United States
           Environmental Protection
           Agency
          Office of Research and
          Development
          Washington, DC 20460
EPA/600/R-97/133
November 1997
vvEPA
Uranium-Radium in Water
Performance Evaluation
Study

A Statistical Evaluation of
the September 12, 1997  Data

-------
      Uranium-Radium in Water
    Performance Evaluation Study
        September 12, 1997
   Environmental Protection Agency
National Exposure Research Laboratory
   Environmental Sciences Division
         Las Vegas, Nevada

-------
            UNITED STATES ENVIRONMENTAL PROTECTION AGENCY
                        OFFICE OF RESEARCH AND DEVELOPMENT
                      NATIONAL EXPOSURE RESEARCH LABORATORY
                     ENVIRONMENTAL SCIENCES DIVISION-LAS VEGAS
                                  P.O. BOX 93478
                            LAS VEGAS, NEVADA 89193-3478
                                  (702/798-2100)
Dear Participant,

   Enclosed are the results of the Environmental Sciences Division (ESD-LV)
Performance Evaluation Study for Uranium-Radium in Water; September 12, 1997.
   The known value for each analysis was determined by gravimetric methods,
checked by chemical analyses performed by ESD-LV's Radiochemistry Laboratory,
and compared to the participating laboratories' grand average.
   The expected precision, determined by the known value, was taken from
'Table 3. Laboratory Precision:  One Standard Deviation Values and Control Limits
for Various Analyses", which is based on data accumulated over the years by the
Performance Evaluation Program, and can be found in the Environmental Radioactivity
Performance Evaluation Studies Program and Radioactive Standards Distribution
Program information brochure.

   Please take a few minutes to review this report and the analytical data your
laboratory submitted to us.  If there are any apparent discrepancies, please notify us
immediately.
   We encourage you to make use of the computer-automated data-entry system
that has been in place for some time now.  As the number of participants increases,
and it becomes unrealistic for us to receive results by mail or FAX, the computer
system will be our only avenue for accepting data.
   If you have any questions or comments, please send a message via the data-entry
system or contact Stephen Pia at 702/798-2102 or Patricia Honsa at 702/798-2141.
                                          Stephen Pia
                                          Team Leader
                                          RADQA Program
Enclosure

-------
               NOTICE

This material has been funded wholly by
the U.S. Environmental Protection Agency.
It has been subjected to the Agency's review,
and has been approved for publication as
an EPA document.

-------
      ESD-LV Performance Evaluation: Uranium-Radium in Water, 12-Sep-1997    1/20


   The following pages consist of separate sections for each of the nuclides in this study with four
parts per section. After the first, each part is separated from the next, by a new page or n thick
horizontal bar.  The first page of each section is a statistical summary for the nuclide and starts
with a statement of the known value, the control limits, and the warning limits.

   The warning limits are placed at two normalized standard deviations above and below the
known value and the control limits are three normalized standard deviations above and below
the known value. If you keep control charts, these values will be useful for anticipating problems
with the accuracy of your analytical methods.

   The coin shaped pie chart at the top of the summary page shows the fate of all the samples
sent out in number and percentage terms.  The pie chart starts at the top and rotates clockwise.
The first sector represents those participants who submitted analytical results within both the
warning and control limits. The next sector represents those who are in the warning region but
not out of control.  The third sector represents those who are out of control, but have passed
the outlier test.  The fourth sector represents those who have failed the outlier test. The last
sector represents those participants who have failed to respond properly. This is the case if no
analytical results were returned, or less than three determinations were reported, or if the results
were received too late. The reeding on the edge of the coin is spaced at one percent intervals, and
the sector shading becomes darker as the data reliability decreases. Sectors with zero width are
not shown.
   The table in the center shows a number of statistical quantities calculated from the submitted
data based on the mean and median values in relation to the known value, both before and after
outlier removal. The lower pie chart uses the same construction as the upper chart and shows
the distribution of properly submitted data in terms of deviation from the known value divided
into sectors representing one, two, three, and greater than three normalized standard deviations.

   The second part is an alphabetical Listing, in lab-code order, of submitted data and several
calculated quantities. An entry that is shaded has been rejected because of one of the reasons
Listed above or failure of the outlier test. The fifth and sixth columns are a measure of laboratory
precision. The Range analysis is a normalized value that you may use to keep precision control
charts. The eighth and ninth columns are the differences from the mean of all non-outliers and
from the known value, respectively.  If this value is between 2.0 and 3.0, your analytical process
precision is in the warning zone; if it exceeds 3.0 it is out of control. A tag symbol may appear in
the last column. Each page with tags has a symbol definition summary at the bottom.  If there is
no tag symbol, the data is within the control limits, but it may be in the warning zone.
    The third part is a three-column Listing of result average, tag symbol, and lab-code in average
order excluding those labs not responding properly. In this order, all outliers and out-of-control
results appear at the top or bottom of the list.
    The last part is two bar chart displays showing frequency distributions of responding
participants. The first chart places the known value at the center and a bar at each 0.2 unit of
expected precision. The second chart places the mean of the reported measurements at the center
and a bar at each 0.2 unit of standard deviation. In both cases,  a bar includes those results within
0.1 unit up to the maximum of six. Any results more than six units from the center value are
shown cumulatively by a shaded bar one past the sixth unit. If the central tendency of the known
value distribution falls away from the center, an error in accuracy is indicated. If the distribution
is broad, poor precision is indicated.  The mean value distribution is similar but uses the average
and standard deviation of reported results as its basis.

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2/20   ESD-LV Performance Evaluation: Uranium-Radium in Water, 12-Sep-1997


     The Range Analysis(R + SR) is calculated from the range, mean range and standard error of
  the range values.  The range is the difference between the maximum and minimum results for the
  laboratory. The mean range is calculated by multiplying the expected precision by 1.693(for three
  results).  The standard error of the range is calculated by multiplying the mean range by 2.575(for
  three results), subtracting the mean range from this product, and dividing the result by 3. If the
  range is greater than the mean range, then the range analysis is calculated by subtracting the
  mean range from the range, dividing the result by the standard error of the range and adding 1.
  If the mean range is greater than or equal to the range, then the range analysis is calculated by
  dividing the range by the mean range.
     The normalized deviation of the mean from the grand average is calculated from the deviation
  of the mean from the grand average and the standard error of the mean values.  The deviation of
  the mean from the grand average is calculated by subtracting the grand average from the
  average of the laboratory's three results. The standard error of the mean is calculated by
  dividing the expected precision by the square root of 3(the number of results). The normalized
  deviation of the mean from the grand average is calculated by dividing the deviation of the mean
  from the grand average by the standard error of the mean.
     The normalized deviation of the mean from the known value is calculated from the deviation of
  the mean from the known value and the standard error of the mean values. The deviation of the
  mean from the known value is calculated by subtracting the known value from the average of the
  laboratory's three results.  The standard error of the mean is calculated by dividing the expected
  precision by the square root of 3(the number of results).  The normalized deviation of the mean
  from the known value is calculated by dividing the deviation of the mean from the known value by
  the standard error of the mean.
     A complete explanation of the statistical calculations involved in the report may be found in
  the Environmental Radioactivity Performance Evaluation Studies Program information brochure
  [Draft Revision of EPA-600/4-81-004], available from Patricia Honsa, ESD-LV, 702/798-2141.

-------
         ESD-LV Performance Evaluation: Uranium-Radium in Water,  12-Sep-1997    3/20
Uranium (Natural)                  Statistical Summary                      146 Participants
The known value of this nuclide is 5.1 pCi/1 with an expected precision of 3.0;  the control limits
are 0.0 to 10.3; the warning regions are 0.0 to 1.6 and 8.6 to 10.3
41 (28.1 %) Failed to respond -.
6(4.1 %) Outliers '
         Statistic
                ; 97(66.4 %) Within all limits
Respondents
"• 2(1.4 %) In warning zone
          but within control


             Non-outliers
Mean
Std. Dev.
Variance
%Coef. ofVar.
% deviation of mean from known value
Norm. dev. of mean from known value
Median
% deviation of median from known value
Norm. dev. of median from known value
6.86
9.02
81.32
131.42
34.54
0.20
5.00
-1.96
-0.01
Grand Avg 5.05
0.85
0.72
16.85
-0.93
-0.06
4.97
-2.61
-0.16
6(5.7 %) More than 3 norm. S.D. -,„
2(1.9 %) Between 2 and 3 norm. S.D. •
            . 95(90.5 %) Within 1 norm. S.D.
                           of known value
      » 2(1.9 %) Between 1 and 2 norm. S.D.

