120 0.00047 0.00000 0.32923 0.00218 0.00002 0.05044 0.01400 0.00043 0.14472

130 0.00040 0.00000 0.32720 0.00192 0.00002 0.04785 0.01308 0.00037 0.14141

140 0.00034 0.00000 0.32534 0.00170 0.00002 0.04556 0.01228 0.00033 0.13839

150 0.00029 0.00000 0.32362 0.00152 0.00001 0.04350 0.01157 0.00029 0.13562

160 0.00025 0.00000 0.32202 0.00137 0.00001 0.04165 0.01094 0.00026 0.13308

170 0.00022 0.00000 0.32054 0.00124 0.00001 0.03997 0.01037 0.00023 0.13072

180 0.00019 0.00000 0.31914 0.00113 0.00001 0.03844 0.00986 0.00021 0.12853

190 0.00017 0.00000 0.31784 0.00103 0.00001 0.03704 0.00940 0.00019 0.12649

200 0.00015 0.00000 0.31660 0.00095 0.00001 0.03575 0.00898 0.00017 0.12457
Appendix 5 89

Appendix 5. Probability of uranium exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

Sgr So SOagr

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

210 0.00014 0.00000 0.31543 0.00087 0.00000 0.03456 0.00859 0.00016 0.12277

220 0.00012 0.00000 0.31433 0.00080 0.00000 0.03346 0.00824 0.00014 0.12107

230 0.00011 0.00000 0.31327 0.00074 0.00000 0.03243 0.00792 0.00013 0.11947

240 0.00010 0.00000 0.31227 0.00069 0.00000 0.03147 0.00761 0.00012 0.11795

250 0.00009 0.00000 0.31131 0.00064 0.00000 0.03057 0.00734 0.00011 0.11651

260 0.00008 0.00000 0.31039 0.00060 0.00000 0.02973 0.00708 0.00011 0.11513

270 0.00008 0.00000 0.30951 0.00056 0.00000 0.02894 0.00683 0.00010 0.11382

280 0.00007 0.00000 0.30867 0.00053 0.00000 0.02820 0.00661 0.00009 0.11257

290 0.00006 0.00000 0.30786 0.00050 0.00000 0.02749 0.00639 0.00009 0.11138

300 0.00006 0.00000 0.30707 0.00047 0.00000 0.02683 0.00620 0.00008 0.11023
90 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 5. Probability of uranium exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

SObo Sp Spsq*

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

1 0.48976 0.21348 0.77127 0.29427 0.16239 0.46127 0.0595698 0.011175 0.202584

2 0.39909 0.15728 0.68945 0.21950 0.10626 0.38165 0.0294494 0.0043667 0.123926

3 0.34817 0.12548 0.64337 0.18137 0.07987 0.33930 0.0186571 0.0023951 0.089506

4 0.31358 0.10434 0.61246 0.15701 0.06409 0.31122 0.0132263 0.0015282 0.069838

5 0.28781 0.08910 0.58970 0.13966 0.05349 0.29057 0.0100116 0.0010642 0.05704

6 0.26754 0.07753 0.57195 0.12650 0.04583 0.27442 0.0079139 0.0007848 0.048033

7 0.25097 0.06843 0.55754 0.11606 0.04003 0.26127 0.0064526 0.000603 0.041346

8 0.23707 0.06108 0.54550 0.10753 0.03547 0.25024 0.0053853 0.0004777 0.036188

9 0.22517 0.05502 0.53521 0.10038 0.03180 0.24080 0.0045774 0.0003876 0.032091

10 0.21482 0.04994 0.52626 0.09429 0.02877 0.23257 0.0039482 0.0003206 0.02876

11 0.20570 0.04562 0.51838 0.08902 0.02624 0.22530 0.003447 0.0002694 0.026002

12 0.19758 0.04190 0.51134 0.08440 0.02408 0.21881 0.0030402 0.0002293 0.023682

13 0.19028 0.03867 0.50501 0.08032 0.02223 0.21296 0.0027047 0.0001975 0.021705

14 0.18367 0.03584 0.49927 0.07667 0.02062 0.20765 0.0024243 0.0001717 0.020001

15 0.17765 0.03335 0.49401 0.07338 0.01921 0.20279 0.0021871 0.0001506 0.01852

16 0.17213 0.03113 0.48918 0.07041 0.01796 0.19832 0.0019846 0.000133 0.01722

17 0.16705 0.02915 0.48472 0.06771 0.01685 0.19419 0.0018099 0.0001183 0.016071

18 0.16235 0.02737 0.48057 0.06523 0.01586 0.19036 0.0016582 0.0001058 0.015049

19 0.15798 0.02576 0.47670 0.06295 0.01496 0.18678 0.0015255 0.0000951 0.014135

20 0.15391 0.02430 0.47307 0.06085 0.01415 0.18343 0.0014086 0.000086 0.013312

21 0.15010 0.02297 0.46967 0.05890 0.01342 0.18029 0.001305 0.000078 0.012569

22 0.14653 0.02176 0.46646 0.05708 0.01274 0.17733 0.0012128 0.0000711 0.011894

23 0.14317 0.02065 0.46342 0.05539 0.01213 0.17454 0.0011303 0.000065 0.011279

24 0.14000 0.01962 0.46055 0.05381 0.01157 0.17190 0.0010562 0.0000596 0.010716

25 0.13700 0.01868 0.45782 0.05233 0.01104 0.16939 0.0009893 0.0000549 0.0102

26 0.13417 0.01781 0.45523 0.05093 0.01056 0.16701 0.0009287 0.0000506 0.009725

27 0.13148 0.01700 0.45275 0.04962 0.01012 0.16474 0.0008736 0.0000469 0.009286

28 0.12893 0.01625 0.45039 0.04838 0.00970 0.16258 0.0008234 0.0000435 0.008879

29 0.12649 0.01555 0.44812 0.04720 0.00932 0.16051 0.0007775 0.0000404 0.008502

30 0.12417 0.01490 0.44596 0.04609 0.00896 0.15853 0.0007354 0.0000377 0.008151

31 0.12196 0.01429 0.44388 0.04504 0.00862 0.15663 0.0006967 0.0000352 0.007824

32 0.11984 0.01371 0.44188 0.04403 0.00830 0.15481 0.000661 0.0000329 0.007518

33 0.11781 0.01318 0.43995 0.04308 0.00801 0.15307 0.000628 0.0000309 0.007232

34 0.11586 0.01268 0.43810 0.04217 0.00773 0.15138 0.0005975 0.000029 0.006964

35 0.11400 0.01220 0.43631 0.04130 0.00746 0.14976 0.0005692 0.0000272 0.006712
Appendix 5 91

Appendix 5. Probability of uranium exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

SObo Sp Spsq*

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

36 0.11221 0.01176 0.43458 0.04047 0.00722 0.14820 0.0005428 0.0000257 0.006475

37 0.11048 0.01133 0.43291 0.03968 0.00698 0.14670 0.0005183 0.0000242 0.006251

38 0.10882 0.01094 0.43130 0.03891 0.00676 0.14524 0.0004954 0.0000229 0.00604

39 0.10722 0.01056 0.42973 0.03818 0.00655 0.14383 0.000474 0.0000216 0.005841

40 0.10568 0.01020 0.42822 0.03748 0.00635 0.14247 0.000454 0.0000205 0.005653

41 0.10419 0.00987 0.42675 0.03681 0.00616 0.14116 0.0004352 0.0000194 0.005474

42 0.10275 0.00955 0.42532 0.03616 0.00598 0.13988 0.0004176 0.0000184 0.005305

43 0.10136 0.00924 0.42393 0.03554 0.00581 0.13864 0.0004011 0.0000175 0.005144

44 0.10001 0.00895 0.42259 0.03494 0.00565 0.13744 0.0003855 0.0000167 0.004991

45 0.09871 0.00867 0.42128 0.03436 0.00549 0.13627 0.0003708 0.0000159 0.004845

46 0.09745 0.00841 0.42000 0.03380 0.00534 0.13514 0.0003569 0.0000151 0.004706

47 0.09623 0.00816 0.41876 0.03326 0.00520 0.13403 0.0003438 0.0000144 0.004574

48 0.09504 0.00792 0.41755 0.03274 0.00507 0.13296 0.0003314 0.0000138 0.004448

49 0.09389 0.00769 0.41637 0.03224 0.00494 0.13192 0.0003197 0.0000132 0.004327

50 0.09277 0.00747 0.41521 0.03175 0.00481 0.13090 0.0003085 0.0000126 0.004212

55 0.08762 0.00651 0.40984 0.02953 0.00426 0.12618 0.0002608 0.0000102 0.003704

60 0.08312 0.00573 0.40503 0.02762 0.00381 0.12199 0.0002233 0.0000084 0.00329

65 0.07913 0.00508 0.40068 0.02596 0.00343 0.11823 0.0001933 0.000007 0.002946

70 0.07556 0.00454 0.39672 0.02449 0.00311 0.11483 0.0001689 0.0000059 0.002657

75 0.07236 0.00408 0.39308 0.02319 0.00283 0.11173 0.0001488 0.000005 0.002412

80 0.06945 0.00369 0.38972 0.02203 0.00260 0.10890 0.0001321 0.0000043 0.002201

85 0.06681 0.00335 0.38660 0.02098 0.00239 0.10628 0.000118 0.0000038 0.002018

90 0.06439 0.00305 0.38369 0.02003 0.00221 0.10386 0.000106 0.0000033 0.001859

95 0.06216 0.00280 0.38096 0.01916 0.00205 0.10161 0.0000957 0.0000029 0.001719

100 0.06010 0.00257 0.37840 0.01837 0.00191 0.09952 0.0000868 0.0000026 0.001595

110 0.05642 0.00219 0.37371 0.01698 0.00167 0.09571 0.0000724 0.000002 0.001386

120 0.05322 0.00189 0.36950 0.01578 0.00147 0.09234 0.0000611 0.0000016 0.001217

130 0.05040 0.00165 0.36568 0.01475 0.00131 0.08932 0.0000523 0.0000014 0.001079

140 0.04790 0.00145 0.36219 0.01384 0.00118 0.08659 0.0000452 0.0000011 0.000965

150 0.04566 0.00128 0.35898 0.01305 0.00106 0.08411 0.0000394 0.000001 0.000868

160 0.04364 0.00114 0.35601 0.01233 0.00097 0.08185 0.0000346 0.0000008 0.000786

170 0.04181 0.00102 0.35325 0.01170 0.00088 0.07976 0.0000307 0.0000007 0.000715

180 0.04015 0.00092 0.35068 0.01112 0.00081 0.07784 0.0000273 0.0000006 0.000654

190 0.03862 0.00083 0.34826 0.01060 0.00075 0.07605 0.0000245 0.0000005 0.0006

200 0.03722 0.00076 0.34599 0.01013 0.00069 0.07439 0.000022 0.0000005 0.000553
92 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 5. Probability of uranium exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

SObo Sp Spsq*

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

210 0.03592 0.00069 0.34384 0.00970 0.00064 0.07283 0.0000199 0.0000004 0.000512

220 0.03472 0.00063 0.34181 0.00930 0.00060 0.07137 0.0000181 0.0000004 0.000475

230 0.03360 0.00058 0.33989 0.00893 0.00056 0.07000 0.0000165 0.0000003 0.000442

240 0.03256 0.00054 0.33806 0.00859 0.00052 0.06871 0.0000151 0.0000003 0.000413

250 0.03159 0.00050 0.33631 0.00828 0.00049 0.06749 0.0000139 0.0000003 0.000386

260 0.03067 0.00046 0.33465 0.00798 0.00046 0.06633 0.0000128 0.0000002 0.000362

270 0.02981 0.00043 0.33305 0.00771 0.00043 0.06523 0.0000118 0.0000002 0.000341

280 0.02901 0.00040 0.33153 0.00745 0.00041 0.06418 0.0000109 0.0000002 0.000321

290 0.02824 0.00037 0.33006 0.00721 0.00038 0.06319 0.0000101 0.0000002 0.000303

300 0.02752 0.00035 0.32865 0.00699 0.00036 0.06224 0.0000094 0.0000002 0.000286
Appendix 5 93

Appendix 5. Probability of uranium exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

Spss Ssqd St

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

1 0.10803 0.01801 0.35292 0.33125 0.15099 0.56326 0.26746 0.12567 0.46258

2 0.05713 0.00474 0.28624 0.22783 0.08919 0.44186 0.16133 0.05813 0.34187

3 0.03757 0.00185 0.25586 0.17694 0.06207 0.37577 0.11419 0.03347 0.28195

4 0.02733 0.00088 0.23708 0.14558 0.04675 0.33218 0.08731 0.02158 0.24424

5 0.02109 0.00048 0.22379 0.12400 0.03693 0.30050 0.06996 0.01493 0.21764

6 0.01693 0.00028 0.21367 0.10811 0.03014 0.27607 0.05786 0.01085 0.19756

7 0.01398 0.00018 0.20555 0.09586 0.02519 0.25646 0.04896 0.00817 0.18170

8 0.01179 0.00012 0.19883 0.08611 0.02145 0.24025 0.04218 0.00634 0.16875

9 0.01012 0.00008 0.19313 0.07814 0.01852 0.22656 0.03684 0.00502 0.15793

10 0.00880 0.00006 0.18819 0.07149 0.01619 0.21479 0.03255 0.00406 0.14871

11 0.00774 0.00004 0.18384 0.06586 0.01429 0.20452 0.02903 0.00333 0.14073

12 0.00687 0.00003 0.17998 0.06103 0.01273 0.19547 0.02610 0.00277 0.13374

13 0.00615 0.00002 0.17650 0.05683 0.01141 0.18740 0.02362 0.00233 0.12756

14 0.00554 0.00002 0.17335 0.05315 0.01030 0.18016 0.02151 0.00198 0.12203

15 0.00502 0.00001 0.17047 0.04990 0.00934 0.17360 0.01969 0.00169 0.11705

16 0.00458 0.00001 0.16783 0.04700 0.00852 0.16763 0.01811 0.00146 0.11255

17 0.00419 0.00001 0.16538 0.04440 0.00781 0.16217 0.01672 0.00127 0.10844

18 0.00386 0.00001 0.16311 0.04206 0.00718 0.15714 0.01550 0.00111 0.10468

19 0.00356 0.00001 0.16100 0.03994 0.00662 0.15250 0.01442 0.00098 0.10121

20 0.00330 0.00000 0.15902 0.03800 0.00613 0.14819 0.01345 0.00087 0.09801

21 0.00307 0.00000 0.15716 0.03624 0.00570 0.14418 0.01258 0.00077 0.09504

22 0.00286 0.00000 0.15540 0.03462 0.00530 0.14044 0.01180 0.00069 0.09228

23 0.00267 0.00000 0.15375 0.03312 0.00495 0.13693 0.01109 0.00061 0.08970

24 0.00251 0.00000 0.15218 0.03174 0.00463 0.13364 0.01044 0.00055 0.08728

25 0.00235 0.00000 0.15069 0.03047 0.00434 0.13054 0.00986 0.00050 0.08502

26 0.00221 0.00000 0.14927 0.02928 0.00408 0.12761 0.00932 0.00045 0.08288

27 0.00209 0.00000 0.14792 0.02817 0.00384 0.12485 0.00883 0.00041 0.08087

28 0.00197 0.00000 0.14663 0.02714 0.00362 0.12223 0.00838 0.00037 0.07897

29 0.00187 0.00000 0.14540 0.02617 0.00342 0.11974 0.00796 0.00034 0.07717

30 0.00177 0.00000 0.14422 0.02527 0.00324 0.11738 0.00758 0.00031 0.07546

31 0.00168 0.00000 0.14308 0.02442 0.00307 0.11513 0.00722 0.00029 0.07384

32 0.00160 0.00000 0.14199 0.02362 0.00291 0.11298 0.00689 0.00026 0.07230

33 0.00152 0.00000 0.14094 0.02286 0.00277 0.11093 0.00658 0.00024 0.07083

34 0.00145 0.00000 0.13993 0.02215 0.00263 0.10897 0.00630 0.00022 0.06942

35 0.00138 0.00000 0.13896 0.02147 0.00251 0.10709 0.00603 0.00021 0.06808
94 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 5. Probability of uranium exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