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4/20 ESD-LV Performance Evaluation: Uranium-Radium in Water, 12-Sep-1997
Uranium (Natural)
Lab Res. 1 Res. 2
A
AE
AF
AH
AJ
AK
AL
AP
AR
AW
AZ
BA
IBB"
BC
'; *>%•'
BH
BK
BM
BN
BO
C
CA
CC
CE
CJ
CS
CX
D
DB
DE
DO
DR
DT
DZ
E
EB
EL
EO
•"jSP*
ER
FE
FJ
• =
0 3
4.4
5.4
5.4
5.1
4.7
4.5
5.6
6.1
4.7
4.5
5.0
	 J5.3_ 	
..',".>9"J1' '
•- ' '"'^^ '•• ',. *;'• ^ •>S*^SV' ; ^ s
5.2
5.3
5.3
2.5
., :,^^,v.^-.,..
5.0
5.1
- > 58 .3 .:- - •-<
4.1
4.5
4.6
5.7
5.2
" ' ., ^''~ \, * }~ ,v~'-.
4.8
4.9
-:\ v;Y- ^V;''-?e
4.2
9.6
4.8
4.9
4.3

4.9
4.5
\ •,"•"
4.7
5.4
5.4
4.9
5.7
4.6
5.4
5.7
4.7
4.7
5.3
J5.8^
ji.9^
' v|"V'v
6.4
5.1
4.9
4.7
""?; :'<:
4.9
5.0
S0;7\. -,
4.6
4.3
4.7
6.0
4.8
rvt T-
4.8
5.4
^•: r
4.8
9.3
5.1
5.1
4.4
,,
5.0
4.5
; %;
Res. 3
4.8
5.4
5.6
4.6
5.4
4.8
5.5
5.7
4.7
' 4.5 '
5.4
_^5.5_
4^9
•, ^J s' ^ ^ """"^p
'*" * ', , / 5 s
5.9
5.0
4.9
2.7
s'! -T, "!C"
5.1
4.9
'jA;60.S^-
4.3
4.4
4.6
6.0
4.9
sv^^C':
5.3
4.8
T"7j <"'^>;^
4.0
9.9
4.9
5.3
4.4

4.9
4.4

No data submitted
Insufficient data

•X. 3
Exper.
Sigma
0.21
0.00
0.12
0.25
0.51
0.15
0.10
0.23
0.00
^V'* '" " "'-
? ' i ;
0.12
0.21
^.,,0.25
0.00

0.60
0.15
0.23
1.22
-\ •","' :^t
0.10
0.10
0.25
0.10
0.06
0.17
0.21 .
- ! " t' - , V
0.29
0.32
•• ''' ^ ••'' f '"'"'•'•-.
0.42
0.30
0.15
0.20
0.06

0.06
0.06
X -• -
Rng anal Normalized deviation
(R + SR) Average (grand-avg) (known) Tag
0.079
0.000
0.039
0.098
0.197
0.059
0.039
0.079
0.000
0.039
0.079
0.098

0.000

0.236
0.059
0.079
0.433

0.039
0.039
0.4*73
0.098
0.039
0.020
0.059
0.079

0.098
0.118

0.158
0.118
0.059
0.079
0.020

0.020
0.020

4.63
5.40
5.47
4.87
5.27
4.63
5.50
5.83
4.70
4.57
5.23
5.53

4.90

5.83
5.13
5.03
3.30
*-'< ' '• ' \< ,>
5.00
5.00
59,77
4.33
4.40
4.63
5.90
4.97

4.97
5.03
- <
4.33
9.60
4.93
5.10
4.37

4.93
4.47

TAG SYMBOLS
Determined to be an
outlier
-0.24
0.20
0.24
-0.11
0.12
-0.24
0.26
0.45
-0.20
-0.28
0.10
0.28

-0.09
' - f.
0.45
0.05
-0.01
-1.01
«" ' . -• "
-0.03
-0.03
-0.42
-0.38
-0.24
0.49
-0.05

-0.05
-0.01

-0.42
2.63
-0.07
0.03
-0.40


-0.07
-0.34

ft s Above
& = Below
-0.27
0.17
0.21
-0.13
0.10
-0.27
0.23
0.42
-0.23
-0.31
0.08
J).25_ 	
' \ - " ' *
-0.12
-V ' »,,'*, -
0.42
0.02
-0.04
-1.04
! , ' '-,:' \ "- , »' "
-0.06
-0.06
-0.44
-0.40
-0.27
0.46
-0.08
* \
-0.08
-0.04
" ' 0 -* '
-0.44
2.60
-0.10
0.00
-0.42
- # '
*
-0.10
-0.37
*
control limit
control limit

-------

ESD-LV Performance Evaluation: Uranium-Radium
Uranium (Natural)
Lab Res. 1 Res. 2 Res. 3
GN
GQ
TTK
HK
HL
HP
JL_
%*$
JE
-.^ V A vWAS-
JK
JN
JS
1^
JY
K
KH
KT
L
LF^
&-.Y -.tJP.^
Jwtt8>\^
. LZ_ ,
NA
NH
NJ
NK
JS9L
/*\T^
\_^rp
\^r *• %
OS
• CKS?:
N PC?'
PB
PG
PX
Q
3.7
4.6
4.9
4.3
5.0
5.4
._^....?JL..
S%U O-^X^iili ^f X^-,' •>
\^ °J*^<^*lH 't?X\/^Vo
^.^^JbSJ.
	 "5.2
6.3
5.3
SVSV hX"" s V^X" XX *
^^;lv-\M^fe
5.3
4.1
f4.9
4.5
5.5
3.5
3.9
4.7
4.1
4.6
5.5
_J5.3__
s\^",ix-tL°x- % *-'
_^,H__™
'5.3
5.4
___5.3 %
4.9
4.3
.-..Mx-x
	 4.7
5.1
3.8
3.2
4.8
4.0
4.1
5.5
_ 4,8_
_5./^
5.1
6.0
5.5
4.5
4.4
4.8
5.0
5.4
4.9 5.1 5.0
S^™^!TS"^^^ ^^^^ — rs
Y^JC
"io"
8.5
4.2
4.3
_^_4-»_
\ r\-Tv:vT,%^
^... ™i;-ll
^Tr-"?^;h"^
ssfj^;:s»^;^
"e.4~ '
4.5
5.4
4.9
7^™ 5.2™_""^
r^f^iMUfv^*
^i£->|jg-A^I^;
s '-x^JlOAJf^xfe'V iv%
	 6JO"^
8.5
4.9
4.4
5.1
₯l7^0^
JieiJ
5.0
8.2
4.8
4.7
5.1 5.4
Tso~tS" ^s x^^?x^x'^?^^:-.'^^\ ^•-'•'•o'' w""
S^^'./usA-C
~ "4.;T^_%
^^/%Vr:!':!v'
of^H^Cf^'^
.. 6^0 "
4.8
__5;U 	
6.8
5.2
o ••'''''' •• ^ ^^ '"'•
! ™Tt6
-,-,;,- , •• • ^ ,
;'f ,4 , ;' ' '
5.6
4.7
	 5.0 ^
6.0
5.2
• s No data submitted
0 s
Insufficient
data
x =
	 ^.
in Water, 12-Sep-1997 5/20
Exper. Rng anal Normalized deviation
Sigma (R + SR) Average (grand-avg) (known) Tag
0.15
0.70
0.10
0.15
0.21
0.06
0.26
lJjpU52T'%"
0.10
0.46
0.12
0.40
0.21
0.06
0.25
0.21
_ 0.10__
0.06
1.00
0.17
0.38
0.21
0.25
•,-- ~\;>>"1r-' ' - !'
aoo

0.25

° '"• •. w^%. - "
0.40
0.15
0.10
0.70
0.17
0.059
0.276
0.039
0.059
0.079
0.020
0.098
_0.177_
0.039
0.177
0.039
0.158
0.079
0.020
0.098
0.079
0.039 __
0.020
0.394
0.059
0.138
0.079
0.098
6.000
, » ;'
0.098
" ' ' ' „'»•",« >*-
•>•-/, ;" l\ ' , ',
0.158
0.059
0.039
0.276
0.059
3.67
3.90
4.80
4.13
4.77
5.47
5.10__
,5.icT"^
5.20
5.90
5.37
4.90
4.47
4.83
' - j; ^-\
4.73
5.33
^^^^^^^
's'.iVJ^
5.00
8.40
4.63
4.47
5.13
j.io" ^
- V"--c- --;
4.37^
, '-, V'c->U
;;•;_; v;- ;-A
6.00
4.67
5.00
6.07
5.10
TAG SYMBOLS
Determined
to be an outlier

-0.80
-0.67
-0.15
-0.53
-0.17
0.24
_ 0.03^
izs^Lir.
0.49
0. 18
-0.09
-0.34
-0.13
-0.18
0.16
-0.03
••iwws'wtS'^'CO* »1*sft'*'*'i% •vw«
-------
=N
6/20 ESD-LV Performance Evaluation: Uranium-Radium in Water, 12-Sep-1997
Uranium (Natural)
Lab
QQ
QU
JO?



g^g
'& JUf ^jffi
"?• ** s ''s ;
RD
•* vyvst r ••
' A Jfcp *
RG
RK
RP
RR

--*H3fc '
RZ
S
sc
SD
SF
Vsi>
SL
SM
SO
ss
sx
sz
T
TD
TN-
TQ
TS
U
UP
UQ
uz
VA
VH
VI
W
';wc
WG
WH
WI
WJ
WO
Res. 1
4.4
6.3
4.0



i!?^tf§
?^'ft'1ki^>'/ Jv^'it s^.^*^
v> ''"" '* /i't'y " ••• ^ •- ** ,
5.2
, ', , ',»*. *v "^' t>'»
>y?~ **K^jfe'^,i<^
5.0
4.9
4.3
( t vCe\ ' ft'f '
' / s ''''" "^ '"*'"> ^ "rf-%|^V ';
^^^^^^^firj-^
' "5.1"
4.2
4.1
^^f^iPl

'; vf i '
4.5
4.7
5.5
5.8
5.0
^V:';4i^T^
4.6
4.9
8.7
5.2
5.0
4.7
5.0
5.3
-'-X'V-,, -^V
, 4.9' ^ ^
^X;'^">7r'
5.0
	 JiJ>^ _
r'"v*Tr^v
> " -'-"-"!-", " - -
4.6
6.1
4.9
5.4


4.5

4.5
4.3
Res. 3
4.9
5.7
3.8



|l||f
^//'^ffi v* JJfvN.
f •• A_. _. _. ' A
5.1
:•, S(j^\^°-\
/^"p^liW,.
5.1
4.5
4.4
^W?