Spss Ssqd St

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

36 0.00132 0.00000 0.13802 0.02083 0.00239 0.10529 0.00578 0.00019 0.06680

37 0.00126 0.00000 0.13711 0.02023 0.00228 0.10357 0.00554 0.00018 0.06557

38 0.00121 0.00000 0.13623 0.01965 0.00218 0.10191 0.00532 0.00017 0.06439

39 0.00116 0.00000 0.13538 0.01911 0.00208 0.10031 0.00511 0.00015 0.06326

40 0.00111 0.00000 0.13456 0.01859 0.00199 0.09878 0.00492 0.00014 0.06218

41 0.00107 0.00000 0.13376 0.01809 0.00191 0.09730 0.00473 0.00013 0.06113

42 0.00103 0.00000 0.13299 0.01762 0.00183 0.09587 0.00456 0.00013 0.06013

43 0.00099 0.00000 0.13223 0.01717 0.00176 0.09450 0.00440 0.00012 0.05916

44 0.00095 0.00000 0.13150 0.01673 0.00169 0.09317 0.00424 0.00011 0.05822

45 0.00091 0.00000 0.13079 0.01632 0.00162 0.09189 0.00409 0.00010 0.05732

46 0.00088 0.00000 0.13010 0.01592 0.00156 0.09064 0.00396 0.00010 0.05645

47 0.00085 0.00000 0.12943 0.01555 0.00150 0.08944 0.00382 0.00009 0.05561

48 0.00082 0.00000 0.12877 0.01518 0.00145 0.08828 0.00370 0.00009 0.05480

49 0.00079 0.00000 0.12813 0.01483 0.00139 0.08715 0.00358 0.00008 0.05401

50 0.00077 0.00000 0.12751 0.01450 0.00134 0.08606 0.00347 0.00008 0.05325

55 0.00065 0.00000 0.12460 0.01300 0.00113 0.08105 0.00297 0.00006 0.04978

60 0.00056 0.00000 0.12200 0.01176 0.00096 0.07668 0.00258 0.00005 0.04677

65 0.00049 0.00000 0.11966 0.01070 0.00083 0.07284 0.00226 0.00004 0.04414

70 0.00043 0.00000 0.11753 0.00980 0.00072 0.06943 0.00199 0.00003 0.04182

75 0.00038 0.00000 0.11557 0.00902 0.00063 0.06637 0.00177 0.00002 0.03975

80 0.00034 0.00000 0.11377 0.00835 0.00055 0.06362 0.00159 0.00002 0.03789

85 0.00030 0.00000 0.11210 0.00775 0.00049 0.06111 0.00143 0.00002 0.03622

90 0.00027 0.00000 0.11055 0.00722 0.00044 0.05883 0.00130 0.00001 0.03469

95 0.00025 0.00000 0.10910 0.00675 0.00039 0.05674 0.00118 0.00001 0.03330

100 0.00022 0.00000 0.10774 0.00633 0.00035 0.05481 0.00108 0.00001 0.03203

110 0.00019 0.00000 0.10525 0.00561 0.00029 0.05137 0.00091 0.00001 0.02977

120 0.00016 0.00000 0.10303 0.00502 0.00024 0.04839 0.00077 0.00001 0.02783

130 0.00014 0.00000 0.10102 0.00452 0.00021 0.04578 0.00067 0.00000 0.02614

140 0.00012 0.00000 0.09919 0.00410 0.00018 0.04348 0.00058 0.00000 0.02465

150 0.00010 0.00000 0.09752 0.00375 0.00015 0.04142 0.00051 0.00000 0.02333

160 0.00009 0.00000 0.09597 0.00344 0.00013 0.03957 0.00045 0.00000 0.02216

170 0.00008 0.00000 0.09454 0.00317 0.00012 0.03789 0.00040 0.00000 0.02110

180 0.00007 0.00000 0.09321 0.00293 0.00010 0.03637 0.00036 0.00000 0.02014

190 0.00007 0.00000 0.09196 0.00272 0.00009 0.03498 0.00033 0.00000 0.01927

200 0.00006 0.00000 0.09080 0.00253 0.00008 0.03370 0.00029 0.00000 0.01847
Appendix 5 95

Appendix 5. Probability of uranium exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

Spss Ssqd St

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

210 0.00005 0.00000 0.08970 0.00237 0.00007 0.03253 0.00027 0.00000 0.01774

220 0.00005 0.00000 0.08866 0.00222 0.00006 0.03144 0.00024 0.00000 0.01707

230 0.00004 0.00000 0.08768 0.00209 0.00006 0.03043 0.00022 0.00000 0.01645

240 0.00004 0.00000 0.08675 0.00196 0.00005 0.02948 0.00021 0.00000 0.01587

250 0.00004 0.00000 0.08587 0.00185 0.00005 0.02860 0.00019 0.00000 0.01533

260 0.00003 0.00000 0.08503 0.00175 0.00004 0.02778 0.00017 0.00000 0.01483

270 0.00003 0.00000 0.08422 0.00166 0.00004 0.02701 0.00016 0.00000 0.01436

280 0.00003 0.00000 0.08346 0.00157 0.00004 0.02628 0.00015 0.00000 0.01393

290 0.00003 0.00000 0.08272 0.00150 0.00003 0.02559 0.00014 0.00000 0.01351

300 0.00003 0.00000 0.08202 0.00142 0.00003 0.02495 0.00013 0.00000 0.01313
96 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 5. Probability of uranium exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