I'jt^si^'".
' "4^9
4.5
5.1
5.7
5.1
?4i';f'
4.2
4.4
8.7
5.3
4.8
4.8
6.4
5.2
%A *; ,"•-•
5.3
\-."-\ '
4.7
5.1


4.8
7.0
5.2
5.1

-••- ,
4.7

4.4
3.7
• = No data submitted
0 s
Insufficient
data
X s
Exper.
Rnganal
Normalized deviation
Sigma (R + SR) Average (grand-avg) (known) Tag
0.29
0.75
0.59



ii|§X27 '-
if-"f^.*-£ s"J'sti'§f> x" s >
J'" / j •" •f
0.06
V ₯* *"' "
v*, '~$*s£' .'/
0.06
0.35
0.15
^^'{^"f %- -

f'-f, -;i6>:''' '
0.21
0.29
0.06
0.26
0.15
0.21
1.16
0.06

0.21

0.17
0.26


0.25
0.55
0.15
0.30


0.53

0.21
0.46
0.098
0.295
0.217



\0,473;;ff>
'' " 'V ••* '"• ' v
^ - ^ ' *
0.020

, ' ' V- - '
0.020
0.138
0.059
s ^ ' > ^

:
0.079
0.039
0.118
0.079
0.059
0,059
0.079
0.098
0.020
0.098
0.059
0.079
0.453
0.020
s '
0.079

0.059
0.098


0.098
0.197
0.059
0.118


0.197
,
0.079
0.177
4.57
5.60
4.23



6&07


5.17
,

5.07
4.53
4.27
"' < * "^ ; - ' ,

'/•
4.77
4.63
5.43
5.63
4.97
4163
4.43
4.73
8.67
5.10
4.97
4.87
5.17
5.23

5.07

4.80
5.20


4.57
6.37
5.03
5.10


4.30

4.57
4.20
TAG SYMBOLS
Determined
to be an outlier

-0.28
0.32
-0.47

'"•'-. ''

36.38
: ^ f' f
"" '' % * j"- " '
0.07


0.01
-0.30
-0.45


j '-.
-0.17
-0.24
0.22
0.34
-0.05
Siiii
-0.36
-0.18
2.09
0.03
-0.05
-0.11
0.07
0.10

0.01

-0.15
0.09


-0.28
0.76
-0.01
0.03
-

-0.43

-0.28
-0.49
ft s Above
•11 = Below
-0.31
0.29
-0.50



36,36 x ',
«.' «. s. t "• f •- » ^ '
Vs "
0.04

\- ,' > '-,-r~ «*
-0.02
-0.33
-0.48
;" '. "'.*[ - *'* '

, ' - ', 9 -''
-0.19
-0.27
0.19
0.31
-0.08
aijro^'- -'*, --
-0.38
-0.21
2.06
0.00
-0.08
-0.13
0.04
0.08
, , - * ,
-0.02
- ; ' >" *
-0.17
0.06
>' ;' ; • ;
' ,,'/'*
-0.31
0.73
-0.04
0.00
•
*
-0.46
•
-0.31
-0.52
control limit
control limit

-------
ESD-LV Performance Evaluation: Uranium-Radium in Water, 12-Sep-1997 7
Uranium (Natural)

Lab Res. 1 Res. 2
WR 4.6 4.9
\*5 "• J"*W>W -.S %v,s^w. vtVAVA SUA VA^, A, VA WAyA-AS -A ^_v. •.
< "Wife-' ^ "• V^ **^ ^ * tC^ Wil f* ""^ *d SS* ""' V
r •.-.•. -^ -, -. V. s s X*, VAWS ss X- V s -A^A ^ -Xv. V -.
X 4.6 4.8
XA 5.0 4.7
''-XCJ^^^T^-"^""'^; f'-T''^ ~
^^fti^ii
\?&SSf^jS4>Jf^1
'3DKt^^^^^^^*^_ -,k'«<£«ii
XL 5.1 5.4
XM 4.0 4.6
Y 4.9 4.9

Exper. Rng anal
Res. 3 Sigma (R + SR)
5.1 0.25 0.098
,vt ^ s •• s w.^ XW N "" ' s \v-% •.«•.•.*•.,. ^ v, s * v.
W / ' "*^ " "V ' ' ' "lx
•.•,•. VS * % W •• \ ^S\S% S^^S-. \^\*s^sx >
4.8 0.12 0.039
6.0 0.68 0.256
•. ^ 	 ™..s ^ ™ A^ ss v f 	 ^ ..V-"-*- •- ^ -.•• « ^ ,"• ^X
i^-.^ ^\'^•.<.^^'• ^^ <** Ov-t *• "^ ^ % ^s ' \
^W-^^t^X' * ,. f^ ^ ^ "V v ^ v\ " ^ •• "
>:r^;v\ ;^r ! %.>^ ' ' :: */
!v|§>i;jx>\; ;,- -xl ' 's,,, V ^*-V/% * 'A'*.-
~5.8 0.35 0.138
4.1 0.32 0.118
4.9 0.00 0.000

Normalized deviation
Average (grand-avg) (known)
4.87 -0.11 -0.13
§•, VA •. % i..\Vt
.^il ' •, ••^•-
4.73 -0.18 -0.21
5.23 0.10 0.08
, - - ««" - - V"'-\r s--.™~»~!«~i--*, v-^-x;-
:> %^^-^*£-K^-:4;l
' ,'-\,, .-A- • \ ' ' - •'*>-' ,,*,->
»'','..,-''. -- • -". -~ ,\'V ''-' s~s -\"5f , t~'-x'.s"«
5.43 0.22 0.19
4.23 -0.47 -0.50
4.90 -0.09 -0.12
/20 1


Tag

S % •,•...%• \A
*v •*v*
\*s •- . s.\ <•


\ '9-° .
* Vx*-
; *-\
-'",*•



Data sorted by Laboratory Average
Average Tag
3.30
3.67
3.90
4.13
4.20
4.23
4.23
4.27
4.30
4.33
4.33
4.37
4.37
4.40
4.43
4.47
4.47
4.47
4.53
4.57
4.57
4.57
4.57
4.63
4.63
4.63
4.63
4.63
4.67
4.70
4.73
• s No data submitted
0 = Insufficient data
Lab Average Tag
BN 4.73
GN 4.73
GQ 4.77
HK 4.77
WO 4.80
XM 4.80
QX 4.83
RP 4.87
WH 4.87
DT 4.87
CE 4.90
OS 4.90
EL 4.90
CJ 4.93
SL 4.93
NK 4.97
K 4.97
FE 4.97
RK 4.97
AW 5.00
WJ 5.00
VA 5.00
QQ 5.00
S 5.00
CS 5.03
NJ 5.03
AK 5.03
A 5.07
PG 5.07
AR 5.10
KT 5.10
TAG SYMBOLS
Lab Average Tag
X 5.10
SM 5.10
RZ 5.10
HL 5.10
U 5.10
HE 5.13
KH 5.13
WR 5.17
SZ 5.17
AH 5.17
Y 5.20
JY 5.20
BC 5.23
ER 5.23
E 5.23
SX 5.27
SF 5.33
DE 5.37
D 5.40
PQ 5.43
NA 5.43
LF 5.47
CA 5.47
C 5.50
VI 5.53
DO 5.60
BM 5.63
RG 5.83
TQ 5.83
W 5.90
SS 5.90
ft = Above control
x = Determined to be an outlier U = Below control
Lab
Q
OB
JE
I
EB
NO
BK
T
RD
LZ
UP
JK
XA
TD
AZ
AJ
L
JS
AE
SC
XL
HP
AF
AL
BA
QU
SD
BH
AP
JN
CX
limit
limit

-------
8/20   ESD-LV Performance Evaluation: Uranium-Radium in Water, 12-Sep-1997
Uranium (Natural)
Average
Tag
  Data sorted by Laboratory Average
Lab |  Average	Tag        Lab  Average
                            Tag
                             Lab
   6.00
   6.07
   6.37
   8.40
           PB
           PX
           VH
           NH
         8.67
         9.60
        15.90
        16.43
x
x
SO
DZ
ID
M
18.47
41.63
59.77
68.07
x
x
X
X
MX
SI
cc
QZ
 % responding labs
                    Frequency distribution
 30
 20
 10



::::::::::::::::::::::::: j
	 	 	 	 p

II
-6 ' -'4 ' -'2 T






n
•_ • _ I
1 'ft ' 'l ' ',
+2 +4 +6
 % responding labs
                     Normalized deviation of the mean from the known value
                    Frequency distribution
 20



	 I
•I
II
__•!•
-6 -4 -2




• 	 	

ll.l ,, 1 	 'I
+2 ' +4 ' +6
                    Normalized deviation of the mean from the grand average
 • = No data submitted
0 s Insufficient data
                       TAG SYMBOLS
                x = Determined to be an outlier
                                           ft = Above control limit
                                           •II s Below control Umit

-------
         ESD-LV Performance Evaluation:  Uranium-Radium in Water, 12-Sep-1997   9/20
Radium-226                         Statistical Summary                      146 Participants
The known value of this nuclide is 20.0 pCi/1 with an expected precision of 3.0; the control limits
are 14.8 to 25.2; the warning regions are 14.8 to 16.5 and 23.5 to 25.2
40(27.4 %) Failed to respond .
5(3.4 %) Outliers •'
4(2.7 %) Out of control •
     but not an outlier


         Statistic
                • 90(61.6 %) Within all limits
Respondents
•- 7(4.8 %) In warning zone
          but within control


             Non-outliers
Mean
Std. Dev.
Variance
% Coef. of Var.
% deviation of mean from known value
Norm. dev. of mean from known value
Median
% deviation of median from known value
Norm. dev. of median from known value
     19.18
      3.17
     10.06
     16.53
     -4.09
     -0.26
     19.62
     -1.92
     -0.12
   Grand Avg  19.55
                2.04
                4.16
               10.43
               -2.25
               -0.22
               19.67
               -1.67
               -0.16
9(8.5 %) More than 3 norm. S.D.
7(6.6 %) Between 2 and 3 norm. S.D.
             71(67.O %) Within 1 norm. S.D.
                           of known value
     19(17.9 %) Between 1 and 2 norm. S.D.