SZtb Zpg Zsg

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

1 0.0700933 0.0257274 0.158045 0.49898 0.26915 0.72915 0.92117 0.78082 0.97987

2 0.0383324 0.0105027 0.108813 0.38066 0.18437 0.61461 0.80805 0.63687 0.91795

3 0.026002 0.0058299 0.086296 0.31565 0.14087 0.54642 0.71006 0.53474 0.84611

4 0.0194307 0.0037291 0.072746 0.27262 0.11357 0.49918 0.62873 0.45674 0.77806

5 0.0153589 0.002593 0.063483 0.24138 0.09466 0.46369 0.56117 0.39469 0.71735

6 0.0125982 0.001906 0.05666 0.21738 0.08075 0.43561 0.50451 0.34407 0.66421

7 0.01061 0.0014581 0.051377 0.19820 0.07007 0.41260 0.45649 0.30207 0.61787

8 0.0091146 0.0011495 0.047139 0.18245 0.06163 0.39324 0.41537 0.26677 0.57735

9 0.0079521 0.0009279 0.043648 0.16922 0.05478 0.37663 0.37985 0.23682 0.54174

10 0.0070249 0.0007635 0.040712 0.15792 0.04913 0.36215 0.34890 0.21119 0.51024

11 0.0062697 0.0006382 0.038202 0.14814 0.04439 0.34936 0.32173 0.18912 0.48222

12 0.005644 0.0005406 0.036025 0.13957 0.04037 0.33795 0.29773 0.17000 0.45712

13 0.005118 0.0004631 0.034117 0.13199 0.03691 0.32767 0.27641 0.15334 0.43452

14 0.0046704 0.0004006 0.032428 0.12523 0.03391 0.31835 0.25735 0.13875 0.41406

15 0.0042854 0.0003495 0.030919 0.11916 0.03129 0.30984 0.24025 0.12593 0.39545

16 0.0039512 0.0003072 0.029563 0.11367 0.02899 0.30202 0.22483 0.11461 0.37843

17 0.0036588 0.0002719 0.028336 0.10868 0.02694 0.29480 0.21087 0.10458 0.36282

18 0.003401 0.000242 0.027219 0.10412 0.02512 0.28811 0.19818 0.09566 0.34843

19 0.0031723 0.0002166 0.026197 0.09994 0.02349 0.28188 0.18662 0.08770 0.33513

20 0.0029683 0.0001948 0.025258 0.09608 0.02201 0.27606 0.17604 0.08058 0.32280

21 0.0027852 0.000176 0.024392 0.09252 0.02068 0.27060 0.16634 0.07418 0.31132

22 0.0026202 0.0001597 0.023591 0.08921 0.01948 0.26548 0.15742 0.06843 0.30062

23 0.0024709 0.0001454 0.022846 0.08614 0.01838 0.26064 0.14920 0.06324 0.29061

24 0.0023352 0.0001328 0.022152 0.08327 0.01737 0.25607 0.14160 0.05854 0.28123

25 0.0022114 0.0001217 0.021504 0.08058 0.01645 0.25175 0.13456 0.05428 0.27241

26 0.002098 0.0001119 0.020897 0.07807 0.01560 0.24764 0.12802 0.05041 0.26411

27 0.001994 0.0001032 0.020326 0.07570 0.01482 0.24374 0.12195 0.04689 0.25629

28 0.0018982 0.0000953 0.019789 0.07347 0.01410 0.24002 0.11629 0.04367 0.24890

29 0.0018097 0.0000883 0.019283 0.07137 0.01343 0.23647 0.11100 0.04073 0.24190

30 0.0017279 0.000082 0.018805 0.06939 0.01281 0.23308 0.10606 0.03804 0.23527

31 0.0016519 0.0000763 0.018352 0.06751 0.01223 0.22984 0.10144 0.03557 0.22897

32 0.0015812 0.0000711 0.017922 0.06572 0.01169 0.22673 0.09711 0.03331 0.22299

33 0.0015154 0.0000664 0.017515 0.06403 0.01119 0.22375 0.09304 0.03122 0.21729

34 0.0014539 0.0000621 0.017127 0.06242 0.01072 0.22088 0.08921 0.02929 0.21186

35 0.0013964 0.0000582 0.016757 0.06089 0.01027 0.21813 0.08561 0.02751 0.20668
Appendix 5 97

Appendix 5. Probability of uranium exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

SZtb Zpg Zsg

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

36 0.0013426 0.0000547 0.016405 0.05943 0.00986 0.21547 0.08221 0.02587 0.20173

37 0.001292 0.0000514 0.016068 0.05803 0.00947 0.21292 0.07900 0.02435 0.19700

38 0.0012444 0.0000484 0.015746 0.05670 0.00911 0.21045 0.07598 0.02294 0.19247

39 0.0011997 0.0000456 0.015438 0.05543 0.00876 0.20807 0.07311 0.02163 0.18813

40 0.0011574 0.000043 0.015143 0.05421 0.00843 0.20577 0.07040 0.02042 0.18396

41 0.0011176 0.0000407 0.01486 0.05304 0.00813 0.20354 0.06784 0.01929 0.17997

42 0.0010799 0.0000385 0.014589 0.05191 0.00784 0.20139 0.06540 0.01823 0.17613

43 0.0010442 0.0000365 0.014327 0.05084 0.00756 0.19930 0.06309 0.01725 0.17244

44 0.0010104 0.0000346 0.014076 0.04980 0.00730 0.19728 0.06089 0.01634 0.16889

45 0.0009784 0.0000328 0.013834 0.04881 0.00705 0.19531 0.05880 0.01548 0.16547

46 0.0009479 0.0000312 0.013601 0.04785 0.00682 0.19341 0.05681 0.01468 0.16217

47 0.000919 0.0000297 0.013377 0.04692 0.00659 0.19156 0.05492 0.01393 0.15899

48 0.0008914 0.0000283 0.01316 0.04603 0.00638 0.18976 0.05311 0.01323 0.15593

49 0.0008652 0.0000269 0.012951 0.04518 0.00618 0.18801 0.05139 0.01257 0.15296

50 0.0008401 0.0000257 0.012749 0.04435 0.00598 0.18631 0.04974 0.01195 0.15010

55 0.0007308 0.0000205 0.011832 0.04060 0.00514 0.17845 0.04254 0.00937 0.13714

60 0.0006426 0.0000166 0.011046 0.03741 0.00446 0.17149 0.03673 0.00745 0.12606

65 0.0005702 0.0000137 0.010364 0.03466 0.00391 0.16528 0.03197 0.00600 0.11648

70 0.00051 0.0000114 0.009766 0.03226 0.00345 0.15969 0.02803 0.00488 0.10812

75 0.0004593 0.0000097 0.009237 0.03016 0.00307 0.15462 0.02473 0.00400 0.10076

80 0.0004162 0.0000082 0.008766 0.02829 0.00275 0.14999 0.02195 0.00332 0.09423

85 0.0003791 0.0000071 0.008342 0.02663 0.00247 0.14575 0.01958 0.00277 0.08841

90 0.0003469 0.0000061 0.00796 0.02513 0.00223 0.14183 0.01755 0.00233 0.08318

95 0.0003189 0.0000053 0.007613 0.02378 0.00203 0.13820 0.01580 0.00197 0.07846

100 0.0002942 0.0000047 0.007296 0.02256 0.00185 0.13483 0.01428 0.00167 0.07419

110 0.0002531 0.0000037 0.006738 0.02043 0.00155 0.12873 0.01178 0.00123 0.06674

120 0.0002203 0.0000029 0.006262 0.01864 0.00132 0.12336 0.00985 0.00092 0.06048

130 0.0001936 0.0000024 0.005851 0.01711 0.00113 0.11857 0.00831 0.00070 0.05515

140 0.0001717 0.0000019 0.005492 0.01579 0.00098 0.11428 0.00709 0.00055 0.05057

150 0.0001533 0.0000016 0.005176 0.01464 0.00086 0.11040 0.00609 0.00043 0.04659

160 0.0001379 0.0000014 0.004896 0.01363 0.00076 0.10686 0.00528 0.00034 0.04310

170 0.0001247 0.0000012 0.004644 0.01274 0.00067 0.10362 0.00460 0.00027 0.04002

180 0.0001133 0.000001 0.004418 0.01195 0.00060 0.10064 0.00403 0.00022 0.03730

190 0.0001035 0.0000009 0.004214 0.01123 0.00054 0.09788 0.00355 0.00018 0.03486

200 0.0000949 0.0000007 0.004027 0.01059 0.00048 0.09533 0.00315 0.00015 0.03267
98 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 5. Probability of uranium exceeding a given concentration, by bedrock unit.—Continued

[Probabilities with bold typeface apply to concentrations at the U.S. Environmental Protection Agency drinking-water standard for public supplies. Multiply 

probability values by 100 to obtain percent probability; *, fewer than five analyses were above the analytical reporting limit and the option to assume a 

common scale was used in the distribution fitting]

Uranium, 

in micrograms 

per liter

Bedrock unit abbreviation

SZtb Zpg Zsg

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

Probability of 

concentration 

being greater 

than concentration listed in 

first column

Lower 

95-percent 

confidence 

bound

Upper 

95-percent 

confidence 

bound

210 0.0000874 0.0000006 0.003857 0.01001 0.00044 0.09295 0.00280 0.00012 0.03070

220 0.0000807 0.0000006 0.003701 0.00949 0.00040 0.09072 0.00251 0.00010 0.02892

230 0.0000748 0.0000005 0.003557 0.00901 0.00036 0.08863 0.00225 0.00009 0.02730

240 0.0000695 0.0000004 0.003424 0.00857 0.00033 0.08667 0.00202 0.00007 0.02582

250 0.0000648 0.0000004 0.0033 0.00816 0.00030 0.08483 0.00183 0.00006 0.02446

260 0.0000605 0.0000004 0.003186 0.00779 0.00028 0.08308 0.00166 0.00005 0.02322

270 0.0000567 0.0000003 0.003079 0.00745 0.00026 0.08143 0.00151 0.00004 0.02207

280 0.0000532 0.0000003 0.002979 0.00713 0.00024 0.07987 0.00137 0.00004 0.02102

290 0.00005 0.0000003 0.002885 0.00683 0.00022 0.07838 0.00125 0.00003 0.02004

300 0.0000471 0.0000002 0.002797 0.00655 0.00020 0.07697 0.00115 0.00003 0.01913
 

Appendix 6. Uranium Log-Normal Fit Statistics by 

Bedrock Unit
100 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 6. Uranium log-normal fit statistics by bedrock unit.