-------
10/20 ESD-LV Performance Evaluation: Uranium-Radium in Water, 12-Sep-1997 1
Radium-226
Lab
A
AE
AF
AH
AJ
AK
AL
AP
•~m
AW
AZ
BA
>BB7
BC
BG
BH
BK
BM
BN
BO
C
CA
CC
CE
CJ
CS
tor
D
DB
DE
DO
DR
DT
DZ
E
EB
EL
EO
EP
ER
FE
FJ
FN
• • =
0 =
Res. 1
20.7
17.1
19.3
17.0
16.5
18.0
18.5
17.9
'^^'^
17.8
19.1
22.4
t-;^':;;*/'fT^'C
J \AU>
*Vv ;'''Y/ ',''.''
20.2
19.0
20.6
19.5
19.5
20.0
20.1
18.0
18.2
19.0
18.6
' 0-. \ Vs •• %
- <\ " v -;/ ' '
18.9

17.5
21.5
18.7
16.7
19.7
18.6
14.7
19.5
22.0

18.3
Res. 2
20.1
17.6
19.1
14.7
21.0
16.9
17.4
20.6
•M*$i&
18.5
19.5
__20;1
'TP'^^";
20J5
;'-"}*', r'sV°l;
21.1
19.4
20.0
16.5
19.9
19.0
19.2
19.5
19.4
22.0
18.2
-• '*' :// ;:""
* "s., ' \ ""/''(
J8.9
, ' Vl^-A,
17.8
19.7
18.3
18.1
19.1
19.2
14.6
18.1
21.0

19.6
Res. 3
16.5
18.9
18.7
16.2
18.9
18.6
20.9
19.4
^SSfsi
19.7
20.3
19.9
^jr«^~rr-
24.4
tj- •••'•'';••;. :?;-,;
19.8
19.1
20.5
16.2
20.9
18.5
20.7
21.0
18.1
19.0
18.6
ix'-;'"' -"';;"' ,'t-^T -
^^-"^ "• f \ y\T "'
''J * ',0 ^ ,. - ^ %•>
^ < t ' V ' *
18.1
20.5
19.3
18.2
20.6
18.9
16.4
17.9
22.0
-\ -" -
21.1
No data submitted
Insufficient
data
X s
Exper. Rng anal
Sigma (R + SR) Average
2.27
0.93
0.31
1.17
2.25
0.86
1.79
1.35
\^.QM^'
0.96
0.61
1.39

3.37
;- > - ' ,„„'> " ' , ; '
0.67
0.21
0.32
1.82
0.72
0.76
0.75
1.50
0.72
1.73
0.23
^V''"V
^""'''i-'-J' *> -
0.00
A. - ' X
0.30
0.90
0.50
0.84
0.75
0.30-
1.01
0.87
0.58

1.40
0.827
0.354
0.118
0.453
0.886
0.335
0.689
0.532
0.217
0.374
0.236
0.492
V '""
1.608

0.256
0.079
0.118
0.650
0.276
0.295
0.295
0.591
0.256
0.591
0.079

', ' . -
0.000

0.118
0.354
0.197
0.295
0.295
0.118
0.354
0.315
0.197

0.551
19.10
17.87
19.03
15.97
18.80
17.83
18.93
19.30
&23
18.67
19.63
20.80

20.87

20.37
19.17
20.37
17.40
20.10
19.17
20.00
19.50
18.57
20.00
18.47


18.90

17.80
20.57
18.77
17.67
19.80
18.90
15.23
18.50
21.67

19.67
TAG SYMBOLS
Determined to
be an outlier

Normalized deviation
(grand-avg) (known) Tag
-0.26
-0.97
-0.30
-2.07
-0.43
-0.99
-0.36
-0.14
-em \
-0.51
0.05
0.72
•"•••-• ^ ' ,
0.76

0.47
-0.22
0.47
-1.24
0.32
-0.22
0.26
-0.03
-0.57
0.26
-0.63
•> \ s / , !

-0.38

-1.01
0.59
-0.45
-1.09
0.14
-0.38
-2.49
-0.61
1.22

0.07
It = Above
•U s Below
-0.52
-1.23
-0.56
-2.33
-0.69
-1.25
-0.62
-0.40
-6,T9?"''x\"
-0.77
-0.21
0.46
v'Y ^ •'
0.50
"' , ' "•'••' *
0.21
-0.48
0.21
-1.50
0.06
-0.48
0.00
-0.29
-0.83
0.00
-0.89
V ^ ^ " • -
•* •,
-0.64
'-.-. ' to*
' "'-: ' *' '
-1.27
0.33
-0.71
-1.35
-0.12
-0.64
-2.75
-0.87
0.96
•
-0.19
control limit
control limit _,

-------
ESD-LV Performance Evaluation: Uranium-Radium in Water, 12-Sep-1997 11/20
Radium-226
Lab
GN
GQ
FffTC
HK
HL
HP
I
JD ~
* j 7"-*
>. % v"
JE
tjJfGK?:
:5j&
JS
JX
JY
K
KH
KL
^"^ ^."TC*"
^TtfTlrt %

fj
•ijrf
LT
LZ
M
. j^-
•• ^ 1 __ s
'-""1ST s
s
v NA\
NH
NJ^
~NK'1
NO
O
Cf\*w% -
Res. 1
17.5
15.8
20.4
20.4
20.7
20.9
21.7
•_ 24.3 ^
H'f " ' ' \t;sS

17.0
^r;-^%
15.4
21.9
19.3
••vr^T^BF
v\ \ s . v 4 v ••
•," "^* * X^ ^ , - ' ^ v\!
v T^"" * *^\\v
\os ;,,,,AV^ ,V;f
20.8
^ ^22.9
fr^^>rfet<
21.2
19.2
r-»~ ' o , ,!-?^ -'>•
'OHbi'"*. •A.\>*tSi-
OF 13.0
OS
ox
p - '-\
PB
PG
PQ
PW
PX
1 Q"'V
21.8
19.9_
-h ^29;9y?
Res. 2 Res. 3
18.2
10.4
22.1
20.5
21.0
19.6
20.3
_JL6.1^_
C>vT^^^"r ^v^1^
s/w^S s% v.4.VM.\v.K«AS •> iw -.V ^ ^
^JM^
^I^'S,?^^
SSftSiS^
18.7
20.5
25.0
20.4
19.7
25.2
V% wwf* ^XJ^ '"^jw.^'w^' \__ *
s s % ^\S> ^ s

20.0
^^-^v^r*"
13.3
21.7
....... 20.19 ____
"'"-•f^^jv:'
% ' ^VV Ox\^\ O '**
v X^o^4-^ \ x° ^^^ \ ^
\r^-;^ -yv ~ , -
^T.'Xj - '> -v-. ttr^J.?,
18.1
^_23.1__^
^v;^™':!,:?'"- vS^
22.2
19.4
•""•^«\~v-^- -." ^ ^-yf ^'
14.5
23.4
_ ,19.9^
"."Xxf^'-'vj^'V"-'^^'
20.5
16.7
^
20.5
19.5
\%H-:27;6i^C'x-
18.0
13.1
20.4
19.1
21.3
22.7
20.1
19.5
1^ \?" '"
•. •,•.-. f. SVW*^ v«
^21.7 _^
"«.t»'-^
:^^S
21.0
20.5
28.3
19.6
20.7
23.2
%^™₯ % s---^ ^


16.0
^i^- ^^ ^-
20.2
21.8
19.8
1:-Si9 ,-
f ^

«
^ <*;;>- 1 *
19.7
.A?J,,
^;;V\r,,, *
25.0
19.4
"%f v^ *"
15.0
24.6
20.1
\fU,^s;x ,
20.5
16.1
^_
19.4
20.7
-'27.3V
• = No data submitted
0 s
Insufficient
data
x =
Exper.
Rng anal Normalized deviation
Sigma (R + SR) Average (grand-avg) (known) Tag
0.36
2.70
0.98
0.78
0.30
1.56
0.87
4.12
*, ,_ , ,» ^ -^ ->

	 6.83 	
>!-/': ,',>' - .
^^\ X^ \ >'* v^v
1.23
0.81
2.54
1.50
0.58
1.00
,..-«• « ^v.^*™.,^
,"'•"' ^ •-

2.08
,' -:-: s *s
3.54
0.10
0.82
- "l&i's" '
^ % ^


-1 'X . - .
1.36
2.02

1.97
0.12

1.04
1.40
0.12

0.06
0.42

1.00
0.61
' ;- IA2 \
0.138
1.120
0.335
0.276
0.118
0.610
0.315
2.170

s •>- * ^ *
4.158

>" *'^y*
0.453
0.276
0.984
0.571
0.197
0.394
^ N«NX^S ^™


0.788

1.683
0.039
0.315
6,276
"" '•• ^ •• ••



0.532
0.709
*' -\ ' ^ !,
0.748
0.039

0.394
0.551
0.039

0.020
0.158

0.394
0.236
0.512
17.90
13.10
20.97
20.00
21.00
21.07
20.70
19.97

<. N - ^ ^ V \ '
	 15.57 	
, f ' - ^ '- 'o - , ' -
,?;' -^x,' ">;;
20.10
20.97
25.53
19.17
20.37
24.23
^v % % ™ s v.w* xv. -.^Vv w-vv w * wy s


17.67

16.30
21.80
20.00
":vr:8r4p~ """

^ \ xi ^
1
• • 'V ~"\! '' - ^ vh%-'^
19.53
21.83

22.80
19.33

14.17
23.27
19.97
"' : "
20^53
16.57

20.43
20.03
:^-:' -28;27;^ :l
TAG SYMBOLS
Determined
to be an
outlier
-0.95
-3.72
0.82
0.26
0.84
0.88
0.66
0.24
•-
% ^ s ^ V >* 1
-2.30
.-;,'*-!'» \ -/.
0.>^-..'--->v
0.32
0.82
3.45
-0.22
0.47
2.70
™ , ^ ..vv*^-* •• -•« «^ «^


-1.09
•• lS v
-1.88
1.30
0.26
T^6.'44" 'v
••'^i ^•>.. *
f

•.^ ""x -•• s^ ^ \
-0.01
1.32
\^ ^^^^ -' "• V
1.88
-0.13
\ V - ,
-3:11
2.15
0.24^
v "" "" ;
0.57
-1.72

0.51
0.28
<^:{xp3; : 'r-
tt = Above
U = Below
-1.21
-3.98 li
0.56
0.00
0.58
0.62
0.40
-0.02
s { ^ *
•• .• •-
-2.56_ 	 ^
: % °v;v*"-
-';j-- ''*';
0.06
0.56
3.19 ft
-0.48
0.21
2.44
wj,™.^^ .... -.^ sv
'%\o - x '" ^

-1.35
• •""'< *
-2.14
1.04
0.00
X6i-70'"";s x
"^ ' " s "
's% ^
* '
x% \^ •
-0.27
J.06
;v^v. "-^r> -1
1.62
-0.38
^ \x ,,V - ' » '
-3.37 &
1.89
-0.02
.- >s^-v! -^ ' i
0.31
-1.98
•
0.25
0.02
l; 4X7 ::^ - X
control limit
control limit

-------
12/20 ESD-LV Performance Evaluation: Uranium-Radium in Water, 12-Sep-1997
Radium-226
Lab
QM
QQ
JSH,
QY
QZ
R
RD
'*jj|P- -
.!>'., jy.'.
» RG r
RK
•'•>RpK
-'Kit,'-"
";"**"*,'';.
^HJ£'v;
RZ
S
sc
SD
SF
SI
SM
ss
sx
sz
T
TD
TN
TQ
-•IB
U
UP
UQ
UZ
VA
VH
VI
W
• WC
WG
WH
WI
WJ
WO
Res. 1
12.3
19.0
T>£W£
19.0
18.9
17.8
26.7
'•'!'V's'Jl"***,J>$>'
*^.o\;,,';i;^.v?!^' "',<>'.
1 •*-;* *•$•''"<•**< _'
18.1
* '* /iWUwS?
V*'^t^v"
.f •, £;^>^J\'V'
- "^ "" ' ''""''I? "'",':
20.0
19.7
19.4
16.6
17.5
20.9
V "*"•-"" *"\, *' ''*'
23.7
19.8
21.3
18.8
17.3
22.5
17.6
21.0
""; ' : S''V
18.7
21.6
19.8
20.5
17.9
20.1
19.7
3.8

19.4

18.9
19.0
Res. 2 Res. 3
16.1
20.6
A\/*C)
19.0
17.9
16.0
25.4
f; A-~/<'' ; ^^|->|^>;
>* Si1!-''" "'/*/5i^₯*
' V-; *'V'r^;:';f A'**^' -^
17.2
/J;^"^^;v"VJ
^•3>r\" :'Vlci?''*•*
',',-'' **•>* - -i'v f^ :*'(v.
19.5
19.5
18.7
21.3
18.1
Xo» JL
23.8
21.3
21.1
20.0
20.1
19.8
23.2
20.3
,. . %",',"< = '"";
18.6
22.0
20.4
19.9
18.2
20.1
19.4
6.8

19.5

18.7
20.7
16.3
19.8
,2?:2,_
19.2
20.6
15.4
25.1
'&„*"$'•?>*'
JV ',*""?" *,' '
V/rv'!"1;- "'
17.5
;^|/C;"
^^"•""^v
^ \* , "'/X'
,^,' .-;•>,
20.3
20.2
18.8
20.1
18.4
23.1
'j22.IB
16.5
21.6
17.9
19.2
18.0
19.7
22.3
","•"--, ,
18.9
20.6
19.3
21.2
16.7
22.2
19.7
"•4;7"

20.1

20.5
19.8
• = No data submitted
0 =

data
x =
Exper. Rng anal Normalized deviation
Sigma (R + SR) Average (grand-avg) (known) Tag
2.25
0.80
_1:5.5,.
0.12
1.37
1.25
0.85
1;X*\\; ;.<,',''" ":- ,-
0.46
fff-'f f- vf ft*.-. ^ r v ^
lYf" /., ;- ,! ',
j; '.. \ •• ".:•.•.•
\* ^1
0.40
0.36
0.38
2.44
0.46
2.51
\ ^ v
0.55
2.46
0.25
1.05
1.43
2.26
2.83
1.01
V*' :
0.15
0.72
0.55
0.65
0.79
1.21
0.17
1.54

0.38

0.99
0.85
0.788
0.315
0.610
61512
0.039
0.532
0.473
0.315

,. , "'-, , , ,
' ,. " '-
0.177

• '/"' ''


0.158
0.138
0.138
0.925
0.177
0.984
0.197
0.945
0.098
0.413
0.551
0.886
1.195
0.394

0.059
0.276
0.217
0.256
0.295
0.413
0.059
0.591

0.138

0.354
0.335
14.90
19.80
20.70
19.07
19.13
16.40
25.73
- ,>, • , . •
•.. ,; ^ , , , ,

17.60
','/,• \-*«y ~~
rs. '**' •'-'•'
" * ^ v ^ "- ^ s *

19.93
19.80
18.97
19.33
18.00
20.70
23.43
19.20
21.33
18.90
18.87
20.10
20.17
21.20

18.73
21.40
19.83
20.53
17.60
20.80
19.60
5.10

19.67

19.37
19.83
TAG SYMBOLS
Determined
to be an
outlier
-2.69
0.14
_9-6

•i"
-1.13
-T""'^""' •••••••'"""• " •••••••••-
- ' -.-."-
^ .y.-
: - s ' ._ '-.
0.22
0.14
-0.34
-0.13
-0.90
0.66
2.24
-0.20
1.03
-0.38
-0.40
0.32
0.36
0.95

-0.47
1.07
0.16
0.57
-1.13
0.72
0.03
-8.34

0.07

-0.11
0.16
ft = Above
II = Below
-2.94
-0.12
J>.4<>_ 	
-0.54
-0.50
-2.08
3.31 ft
',- ";'--' \* '/-

-;' o -„- ' * '
-1.39
,,, ,..,, ^,,, , ^,, ,
' ' ' -- - * '
,,„„.* .- .- ^ * ,.-,
"'' ' :#":
-0.04
-0.12
-0.60
-0.38
-1.15
0.40
1.98
-0.46
0.77
-0.64
-0.65
0.06
0.10
0.69
- ,-.\ -•• •-
-0.73
0.81
-0.10
*
0.31
-1.39
0.46
-0.23
-8.60 X
. *
-0.19
•
-0.37
-0.10
control limit
control limit

-------
ESD-LV Performance Evaluation: Uranium-Radium in Water, 12-Sep-1997 13
Radium-226
Lab Res. 1 Res. 2

4?:* ~,xf^A\i'TCxx?-?;,'\'*-" ' ^&3&Ur^Kv
X 17.7 18.3
_XAi(_ 	 22.8 __ 21.1
?xb|l^^^l8
:;xi^|||;^|^g^
•XH^'p '-\:rS;d-^-st\\r\'-: '* > ' , • ' x " '
17.4 0.46 0.177
21.4 0.91 0.335
ftS^r^y;!--r *;•• -\;<;\
"v/,:;;^|gvv:^::"^x;>:^ ) ->;
, H; ^ti:f'V -' , i:' •" ' ', \ -Y\-\ '
21.1 0.30 0.118
17.9 0.98 0.335
22.3 0.12 0.039

Normalized deviation
Average (grand-avg) (known)
x- -• > >' "'*';, - \'"\ (""^'-o^
. , i _ _ - - _ ,* » ^ ..-..»
17.80 -1.01 -1.27
21.77 1.28 1.02
, ': >v- V:v;'v; :;— V^->^
,v ;-;\^,-\ , - -Y^Y^\ %:>1 : ;-~^
„ :" \ .-! '\- •„ , -, ^ , , ^j-'.-'K1 -
20.80 0.72 0.46
19.03 -0.30 -0.56
22.37 1.63 1.37
/20
"^
Tag
•;,• •
'