[CI, confidence interval; %, percent; *, fewer than five analyses were above the analytical reporting limit and the Minitab option to assume a common scale was 

used in the distribution fitting]

Bedrock unit abbreviation

Dcgr Dfgr

Censoring information Count Censoring information Count

Uncensored value 7 Uncensored value 8

Left censored value 0 Left censored value 0

Distribution Log normal Distribution Log normal

Parameter estimates Parameter estimates

Parameter Estimate Standard 

error

95% normal CI

Parameter Estimate Standard 

error

95% normal CI

Lower Upper Lower Upper

Location 2.31035 0.548184 1.23593 3.38477 Location 0.872357 0.890096 -0.872199 2.61691

Scale 1.35299 0.49093 0.664417 2.75519 Scale 2.33772 0.529608 1.49953 3.64445

Log-likelihood -29.247 Log-likelihood -32.057

Goodness-of-fit Goodness-of-fit

Anderson-Darling (adjusted) 3.306 Anderson-Darling (adjusted) 2.951

Correlation coefficient 0.957 Correlation coefficient 0.973

Characteristics of distribution Characteristics of distribution

Descriptor Estimate Standard

error

95% normal CI

Descriptor Estimate Standard

error

95% normal CI

Lower Upper Lower Upper

Mean 25.1698 17.4269 6.47937 97.7751 Mean 36.7756 45.1462 3.31599 407.855

Standard 

deviation 57.6032 78.2128 4.02436 824.511 Standard deviation 564.077 1.30 × 103 6.16399 5.16 × 104

Median 10.0779 5.52457 3.44157 29.5112 Median 2.39254 2.12959 0.418031 13.6934

First quartile 

(Q1) 4.04616 2.97585 0.957207 17.1033 First quartile (Q1) 0.494398 0.531543 0.0601067 4.06659

Third quartile 

(Q3) 25.1016 13.2678 8.90814 70.7318 Third quartile (Q3) 11.5782 9.57458 2.28952 58.5518

Interquartile 

range (IQR) 21.0554 12.088 6.83416 64.8697 Interquartile range (IQR) 11.0838 9.18399 2.1847 56.2328
Appendix 6 101

Appendix 6. Uranium log-normal fit statistics by bedrock unit.—Continued

[CI, confidence interval; %, percent; *, fewer than five analyses were above the analytical reporting limit and the Minitab option to assume a common scale was 

used in the distribution fitting]

Bedrock unit abbreviation

Dl DSw

Censoring information Count Censoring information Count

Uncensored value 9 Uncensored value 8

Left censored value 0 Left censored value 0

Distribution Log normal Distribution Log normal

Parameter estimates Parameter estimates

Parameter Estimate Standard 

error

95% normal CI

Parameter Estimate Standard 

error

95% normal CI

Lower Upper Lower Upper

Location -1.42001 0.492276 -2.38486 -0.455172 Location -0.82093 0.518637 -1.83744 0.19558

Scale 1.4107 0.415304 0.792216 2.51203 Scale 1.40474 0.552648 0.64971 3.0372

Log-likelihood -4.421 Log-likelihood -32.057

Goodness-of-fit Goodness-of-fit

Anderson-Darling (adjusted) 2.64 Anderson-Darling (adjusted) 2.878

Correlation coefficient 0.982 Correlation coefficient 0.989

Characteristics of distribution Characteristics of distribution

Descriptor Estimate Standard

error

95% normal CI

Descriptor Estimate Standard

error

95% normal CI

Lower Upper Lower Upper

Mean 0.653782 0.421119 0.184991 2.31055 Mean 1.18024 0.943965 0.246135 5.65936

Standard 

deviation 1.64306 1.99408 0.152267 17.7297 Standard deviation 2.93744 4.72115 0.12586 68.5566

Median 0.24171 0.118988 0.0921021 0.634339 Median 0.440022 0.228212 0.159225 1.21602

First quartile 

(Q1) 0.0933392 0.0592101 0.0269216 0.323614 First quartile (Q1) 0.170604 0.122943 0.0415511 0.700477

Third quartile 

(Q3) 0.625932 0.306129 0.240006 1.63242 Third quartile (Q3) 1.13491 0.618028 0.390328 3.29984

Interquartile 

range (IQR) 0.532592 0.279416 0.19047 1.48924 Interquartile range (IQR) 0.964306 0.588827 0.291375 3.19138
102 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 6. Uranium log-normal fit statistics by bedrock unit.—Continued

[CI, confidence interval; %, percent; *, fewer than five analyses were above the analytical reporting limit and the Minitab option to assume a common scale was 

used in the distribution fitting]

Bedrock unit abbreviation

Ops* OZf

Censoring information Count Censoring information Count

Uncensored value 3 Uncensored value 8

Left censored value 7 Left censored value 0

Distribution Log normal Distribution Log normal

Parameter estimates Parameter estimates

Parameter Estimate Standard 

error

95% normal CI

Parameter Estimate Standard 

error

95% normal CI

Lower Upper Lower Upper

Location -4.59511 0.651571 -5.87217 -3.31806 Location -0.861046 0.430412 -1.70464 -0.0174541

Scale 1.70447 0.0790912 1.55629 1.86675 Scale 1.14421 0.3512 0.626965 2.0882

Log-likelihood -7.89 Log-likelihood -6.792

Goodness-of-fit Goodness-of-fit

Anderson-Darling (adjusted) 1.393 Anderson-Darling (adjusted) 2.89

Correlation coefficient 0.86 Correlation coefficient 0.986

Characteristics of distribution Characteristics of distribution

Descriptor Estimate Standard

error

95% normal CI

Descriptor Estimate Standard

error

95% normal CI

Lower Upper Lower Upper

Mean 0.0431743 0.0280004 0.0121111 0.15391 Mean 0.813481 0.388955 0.318682 2.07653

Standard 

deviation 0.179415 0.121157 0.0477589 0.674006 Standard deviation 1.3375 1.20545 0.228632 7.82445

Median 0.0101011 0.0065816 0.0028168 0.0362231 Median 0.42272 0.181944 0.181838 0.982697

First quartile 

(Q1) 0.0031995 0.002113 0.0008769 0.0116741 First quartile (Q1) 0.195381 0.108958 0.0654924 0.58287

Third quartile 

(Q3) 0.0318898 0.0206335 0.0089723 0.113345 Third quartile (Q3) 0.914585 0.379014 0.405954 2.0605

Interquartile 

range (IQR) 0.0286903 0.0185514 0.0080787 0.101889 Interquartile range (IQR) 0.719205 0.330712 0.292041 1.77117
Appendix 6 103

Appendix 6. Uranium log-normal fit statistics by bedrock unit.—Continued

[CI, confidence interval; %, percent; *, fewer than five analyses were above the analytical reporting limit and the Minitab option to assume a common scale was 

used in the distribution fitting]

Bedrock unit abbreviation

OZm OZn

Censoring information Count Censoring information Count

Uncensored value 10 Uncensored value 30

Left censored value 0 Left censored value 1

Distribution Log normal Distribution Log normal

Parameter estimates Parameter estimates

Parameter Estimate Standard 

error

95% normal CI

Parameter Estimate Standard 

error

95% normal CI

Lower Upper Lower Upper

Location -0.655272 0.788995 -2.20167 0.89113 Location 0.0159391 0.258203 -0.490129 0.522007

Scale 2.41324 0.682883 1.3859 4.20212 Scale 1.42905 0.185068 1.1087 1.84197

Log-likelihood -18.878 Log-likelihood -62.614

Goodness-of-fit Goodness-of-fit

Anderson-Darling (adjusted) 2.451 Anderson-Darling (adjusted) 1.108

Correlation coefficient 0.977 Correlation coefficient 0.973

Characteristics of distribution Characteristics of distribution

Descriptor Estimate Standard

error

95% normal CI

Descriptor Estimate Standard

error

95% normal CI

Lower Upper Lower Upper

Mean 9.55049 15.6289 0.386439 236.032 Mean 2.82083 0.990952 1.41694 5.61568

Standard 

deviation 175.384 559.999 0.33582 9.16 × 104 Standard 

deviation 7.30561 4.39151 2.24898 23.7315

Median 0.519301 0.409726 0.110618 2.43788 Median 1.01607 0.262351 0.612547 1.68541

First quartile 

(Q1) 0.10198 0.102956 0.0140984 0.737666 First quartile (Q1) 0.387538 0.115277 0.21633 0.694244

Third quartile 

(Q3) 2.64437 2.13213 0.544513 12.8421 Third quartile (Q3) 2.66398 0.734496 1.55182 4.57318

Interquartile 

range (IQR) 2.54239 2.08213 0.51067 12.6574 Interquartile range (IQR) 2.27644 0.668797 1.27991 4.04884
104 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 6. Uranium log-normal fit statistics by bedrock unit.—Continued

[CI, confidence interval; %, percent; *, fewer than five analyses were above the analytical reporting limit and the Minitab option to assume a common scale was 

used in the distribution fitting]

Bedrock unit abbreviation

OZnb Ph

Censoring information Count Censoring information Count

Uncensored value 14 Uncensored value 8

Left censored value 6 Left censored value 1

Distribution Log normal Distribution Log normal

Parameter estimates Parameter estimates

Parameter Estimate Standard 

error

95% normal CI

Parameter Estimate Standard 

error

95% normal CI

Lower Upper Lower Upper

Location -1.75943 0.483527 -2.70713 -0.811735 Location -1.75943 0.483527 -2.70713 -0.811735

Scale 2.1023 0.305023 1.58196 2.7938 Scale 2.1023 0.305023 1.58196 2.7938

Log-likelihood -34.212 Log-likelihood -25.95

Goodness-of-fit Goodness-of-fit

Anderson-Darling (adjusted) 1.676 Anderson-Darling (adjusted) 2.642

Correlation coefficient 0.857 Correlation coefficient 0.896

Characteristics of distribution Characteristics of distribution

Descriptor Estimate Standard

error

95% normal CI

Descriptor Estimate Standard

error

95% normal CI

Lower Upper Lower Upper

Mean 1.56895 1.24124 0.332813 7.39637 Mean 91.6336 231.335 0.650347 1.29 × 104

Standard 

deviation 14.2135 19.3858 0.981158 205.902 Standard deviation 1.04 × 104 5.03 × 104 0.801103 1.35 × 108

Median 0.172143 0.0832357 0.0667283 0.444087 Median 0.806891 0.840909 0.104647 6.2216

First quartile 

(Q1) 0.0416934 0.0221509 0.0147177 0.118112 First quartile (Q1) 0.101305 0.123643 0.0092627 1.10796

Third quartile 

(Q3) 0.71074 0.369306 0.256697 1.96789 Third quartile (Q3) 6.42687 7.16985 0.721764 57.2274

Interquartile 

range (IQR) 0.669046 0.354301 0.236969 1.88895 Interquartile range (IQR) 6.32557 7.09744 0.701505 57.0385
Appendix 6 105

Appendix 6. Uranium log-normal fit statistics by bedrock unit.—Continued

[CI, confidence interval; %, percent; *, fewer than five analyses were above the analytical reporting limit and the Minitab option to assume a common scale was 

used in the distribution fitting]

Bedrock unit abbreviation

Sacgr Sagr

Censoring information Count Censoring information Count

Uncensored value 53 Uncensored value 10

Left censored value 0 Left censored value 1

Distribution Log normal Distribution Log normal

Parameter estimates Parameter estimates

Parameter Estimate Standard 

error

95% normal CI

Parameter Estimate Standard 

error

95% normal CI

Lower Upper Lower Upper

Location 0.936261 0.246092 0.45393 1.41859 Location 0.494757 0.780732 -1.03545 2.02496

Scale 1.79023 0.178323 1.47273 2.17619 Scale 2.5312 0.64904 1.53131 4.18396

Log-likelihood -157.38 Log-likelihood -36.858

Goodness-of-fit Goodness-of-fit

Anderson-Darling (adjusted) 1.382 Anderson-Darling (adjusted) 2.278

Correlation coefficient 0.959 Correlation coefficient 0.969

Characteristics of distribution Characteristics of distribution

Descriptor Estimate Standard

error

95% normal CI

Descriptor Estimate Standard

error

95% normal CI

Lower Upper Lower Upper

Mean 12.6636 5.00803 5.83356 27.4903 Mean 40.3759 68.0789 1.48213 1.10 × 103

Standard 

deviation 61.5898 42.368 15.9942 237.167 Standard deviation 993.15 3.22 × 103 1.7375 5.68 × 104

Median 2.55043 0.62764 1.57449 4.1313 Median 1.6401 1.28048 0.355067 7.57584

First quartile 

(Q1) 0.762438 0.212005 0.442097 1.3149 First quartile (Q1) 0.29745 0.286112 0.0451501 1.95961

Third quartile 

(Q3) 8.53142 2.3009 5.02868 14.474 Third quartile (Q3) 9.04329 7.44166 1.80251 45.3706

Interquartile 

range (IQR) 7.76898 2.17703 4.4858 13.4551 Interquartile 

range (IQR) 8.74584 7.29465 1.70545 44.8501
106 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 6. Uranium log-normal fit statistics by bedrock unit.—Continued

[CI, confidence interval; %, percent; *, fewer than five analyses were above the analytical reporting limit and the Minitab option to assume a common scale was 

used in the distribution fitting]

Bedrock unit abbreviation

Sb Sbs

Censoring information Count Censoring information Count

Uncensored value 16 Uncensored value 12

Left censored value 0 Left censored value 0

Distribution Log normal Distribution Log normal

Parameter estimates Parameter estimates

Parameter Estimate Standard 

error

95% normal CI

Parameter Estimate Standard 

error

95% normal CI

Lower Upper Lower Upper

Location -0.202141 0.371811 -0.930878 0.526595 Location -0.518142 0.27691 -1.06087 0.0245912

Scale 1.46215 0.283057 1.00048 2.13686 Scale 0.930099 0.211768 0.595285 1.45323

Log-likelihood -27.626 Log-likelihood -11.145

Goodness-of-fit Goodness-of-fit

Anderson-Darling (adjusted) 1.715 Anderson-Darling (adjusted) 2.019

Correlation coefficient 0.97 Correlation coefficient 0.994

Characteristics of distribution Characteristics of distribution

Descriptor Estimate Standard

error

95% normal CI

Descriptor Estimate Standard

error

95% normal CI

Lower Upper Lower Upper

Mean 2.37929 1.19732 0.88736 6.3796 Mean 0.917962 0.27353 0.511902 1.64612

Standard 

deviation

6.50789 5.81329 1.13003 37.4792 Standard 

deviation

1.07649 0.582141 0.372989 3.10685

Median 0.816979 0.303762 0.394208 1.69316 Median 0.595626 0.164935 0.346153 1.0249