'x X-
<*\.
-• ,



Data sorted by Laboratory Average
Average Tag
5.10 x
8.23 x
8.40 x
8.70 x
13.10 &
14.17 U
14.90
15.23
15.57
15.97
16.30
16.40
16.57
17.40
17.60
17.60
17.67
17.67
17.80
17.80
17.83
17.87
17.90
18.00
18.47
18.50
18.57
18.67
18.73
18.77
18.80
• = No data submitted
0 = Insufficient data
Lab Average Tag
WC 18.87
AU 18.90
MX 18.90
QX 18.90
GQ 18.93
OF 18.97
QM 19.03
EP 19.03
JE 19.07
AH 19.10
LT 19.13
R 19.17
PG 19.17
BN 19.17
VH 19.20
RK 19.30
L 19.33
EB 19.33
X 19.37
DT 19.50
AK 19.53
AE 19.60
GN 19.63
SF 19.67
CS 19.67
ER 19.80
CE 19.80
AW 19.80
U 19.83
E 19.83
AJ 19.93
TAG SYMBOLS
Lab Average Tag
T 19.97
SZ 19.97
EO 20.00
DE 20.00
AL 20.00
SC 20.00
XM 20.03
AF 20.10
QY 20.10
A 20.10
QZ 20.17
K 20.37
C 20.37
BK 20.37
SS 20.43
AP 20.53
SD 20.53
O 20.57
WJ 20.70
CC 20.70
NH 20.70
W 20.80
AZ 20.80
WH 20.80
FN 20.87
S 20.97
QQ 20.97
EL 21.00
WO 21.07
UQ 21.20
RZ 21.33
It 3 Above control
x = Determined to be an outlier & = Below control
Lab
OX
ID
M
HK
CJ
CA
PX
TD
JS
BO
TN
KH
BM
BH
PW
VA
PB
DZ
SI
QU
I
XL
VI
BA
BC
JX
HE
HL
HP
TQ
SX
limit
limit

-------
14/20  ESD-LV Performance Evaluation: Uranium-Radium in Water, 12-Sep-1997
Radium-226
Average
Tag
  Data sorted by Laboratory Average
Lab   Average	Tag       Lab  Average
                   Tag
                     Lab
  21.40
  21.67
  21.77
  21.80
           UP
           FE
           XA
           LZ
        21.83
        22.37
        22.80
        23.27
NJ
Y
NO
OS
23.43
24.23
25.53
25.73
28.27
IT
tr
X
SM
KL
JY
RD
Q
 % responding labs
                    Frequency distribution
 10
                      •  »••••? •
     -6
 % responding labs
    -4-20            +2            +4
       Normalized deviation of the mean from the known value
                    Frequency distribution
 10
                                     4
                       •1.1
     -6
    -4           -20            +2            +4
       Normalized deviation of the mean from the grand average
 • = No data submitted
 0 = Insufficient data
                       TAG SYMBOLS
                x s Determined to be an outlier
                                           ft s Above control limit
                                           •U = Below control limit

-------
        ESD-LV Performance Evaluation: Uranium-Radium in Water, 12-Sep-1997  15/20
Radium-228                        Statistical Summary                      146 Participants
The known value of this nuclide is 8.0 pCi/1 with an expected precision of 2.0; the control limits
are 4.5 to 11.5; the warning regions are 4.5 to 5.7 and 10.3 to 11.5
55(37.7 %) Failed to respond .
2(1.4 %) Outliers	
7(4.8 %) Out of control —
     but not an outlier


         Statistic
               . 76(52.1 %) Within all limits
Respondents
--•- 6(4.1 %) In warning zone
            but within control


              Non-outliers
Mean
Std. Dev.
Variance
% Coef. of Var.
% deviation of mean from known value
Norm. dev. of mean from known value
Median
% deviation of median from known value
Norm. dev. of median from known value
      8.30
      2.82
      7.98
     34.04
      3.74
      0.11
      8.10
      1.25
      0.04
      Grand Avg 7.99
                 1.87
                 3.50
                23.40
                 -0.07
                 0.00
                 8.00
                 0.00
                 0.00
9(9.9 %) More than 3 norm. S.D.
6(6.6 %) Between 2 and 3 norm. S.D
            .53(58.2 %) Within 1 norm. S.D.
            •               of known value
     23(25.3 %) Between 1 and 2 norm. S.D.

-------
16/20 ESD-LV Performance Evaluation: Uranium-Radium in Water, 12-Sep-1997
Radium-228
Lab
A
AE
AF
AH
AJ
AK
AL
AP
:?Alt-.
x i W V"
xAU*
AW
AZ
BA
Vm:
BC
' ;BCi'r"
BH
BK
BM
nw
BO
C
CAr
f'- f^f^t '
•A^f^^ ,
CE
CJ
cs
cat
BB
DE
DI
DO!
DB
DT
DZ
E
EB
EL
EO
EP
ER
FE'
FJ
FN
Res. 1
8.4
7.1
9.9
6.2
5.5
10.0
6.7
6.9
:":.';' ^v^.r:
" "' <>£%/" ''*''
'*' "V " y* A '
9.3
7.0
5.4
"i^v^s^-i
7.7
x-; |« .'<<" ,,_
7.9
8.2
9.2

8.5
8.9
6.9
7" v.^jj43<,;,;?
7.9
7.6
11.1
1 ,,,; ',"/,
~~^rt .; ^ ~
9.8
; ' / ..-Xv /-"^ -..
' ' ' \
- . ' • :< ~
8.2
7.3
10.3
7.5
7.7
7.1
6.9



7.2
Res. 2 Res. 3
9.7
9.3
10.2
6.2
5.6
9.7
7.8
8.4
J^^^j^iJi
j Jv^sfi^' * "", <*> / ^ '£*'
^=^;j^ -/^ ^^
9.4
7.2
6.0
^Y;7':;"Sp5
7.1
•I---, ™, r-vy;?. -
8.2
8.2
8.7
>>' , * " -" - i
9.1
8.4
7.1
1%":%B$'£^ ;\
6.2
7.3
11.3
\: ••;••••--' i* ••--•••• ~
' "• "-""X f j^
9.9
•' J" J-X^'vl' \U;'V^';'
- ;^'r^'^"*v
*'V>p:?':'>,i \;
7.9
7.8
10.6
6.4
9.1
6.7
6.5
"' :;
s ;•;''

6.5
9.1
9.5
9.5
6.8
5.3
8.9
7.8
9.0
ar-44,^
; ^Vy' v ' ;

9.4
7.1
5.8
> ' -T" /' ' ' ; o -
;• -.-• '
0.06
0.10
0.31

0.38
<. "<.
0.74
0.12
0.32

0.42
0.36
0.10
"' 3 ^188
1.28
0.17
0.59
->;>,;

0.06
»'
0.207
v - v
0.413
0.059
0.177

0.236
0.207
0.059
' ;im
0.738
0.089
0.325


0.030



0.266
0.148
0.325
0.325
0.413
0.236
0.177
'' '' '' •''' •'•'


0.236
9.07
8.63
9.87
6.40
5.47
9.53
7.43
8.10
,-,


9.37
7.10
5.7^3

7.27

8.47
8.27
8.83

8.97
8.50
7.00
: . 1 ' ' 25.97=
7.60
7.40
10.87


9.87
- •


7.80
7.50
10.13
6.80
8.40
7.10
6.83



7.00
TAG SYMBOLS
Determined to be an
outlier
Normalized deviation
(grand-avg) (known) Tag
0.93
0.55
1.62
-1.38
-2.19
1.33
-0.49
0.09
'" - ' '- ! * ;'-


1.19
-0.77
-1.96
T * " - ' ^
-0.63
,• - *"."> _ ~ '
0.41
0.24
0.73

0.84
0.44
-0.86
15.56
-0.34
-0.51
2.49

,„;,,,„ -
1.62
' "" ' <•


-0.17
-0.43
1.85
-1.03
0.35
-0.77
-1.01



-0.86
ft = Above
•11 = Below
0.92 -
0.55
1.62
-1.39
-2.19
1.33
-0.49
0.09
--', , * ' 'i
* V
'- - •
1.18
-0.78
-1.96
:'; ^y- Vv^
-0.64
\ *™~ ^ ^
6.40
0.23
0.72
»
0.84
0.43
-0.87
16.56 x
-0.35
-0.52
2.48
,„,,,, •
.IrV-'
1.62
' ' •-"'-* V.
'.\ -, - ' *' ''
•
-0.17
-0.43
1.85
-1.04
0.35
-0.78
-1.01
• .
•-
•
-0.87
control limit
control limit

-------
ESD-LV Performance Evaluation: Uranium-Radium in Water, 12-Sep-1997 17/20
.
Radium-228
Lab
,,Gtft;
GQ
TTR
HK
HL
HP
I
ID
" jY _
JE
°:JCP
VJK*-
';*nsK
JS
JX
JY
K
KH
KL
"jnftl
L
Res. 1
^t^Wsfy
11.6
5.9
7.6
9.5
2.6
8.4
3.3
sYY-^Y,Xv<.
II1,H_
'""3") ',™',;T;X^''^!™J-,
*^?i"^45
£|V ;:;;^;s^Jv
7.6
8.0
9.2
9.6
7.0
11.2
^r^p'Tp*
7.9
Res. 2 Res. 3
"l4.6
4.9
7.2
9.3
2.5
9.6
4.0
\^3 ^STf-"V*>!l
10.1
^™;,^ i,.r_,,^..»
|;V^>^;!;|SN:^
^" '' >^';t"HxV<
8.0
8.6
9.2
11.3
7.2
12.1
^IPplpJI^
7.9
'fLFlp^ C^SI^^^^IPSI
'ml
LT
"LZV
M
MX

^N'lt
NA -*
^NH^
NJ
	 '••im^
NK-:-
NO
O
V. '>* ^K^**j^.|
6.4
₯^^^1,^'
5^.4 	 "
12.8
6.7
7.3
9.2
3.9
8.7
3.7
,_ .,, ,
'&ir
j™v _,,,
-'v-\xf
;t>-v:>x;
6.6
8.1
9.7
7.8
7.5
10.2
<• !:1\t^-.^«^
8.2
Exper.
Sigma
1.80
0.90
0.21
0.15
0.78
0.62
0.35

0.31

-.-; -x;;-"-"- --/;
0 " _ jS ,. >X°\~ *
0.72
0.32
0.29
1.75
0.25
	 _0.95_ ^
"" s s "• •• ;5? \ ; '
0.17
Rnganal
Normalized deviation
(R + SR) Average
1.120
0.532
0.118
0.089
0.413
0.354
0.207
;• ---• - - ' ^^'"^
0.177
••''-•, " - \ % %
" V ^Vt^t ; tx *
••'• ^ * ^ s
0.413
0.177
0.148
1.064
0.148
0.561
> ?T'7? ''''-" ;™
0.089
12.80
5.83
7.37
9.33
3.00
8.90.
3.67

9.83
•r ^ - -
•C*" *"" *N s

7.40
8.23
9.37
9.57
7.23
11.17
~ , -s VC'
8.00
(grand-avg) (known) Tag
4.16
-1.87
-0.54
1.16
-4.32
0.78
-3.75
V,\0 	 k ^v^'MJ,
1.59^
.. »", ."' V~ ,"' > -;"";
4.16 It
-1.88
-0.55
1.15
-4.33 U
0.78
-3.75 11
^'~!:;"7' • »> '
1.59
" - Y- ' ,' • *
l-;':^x'^' -x^' :-:^; '- ''' , • •
* *\ ' i ^ V ""
-0.51
0.21
1.19
1.36
-0.66
^__,2:7,^^
"•:* "-\ -^ ^ -; ,,
0.01
0° •
-0.52
0.20
1.18
1.36
-0.66
2;11__
^>v;y\~f 7"»^
0.00
v" "^ % \ sss ^ ^ O •• ^ *"" ^ ^ % •? >> ^ ^ v s A ., % % % V<1'< s \ ''"^'•^ '•X^iS^-.^t*'* Xv^ J"'S % ^^^ >%1- v "S '"'•'"••.
V •- \^ ; oV^X*" ** ->X,; Y -.'^ "• \s •.^ \ ^ _^w \^ ^ ^ % ^ ^ ^- •i. -.^ '?•<''"'" !^^X'\'* •••• *•• •.\SV""- % v vv'' ""v •t5'- Si- ^4
•X s ^5 ^ \ s
••-"^ s\
7.4
^ v;»s. v-.v;;;^;; ^£^»»C£s^V^"
4 • \-M\x\ •— v.; -^- fev' vr^x^f^H^r -Vl;x'! ","
8.4 *
9.3

S^^-l^^:^
!^HB~^~":-V^
%\*Sfea^
8.4
y.%. %v%t%% •.% -.^..w sj-v^w^ % -. AW^
;-\?' 'T^WS!f fl
7.3
6.1
8.6
9.0

^^^^^^j;x
lS^^?^:^Sx^S

9'.0~" 	
's\Xi!™Sv;" vv1""1 •.vA\-f1'$*'Si;i*'i»<\X-.s^
-^^};€8lf^S
8.6
6.6
8.4
8.5

sT™vA'
'^^Ty-

8.6
<.v\^' ^;*. __
^^•\x
9.8
6.2
"' ~;x -\;; - " 'v'v
1.00
fe;H^,":V\;
0.12
0.40

•\-\.j\>- _ ^ „, ^«>
f:'Vc>,-^ "'- ''•"v
K»-; :8:29' :/
0.31
"" I"N ^ '""''-
^V'4;*^ fv^Sv
1.25
0.26
'U".*V;!^V'V^
0.591
-,>= ry-";^!- ^>
0.059
0.236

~*~ '' "\-V - ' >
V. '^ »^'° ~'s>;
- \7^«C c ; ; ;
0.177
'^v' •> -. ""T
v - , -.>: 'c1-"-''" '! •-
0.738
0.148
j \ -"^
6.40
,\X^
8.47
8.93

:1" 0~ -\
$ ' ••
ti:if
8.67

-'^ ' ,",
8.57
6.30
;^:;=:-^'{v ^
-1.38
r^^r.Vf#?'%:i
0.41
0.81

\!b ,v;^"v-~; - - -^
.* 'Y-%V' N-, ?-~; > ' T
'V""*' 8-^V':-^
0.58
^ •• % x" ;„ ^^ , " " c£
t;T\kV\-" W" : ' I
0.50
-1.47
* - Vx ' '„"> , *'
-1.39
Fi^i-;* :
0.40
0.81

.,'\0V-v "- *
-\V\, ' ,*' s
>hl8:46^' x
0.58

?-\ •',?„-;, - *"
0.49
-1.47
^s •.«,". -.^ v.S^% ^v.^sv.^^^s^-^-. v^ * «^^% ™^,S.^™VN ^^^^ ^ ^ \ s '" s s^-,% ., v^ -.\^tl ^v \ .. ^ ""• v " * " " ^X X"" -, \ X -. s^ ,' , ^ X .. -. ^ •," "• ^ X "" ' V-\" " "-
' CjT^^-.

OF
OS;
OX
•" -j. %
Xs 1Q> ^
"* i --
PB
PG
PQ
PW
PX
Q
• =
0 a
	 " N^. ^X^Xx^^JWs-.-- /

	 ^4.6^
, ' •\-x;"'\""T-v"^?
7.9
m %I «^W- w * ™\ ^ *-* jx*1 ""*
s \ I "••'- -. V^.^^'- \- i!'s
^ v s^.-."' ' ^ v ^ ^ ..
8.8
, >v- . •> , •' "
\
8.0
^ ^ " \ s \- \ " *
7.3
"• N ^^^x^*^-*?* "" %^^^ ""

7.5
•?& >\ \~-"t^ HT, f _ v
7.8 " 	
vw&^-\\ ^^•.^^^^^^•.y.™•.^^^^.;^•,^^ -.
^ %%VT'V w^'1-^'*1- * * ' •• '•^v^
- \X wX^ V- \0*" % X"-x * x^V ^ «
8.6
• • x _ ; s
\;%:^r\'-^;
8.3
r:/ y - " \
6.9
" V

7.8

7.8
vs* wvs^-^vv^
^ V ^ '\" t "

9.0

,-• ,'-.
8.4

6.5
No data submitted
Insufficient
data
x =


1.77
s \ ^
0.06
s «X \ -w * N T "^ V ™
- ^ "• ""• •> " s ^
^ - - "" ^ v ^ ^ v s t
0.20

'-;
0.21

0.40


0.945

0.030
v^ ^% vv" NW ^ %%%V%sv.s
\^ % „., -• \ v - v x; ^
T " " '-•-- x sx-
0.118


0.118

0.236
^ '• ••

6.63

7.83
v\ ^™ci ••••••••••••••••••^

-. -.s
8.80


8.23

6.90
TAG SYMBOLS
Determined
to be an outlier

s"" •- ^" •• " ? V S - "• -^

-1.18
>>^;>vv"r:-v:
-0.14
^"•.w-^ •••'•• -.•-••_ •> - --^ N1-1- •-•• ^SWWVA
-.-•v ^, ^ s * *" \ „- xsr* "^ 7 , *-.
^ v^v '. \\ "•"•-." ^ •* ""
0.70
• ! > ' - "
»^ " X ^
0.21

-0.95
tt = Above
li = Below
s "^ ° i ^Xs • "","''''•

-1.18
\ ^ ^ "•
-0.14
V..V.V. WW ^A., w^ w^ ^ WAV.
-%\ ^ ^ ,-. ^ "\ V • -.""""