First quartile 

(Q1)

0.304725 0.136503 0.126651 0.733174 First quartile 

(Q1)

0.31807 0.108532 0.162958 0.620827

Third quartile 

(Q3)

2.19036 0.844705 1.02861 4.66421 Third quartile 

(Q3)

1.11539 0.31097 0.645817 1.92637

Interquartile 

range (IQR)

1.88563 0.772188 0.845045 4.20759 Interquartile 

range (IQR)

0.797316 0.261822 0.418903 1.51757
Appendix 6 107

Appendix 6. Uranium log-normal fit statistics by bedrock unit.—Continued

[CI, confidence interval; %, percent; *, fewer than five analyses were above the analytical reporting limit and the Minitab option to assume a common scale was 

used in the distribution fitting]

Bedrock unit abbreviation

Se Sgr

Censoring information Count Censoring information Count

Uncensored value 8 Uncensored value 7

Left censored value 0 Left censored value 0

Distribution Log normal Distribution Log normal

Parameter estimates Parameter estimates

Parameter Estimate Standard 

error

95% normal CI

Parameter Estimate Standard 

error

95% normal CI

Lower Upper Lower Upper

Location -0.292614 0.287496 -0.856096 0.270868 Location -0.822002 0.675265 -2.1455 0.501493

Scale 0.766477 0.228921 0.426849 1.37633 Scale 1.69502 0.788348 0.681216 4.21761

Log-likelihood -7.605 Log-likelihood -8.001

Goodness-of-fit Goodness-of-fit

Anderson-Darling (adjusted) 2.986 Anderson-Darling (adjusted) 3.238

Correlation coefficient 0.963 Correlation coefficient 0.974

Characteristics of distribution Characteristics of distribution

Descriptor Estimate Standard

error

95% normal CI

Descriptor Estimate Standard

error

95% normal CI

Lower Upper Lower Upper

Mean 1.00113 0.282716 0.57559 1.74128 Mean 1.84882 2.39012 0.146717 23.2976

Standard 

deviation 0.895135 0.489043 0.306795 2.61174 Standard deviation 7.55348 19.7808 0.0445706 1.28 × 103

Median 0.74631 0.214561 0.424817 1.3111 Median 0.439551 0.296813 0.11701 1.65118

First quartile 

(Q1) 0.445038 0.164209 0.215935 0.917215 First quartile (Q1) 0.140117 0.137691 0.0204188 0.961507

Third quartile 

(Q3) 1.25153 0.346937 0.726907 2.15478 Third quartile (Q3) 1.37888 0.986436 0.339304 5.60359

Interquartile 

range (IQR) 0.806491 0.286032 0.402448 1.61618 Interquartile range (IQR) 1.23877 0.961806 0.270456 5.6739
108 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 6. Uranium log-normal fit statistics by bedrock unit.—Continued

[CI, confidence interval; %, percent; *, fewer than five analyses were above the analytical reporting limit and the Minitab option to assume a common scale was 

used in the distribution fitting]

Bedrock unit abbreviation

So SOagr

Censoring information Count Censoring information Count

Uncensored value 12 Uncensored value 10

Left censored value 2 Left censored value 2

Distribution Log normal Distribution Log normal

Parameter estimates Parameter estimates

Parameter Estimate Standard 

error

95% normal CI

Parameter Estimate Standard 

error

95% normal CI

Lower Upper Lower Upper

Location -0.910549 0.544193 -1.97715 0.156049 Location -1.84542 0.919828 -3.64825 -0.0425933

Scale 1.99838 0.413305 1.3324 2.99726 Scale 3.01868 0.795339 1.80115 5.05924

Log-likelihood -25.899 Log-likelihood -19.087

Goodness-of-fit Goodness-of-fit

Anderson-Darling (adjusted) 1.719 Anderson-Darling (adjusted) 2.108

Correlation coefficient 0.968 Correlation coefficient 0.969

Characteristics of distribution Characteristics of distribution

Descriptor Estimate Standard

error

95% normal CI

Descriptor Estimate Standard

error

95% normal CI

Lower Upper Lower Upper

Mean 2.96306 2.75646 0.478508 18.3481 Mean 15.0412 35.1856 0.153493 1.47 × 103

Standard 

deviation 21.6215 36.4911 0.791215 590.851 Standard deviation 1.43 × 103 6.66 × 103 0.157509 1.30 × 107

Median 0.402303 0.218931 0.138464 1.16888 Median 0.157959 0.145295 0.0260366 0.958301

First quartile 

(Q1) 0.104513 0.0670819 0.029705 0.367718 First quartile (Q1) 0.02062 0.0242945 0.0020484 0.207574

Third quartile 

(Q3) 1.54858 0.897307 0.497413 4.82117 Third quartile (Q3) 1.21003 1.13483 0.192528 7.60502

Interquartile 

range (IQR) 1.44407 0.859624 0.449662 4.63757 Interquartile 

range (IQR) 1.18941 1.12275 0.186997 7.56538
Appendix 6 109

Appendix 6. Uranium log-normal fit statistics by bedrock unit.—Continued

[CI, confidence interval; %, percent; *, fewer than five analyses were above the analytical reporting limit and the Minitab option to assume a common scale was used 

in the distribution fitting]

Bedrock unit abbreviation

SObo Sp

Censoring information Count Censoring information Count

Uncensored value 6 Uncensored value 17

Left censored value 1 Left censored value 5

Distribution Log normal Distribution Log normal

Parameter estimates Parameter estimates

Parameter Estimate Standard 

error

95% normal CI

Parameter Estimate Standard 

error

95% normal CI

Lower Upper Lower Upper

Location -0.077395 1.18885 -2.40749 2.2527 Location -1.60967 0.664053 -2.91119 -0.308154

Scale 3.01338 1.16867 1.40908 6.44427 Scale 2.9756 0.556342 2.06266 4.29262

Log-likelihood -21.941 Log-likelihood -41.869

Goodness-of-fit Goodness-of-fit

Anderson-Darling (adjusted) 3.218 Anderson-Darling (adjusted) 1.409

Correlation coefficient 0.982 Correlation coefficient 0.984

Characteristics of distribution Characteristics of distribution

Descriptor Estimate Standard

error

95% normal CI

Descriptor Estimate Standard

error

95% normal CI

Lower Upper Lower Upper

Mean 86.7332 297.632 0.104044 7.23 × 104 Mean 16.7339 27.7695 0.647216 432.658

Standard 

deviation 8.13 × 103 5.57 × 104 0.0119581 5.52 × 109 Standard 

deviation 1.40 × 103 4.55 × 103 2.40745 8.14 × 105

Median 0.925524 1.10031 0.0900407 9.51342 Median 0.199953 0.132779 0.0544107 0.734802

First quartile 

(Q1) 0.121251 0.191379 0.0054977 2.67421 First quartile (Q1) 0.0268715 0.0221378 0.0053461 0.135066

Third quartile 

(Q3) 7.06462 8.87495 0.602233 82.8731 Third quartile (Q3) 1.48786 1.03601 0.380072 5.82452

Interquartile 

range (IQR) 6.94337 8.80026 0.579067 83.2552 Interquartile range (IQR) 1.46099 1.0246 0.36957 5.77562
110 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 6. Uranium log-normal fit statistics by bedrock unit.—Continued

[CI, confidence interval; %, percent; *, fewer than five analyses were above the analytical reporting limit and the Minitab option to assume a common scale was 

used in the distribution fitting]

Bedrock unit abbreviation

Spsq* Spss

Censoring information Count Censoring information Count

Uncensored value 4 Uncensored value 7

Left censored value 5 Left censored value 0

Distribution Log normal Distribution Log normal

Parameter estimates Parameter estimates

Parameter Estimate Standard 

error

95% normal CI

Parameter Estimate Standard 

error

95% normal CI

Lower Upper Lower Upper

Location -3.26786 0.765784 -4.76876 -1.76695 Location -2.5205 0.796308 -4.08124 -0.959767

Scale 2.09694 0.118607 1.87689 2.34278 Scale 2.09694 0.118607 1.87689 2.34278

Log-likelihood -11.6 Log-likelihood -1.372

Goodness-of-fit Goodness-of-fit

Anderson-Darling (adjusted) 1.645 Anderson-Darling (adjusted) 2.819

Correlation coefficient 0.948 Correlation coefficient 0.998

Characteristics of distribution Characteristics of distribution

Descriptor Estimate Standard

error

95% normal CI

Descriptor Estimate Standard

error

95% normal CI

Lower Upper Lower Upper

Mean 0.343254 0.271361 0.0728944 1.61635 Mean 0.724747 0.587722 0.147883 3.55185

Standard 

deviation 3.07434 2.73261 0.538474 17.5525 Standard deviation 6.49117 5.83285 1.11544 37.7744

Median 0.038088 0.0291672 0.0084909 0.170854 Median 0.0804192 0.0640385 0.0168866 0.382982

First quartile 

(Q1) 0.0092585 0.0071735 0.0020278 0.0422721 First quartile (Q1) 0.0195484 0.0157948 0.0040119 0.0952511

Third quartile 

(Q3) 0.156689 0.119878 0.0349793 0.701883 Third quartile (Q3) 0.330833 0.262209 0.0699794 1.56404

Interquartile 

range (IQR) 0.14743 0.112868 0.0328802 0.661059 Interquartile range (IQR) 0.311285 0.246747 0.0658315 1.47191
Appendix 6 111

Appendix 6. Uranium log-normal fit statistics by bedrock unit.—Continued

[CI, confidence interval; %, percent; *, fewer than five analyses were above the analytical reporting limit and the Minitab option to assume a common scale was 

used in the distribution fitting]

Bedrock unit abbreviation

Ssqd St

Censoring information Count Censoring information Count

Uncensored value 10 Uncensored value 14

Left censored value 1 Left censored value 1

Distribution Log normal Distribution Log normal

Parameter estimates Parameter estimates

Parameter Estimate Standard 

error

95% normal CI

Parameter Estimate Standard 

error

95% normal CI

Lower Upper Lower Upper

Location -0.977338 0.709125 -2.3672 0.412522 Location -1.16725 0.499365 -2.14599 -0.188511

Scale 2.23919 0.386238 1.59686 3.13989 Scale 1.88108 0.379981 1.26609 2.7948

Log-likelihood -26.615 Log-likelihood -20.191

Goodness-of-fit Goodness-of-fit

Anderson-Darling (adjusted) 2.275 Anderson-Darling (adjusted) 1.712

Correlation coefficient 0.975 Correlation coefficient 0.985

Characteristics of distribution Characteristics of distribution

Descriptor Estimate Standard

error

95% normal CI

Descriptor Estimate Standard

error

95% normal CI

Lower Upper Lower Upper

Mean 4.61653 4.38346 0.717942 29.6854 Mean 1.82574 1.42605 0.394987 8.43907

Standard 

deviation 56.4465 94.6883 2.10744 1.51 × 103 Standard 

deviation 10.5537 15.1096 0.637893 174.606

Median 0.376312 0.266852 0.093743 1.51062 Median 0.311222 0.155413 0.116953 0.828192

First quartile 

(Q1) 0.0831052 0.0683251 0.0165887 0.416337 First quartile (Q1) 0.0875086 0.0531504 0.0266105 0.287772

Third quartile 

(Q3) 1.70399 1.16261 0.447404 6.48982 Third quartile (Q3) 1.10685 0.565689 0.406499 3.01384

Interquartile 

range (IQR) 1.62088 1.11047 0.423246 6.20742 Interquartile range (IQR) 1.01935 0.535954 0.363726 2.85672
112 Arsenic and Uranium in Water from Private Wells Completed in Bedrock of East-Central Massachusetts 

Appendix 6. Uranium log-normal fit statistics by bedrock unit.—Continued

[CI, confidence interval; %, percent; *, fewer than five analyses were above the analytical reporting limit and the Minitab option to assume a common scale was 

used in the distribution fitting]

Bedrock unit abbreviation

SZtb Zpg

Censoring information Count Censoring information Count

Uncensored value 21 Uncensored value 10

Left censored value 12 Left censored value 1

Distribution Log normal Distribution Log normal

Parameter estimates Parameter estimates

Parameter Estimate Standard 

error

95% normal CI

Parameter Estimate Standard 

error

95% normal CI

Lower Upper Lower Upper

Location -3.4627 0.477822 -4.39922 -2.52619 Location -0.005913 0.71992 -1.41693 1.4051

Scale 2.34744 0.380468 1.70857 3.22519 Scale 2.30151 0.483285 1.52501 3.47339

Log-likelihood -18.676 Log-likelihood -33.305

Goodness-of-fit Goodness-of-fit

Anderson-Darling (adjusted) 1.832 Anderson-Darling (adjusted) 2.335

Correlation coefficient 0.966 Correlation coefficient 0.958

Characteristics of distribution Characteristics of distribution

Descriptor Estimate Standard

error

95% normal CI

Descriptor Estimate Standard

error

95% normal CI

Lower Upper Lower Upper

Mean 0.492893 0.403814 0.0989431 2.45539 Mean 14.0493 16.4147 1.42277 138.73

Standard 

deviation 7.73496 12.7591 0.305047 196.133 Standard deviation 198.055 429.793 2.81588 1.39 × 104

Median 0.0313449 0.0149773 0.012287 0.0799632 Median 0.994104 0.715676 0.242457 4.07595

First quartile 

(Q1) 0.0064348 0.0040499 0.0018742 0.0220932 First quartile (Q1) 0.210502 0.180952 0.0390432 1.13492

Third quartile 

(Q3) 0.152685 0.0669433 0.064654 0.360577 Third quartile (Q3) 4.6947 3.35313 1.15784 19.0357

Interquartile 

range (IQR) 0.14625 0.0646419 0.0614992 0.347795 Interquartile 

range (IQR) 4.4842 3.23448 1.09071 18.4358
Appendix 6 113

Appendix 6. Uranium log-normal fit statistics by bedrock unit.—Continued

[CI, confidence interval; %, percent; *, fewer than five analyses were above the analytical 

reporting limit and the Minitab option to assume a common scale was used in the 

distribution fitting]

Bedrock unit abbreviation

Zsg

Censoring information Count

Uncensored value 23

Left censored value 0

Distribution Log normal

Parameter estimates

Parameter Estimate Standard error

95% normal CI

Lower Upper

Location 1.80621 0.268843 1.27929 2.33314

Scale 1.2783 0.201315 0.938816 1.74055

Log-likelihood -81.557

Goodness-of-fit

Anderson-Darling (adjusted) 1.276

Correlation coefficient 0.989

Characteristics of distribution

Descriptor Estimate Standard

error

95% normal CI

Lower Upper

Mean 13.7803 4.78246 6.97989 27.2062

Standard 

deviation 27.9866 16.9035 8.56714 91.4248

Median 6.08735 1.63654 3.59408 10.3102

First quartile 

(Q1) 2.57027 0.813775 1.38191 4.78056

Third quartile 

(Q3) 14.4171 4.10789 8.24788 25.2007

Interquartile 

range (IQR) 11.8468 3.68061 6.44387 21.7799

Prepared by the Pembroke and the Ft. Lauderdale 

Publishing Service Centers

For more information concerning this report, contact:

Director

U.S. Geological Survey

Massachusetts-Rhode Island Water Science Center

10 Bearfoot Road

Northborough, MA 01532

dc_ma@usgs.gov

or visit our Web site at:

http://ma.water.usgs.gov
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