0.69
; • •
:;
0.20
•
-0.95
control limit
control limit

-------
18/20 ESD-LV Performance Evaluation: Uranium-Radium in Water, 12-Sep-1997
Radium-228
Lab
QM
Res. 1
'W!'Arb"^'M^
Res. 2
'^K;:?i^^'..\^
Res. 3
;-^;K;; ' :-'
Exper.
Rng anal Normalized deviation
Sigma (R + SR) Average (grand-avg) (known) Tag



•• % •• \ *
- \;- -\ » •
^Uy^j^^Sjn,-^'^-^,?.*'^^^?^*'^' k ,t , •"•''' v! - ''''•-> * '=* " "--'' -' ' ' - - '-<"'"' s" V;" ,• ' V ']', * *• '
"'''*»*»"
QU
QX
J3Z_
\R ,"v
RD
BF
• , !,
RG
RK
RP
Eft

RZ
S
sc
SD
SF
SI
•%L-'
SM
SO
ss
sx
sz
T
TD
TN
TQ
*T&'
U
UP
UQ
UZ
VA
VH
VI
W
we
WG
WH
Wl
WJ
WO
• =
1 , "V*':', -'; , •**,•
6.5
"V, ?;<*-,•
.,. J,-M.,\
^'- J! ' "***';-, f'"J''*]
12.1
,V; :-'^!iC»
-j - ;>''",'V^'"*4
, ' „ .5-3 t'
. ;-'Tl -' '„ o
-i'\ -'r^'^'v.
;»,K! ;:.'4v^
8^2
7.7
9.3
11.9
6.6
7.4
/ :-/»',"," :;V/-X
' 7.4\
,
9.7
7.0
5.4
9.2
10.0
2.9
7.0
. ',--'"•
7.3
10.6
8.2
_ - \ ' '- ' ;- -;
9.1
12.1
9.6
7.8
2.7

7.7


4.1
'• •.'• \"'-;r, ' *' '*'?''?>
7.9
.,,,.94-,^..
_8.1^_
*''''"'':*,'•* - ''-VY'-
13.5
/~~is--:'fr-^l"-:^
xJrl^-fM
..,.ti 4-4
•.^ & "•/* -
,S -.' -• ^ -f 4 f J<- ^^.v

7?«;%;V:!^^
8.0
7.0
8.1
11.3
6.9
8.0
~r,-:',.';f :,'""„•; ?
7.3
-. " >••
8.5
5.8
7.1
10.0
6.8
2.5
8.3
< s ^ V v ^ '
'7.1'"
10.2
8.9
~'-' ! * ^\"
8.9
10.3
9.5
8.1
3.1

7.2


4.9
~'« '','" '
7.2
9.8
8.2
'< /
0.70
0.85
v s V , '
0.06

0.413
0.502
0.030
, ""
7.20
9.00
8.17

-6.69
0.87
0.15
' si ,'.'x-r,, ,- *.< ' -
-6.69
0.87
0.14
:^'~^A ,fv-,,"V ; - . ~: " >^ ^ -, V - '"' 	 : 	 "' 'Vv-'"^'"^: irr
15.4

S-w?:-^>-':-';"
r."j?\?...
^ %V\T "'"
,Vt% \ (7'' '
;>>; •->'' -';
8.4
7.4
9.0
11.6
7.4
6.5
- 1?T '„.?•
9.1

10.2
9.2
9.0
9.3
7.1
2.6
7.7
^ •. < ^ •• -\ * ••
7.3
9.5
9.3
' -'• r"',-.^ ,
7.8
8.5
9.2
7.6
3.0

6.9


4.9
No data submitted
0 s Insufficient
data
x =
1.66
"-'--" - '- • ,' -.
SM>'. ''-.-"
0.59

•, '•-• ' '' ' ;' ** '•
O ' !• , ''i*
••* jf •• Vj, ^ % ,
0.20
0.35
0.62
0.30
0.40
0.75
"•".':- A •'•'
1.01

0.87
1.72
1.80
0.44
1.77
0.21
0.65
J
0.12
0.56
0.56
A<" ->'• - "
0.70
1.80
0.21
0.25
0.21

0.40


0.46
0.975
/- : ,' '--'•
'><».>",
0.325


\'--'~
0.118
0.207
0.354
0.177
0.236
0.443
•s v x ^
0.532

0.502
1.008
1.120
0.236
0.945
0.118
0.384

0.059
0.325
0.325

0.384
1.120
0.118
0.148
0.118

0.236


0.236
13.67
" , -
-/ •• V ^ 'ffff •. * ^
5.07

, •' '' '-' - ' "'- " ' '

8.20
7.37
8.80
11.60
6.97
7.30
*" --• • •••:•;/. 	
7.93

9.47
7.33
7.17
9.50
7.97
2.67
7.67

7.23
10.10
8.80

8.60
10.30
9.43
7.83
2.93

7.27
;

4.63
TAG SYMBOLS
Determined
to be an
outlier
4.91
'' ' . " ' • ?i' "
,^'V, ,--* ! '<
-2.54


"• ,". -- '-«
0.18
-0.54
0.70
3.12
-0.89
-0.60

-0.05

1.28
-0.57
-0.72
1.30
-0.02
-4.61
-0.28

-0.66
1.82
0.70
,
0.52
2.00
1.25
-0.14
-4.38

-0.63


-2.91
It = Above
U = Below
4.91 tr
o^ v t" ^\ ,. -. ^ '
^^:W;;jy
-2.54
-V^'* * '
'**"• \"'- ,-»
""-'''•-4 '• • ";
0.17
-0.55
0.69
3.12 IT
-0.89
-0.61
'- ' %"'-" ,"j--?
-0.06
• , '
1.27
-0.58
-0.72
1.30
-0.03
-4.62 II
-0.29
' / •;
-0.66
1.82
0.69
* '"
0.52
1.99
1.24
-0.14
-4.39 li
*
-0.64
' * ." '
'• •
-2.92
control limit
control limit

-------
ESD-LV Performance Evaluation: Uranium-Radium in Water, 12-Sep-1997 19
Radium-228
Lab Res. 1 Res. 2
JWR_ 	 ^>~«~>--~**£*
;WX;£:.~ : '•> xr-^>-;fliVs"f -:^'?
JL^l-^.JH.' J".' '^X~
'• ' --i^. --,' >-'-V '.^"'-V1* ' !< ~L*yo» , ,; "
XCx 1^-(S*xj4 s\ " '*W. 'x/"v,">x>*
'^yn':'':f-' A-'"V~v- ;; v^'^' ', \ ' ,-
V^M^:^^*'t^;^Ar i'|^'
C^V^ ^U'-j'C; ; r x-o ^i^Xx/v^V
vJufe-* ,"; •-'•-Vx^t^*;'^*''^-^- '-
XL 	 8.5 	 8.6
JSM_ 	 J?JL~^ ~.T;!

Exper. Rng anal
Res. 3 Sigma (R + SR)
_s_6-6 °-81 °d13
' * 'r^lvLv \' ^ \ ^"^ " Vs i^ sXt" •" * ^
\^lH:?^ ,,P,-72,^ . 0.384 '
^ *t~-*i&f*'*.l Jx«x\ " C ,--'*'- "''
~>\~5?;:>K4xt><^,'s. - \ - \; -'' •
%'':??\"^ x - ,-"'."''' '. r :'<
^;i^J^^44v:>r,,, ,\\\- v , *, , ,
.V'v^^.'Vv.v^ ;' ! •--' -,.'"'' ** '"• ',
"J,", Vs%- T*" -' " ;V^~
8.6 0.06 0.030
7.5 0.57 0.325

Normalized deviation
Average (grand-avg) (known)
6.13^ __:1;61 _,;l-62_
1 x?^''o-,s-"'->>? ^!v '-, ^:^S:!'';
10.53 ^,2.20 ^J ^,,2.19^
- • v ;, ;. . ! ^ '• , * s.' s ^Vr-v^-1 ~ ' -;'~ -\s • " s 3 >»
"N"'~ ~\\\4,'!\ s,;sxH' ' ''^'
-,;».'•! ,\, ,y^ V'-T^; . .'.^f
-\ "*v, fy;- ""- - ;0:o-t/V. V- ^^^ "
- - "• * * >^ '•^v'' \ v '"'
8.57 0.50 0.49
7.33 -0.57 -0.58
; , . r»'".'^>^.\, ?v\ v-^
720 1
1
Tag

•;, 4 ,\ -
•%~;ir.:
5 * J
V • -;
%'
X -~>
, TsJ '
1 • '

;>\ '
Data sorted by Laboratory Average
Average Tag
2.67 Jl
2.93 Jl
3.00 11
3.67 11
4.63
5.07
5.47
5.73
5.83
6.13
6.30
6.40
6.40
6.63
6.80
6.83
6.90
6.97
7.00
7.00
7.10
7.10
7.17
7.20
7.23
7.23
7.27
7.27
7.30
7.33

• = No data submitted
0 = Insufficient data
Lab Average Tag
TN 7.33
WC 7.37
HP 7.37
ID 7.40
WO 7.40
EK 7.43
AJ 7.50
BA 7.60
HE 7.67
WR 7.80
O 7.83
LT 7.83
AH 7.93
OF 7.97
EB 8.00
EP 8.10
Q 8.17
SF 8.20
FN 8.23
CA 8.23
EO 8.27
AZ 8.40
SZ 8.47
QU 8.47
U 8.50
KB. 8.57
WH 8.57
BC 8.60
SI 8.63
XM 8.67

TAG SYMBOLS
Lab Average Tag
SX 8.80
S 8.80
HK 8.80
JS '8.83
CJ 8.90
AL 8.93
DZ 8.97
CE 9.00
TQ 9.07
DT 9.33
W 9.37
OX 9.37
SM 9.43
TD 9.47
L 9.50
AP 9.53
QZ 9.57
RZ 9.83
PW 9.87
JX 9.87
BK 10.10
EL 10.13
M 10.30
BH 10.53
C 10.87
XL 11.17
NO 11.60 ft
VA 12.80 ft
AE 13.67 ft
NJ - 17.77 x
25.97 x
ft = Above control
x = Determined to be an outlier li = Below control
Lab
UQ
SC
PB
BM
I
MX
BO
QX
A
HL
JY
AW
VI
ss
T
AK
K
JE
DE
AF
UP
E
VH
X
CS
KL
SD
GQ
RD
NH
CC
limit
limit

-------
20/20  ESD-LV Performance Evaluation: Uranium-Radium in Water,  12-Sep-1997
Radium-228

 % responding labs	Frequency distribution
 10
     -6            -4            -20            +2           +4            +6
                     Normalized deviation of the mean from the known value



 % responding labs         	   Frequency distribution	
   «

 10-
                                                 l-liiV.—  - -
                  -4      '      -2            0           +2           *«           +6
                    Normalized deviation of the mean from the grand average

-------