EPA-670/4-75-004a
April 1975
FORTRAN PROGRAMS FOR ANALYZING COLLABORATIVE TEST DATA
PART I: GENERAL STATISTICS
By
Elmo C. Julian
METHODS DEVELOPMENT AND QUALITY ASSURANCE LABORATORY
Program Element No. 1HA327
NATIONAL ENVIRONMENTAL RESEARCH CENTER
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CINCINNATI, OHIO 45268
-------
REVIEW NOTICE
The National Environmental Research Center—Cincinnati has
reviewed this report and approved its publication. Mention of trade
names or commercial products does not constitute endorsement or
recommendation for use.
-------
FOREWORD
Man and his environment must be protected from the adverse effects
of pesticides, radiation, noise and other forms of pollution, and the
unwise management of solid waste. Efforts to protect the environment
require a focus that recognizes the interplay between the components of
our physical environment—air, water, and land. The National
Environment Research Centers provide this multidisciplinary focus
through programs engaged in
studies on the effects of environmental contaminants on man
and the biosphere, and
a search for ways to prevent contamination and to recycle
valuable resources.
This work provides a method for understanding the deeper meaning
of interlaboratory collaborations. This work also represents one
effort to achieve a more complete knowledge of the effectiveness of
various analytical methods.
A. W. Breidenbach, Ph.D.
Director
National Environmental
Research Center, Cincinnati
i i i
-------
ARSTRACT
A FORTRAN program for IBM 1130 is described by which general
statistics on inter1aboratory studies of chemical analytical methods
may be obtained. Data screening followed by a statistical t-test for
identifying outliers is included. A histogram of data in ascending
order is also provided.
i v
-------
PREFACE
These program systems for general statistics and plotting of data
scatter diagrams were programmed in Fortran 1130. These program
systems were desicmed to be executed on IBM 1130, Version 2,
Modification 11, Core Size 16K.
General statistics were obtained on data from interlaboratory
method studies. These statistical approaches are based on a procedure
described by Youden (1). In his procedure, closely related pairs of
samples, A and B, for example, are analyzed by each of the
participating laboratories. The data from all of the participants for
each of the samples is subjected to the statistical program, COLST.
The data from each sample pair was plotted, values of A versus
values of B. In the application for this particular plot program,
SCAT, the data from three pairs of samples, making three plots, or
diagrams, were drawn on each page. This presentation of data provided
a vivid visual display for purposes of comparison.
The general statistics program was adapted from a data
summarization program written in Fortran IV (2). This program was
adapted to the 1130 Model and expanded to provide for data input in any
one of several forms of decimal expression, data screening, and the
application of a statistical t-test to expose outliers and to leave a
reduced vector of "retained" data. The plotter program, SCAT, utilized
the plotter routines as supplied by IBM.
-------
TABLE OF CONTENTS
Foreword i i i
Abstract iv
Preface v
Acknowledgement vii
References vl i
PROGRAMS
COLST
Introduction 1
Use 1
Description 1
Input Requirements 2
Output Variables 3
Program Listing k
SUBROUTINES
THEAD lU
REALT 15
CONV2 17
COLS1 18
COLT2 19
COLS3 21
COLS'* 22
COLS5 23
COLS6 24
COLS7 25
COLS8 26
COL1, COL2, COL3, COLU. 27
DLIST 29
HEADER & DATA DECK
CONFIGURATION 30
TYPICAL SAMPLE PRINTOUT 32
APPENDIX I 37
v i
-------
ACKNOWLEDGEMENT
The assistance of IBM programmers and the assistance of staff
members of the Computer Services and Systems Division, NERC,
Cincinnati, is greatly appreciated. The encouragement of John A.
Winter, Chief, Quality Assurance & Laboratory Evaluation Branch and the
manuscript review and helpful suggestions of Paul W. Britton,
Statistician in the above Branch, Methods Development and Quality
Assurance Laboratory, NERC. Cincinnati, is also greatly appreciated.
REFERENCES
1. Youden, W.J.,Statistical Techniques for Collaborative Tests, AOAC,
Washington, D.C.(1967).
2. Larson, K.E.,Ed.,The Summarization of Data, Journal of Quality
Technology,1,68(1969).
v i i
-------
-------
INTRODUCTION
The program, COLST, is designed to provide elementary statistics
on data obtained by an official test method. The program is designed
to treat data from interlaboratory method studies.
USE
The data as obtained from the participants include missing values,
censored values, wild values, and reasonable values. Furthermore, some
of the participant's results had been obtained by using a different
method instead of the official method of the test. The data as
received, the input data, are screened to ignore missing and censored
data, as well as data obtained by a different method. The data
remaining after screening were termed "raw data."
After the standard deviation was obtained on the raw data vector,
extreme data values equal to or greater than + 4s are discarded. The
symbol s is the estimated standard deviation on the raw data vector.
These discarded values were termed "unacceptable data." The remaining
values of the raw data vector are termed "acceptable data."
A statistical t-test is then applied to the acceptable data vector
in order to identify and remove any "outliers." The outliers are marked
with the letter R which indicates that the value is rejected as an
outlier. The data vector remaining is termed "retained data." This t-
test is applied in a rather conservative manner since an alpha of
0.0050 is used in a two-tailed test. That is, only 0.25% of a normal
distribution was truncated from each extreme.
In reviewing, the input data are screened to produce raw data,
which are tested for wild values to produce an acceptable data vector.
The acceptable data vector is searched for outliers, which, when noted
leave the retained data vector from which general statistics
arecalculated. The statistics obtained are listed below:
number of data points
mean of acceptable data
accuracy based on retained data
range of retained data
variance of retained data
standard deviation on retained data
confidence limits, 95%, on a single determination of retained data
coefficient of variation on retained data
skewness of retained data
number of cells in the histogram
-------
DESCRIPTION
The main program, COLST/ utilizes sixteen subroutines by which
input/ calculations/ editing and output are accomplished. This main
program was developed from a program listing in a paper on the
summarization of data by Thayer and Snyder of the Applied Statistics
Group in the Engineering Research Center of the Western Electric
Company (2).
Data input is accomplished by the subroutine/ REALT/ which is part
of the data screening step. The acceptable data are subjected to the
statistical t-test as described above. A histogram is developed using
for the number of cells/ the square root of the number of data points.
This program accepts up to and including 120 data points. Appendix I
shows the t-table at t(0.99).
In the following requirement lists/ a variable like JOBS has a
single location and a variable like NDF(I) is a one-dimension array or
a vector.
INPUT REQUIREMENTS
Vari able Purpose Format
JOBS Number of sets of data to be \k
evaluated
NDF( I )/CVT(l ) Degrees of freedom; critical I3,5X,F6.1»
value of t
BLANK A blank character; the chara- 2A1
ASTER cter/'R'
EX The character/'X1 Al
DA/TY Date of evaluation/ xx,xx/xx 2A4
ARK I)/ AR2(I) Text of heading/ each 2QAk
AR3(I)/ ARiU(l)/
ARU2CI )/ ARU3CI )/
ARUi*(l)/ AR5CI)
BRKI}/ BR2CI).
NR, NCELL/ Number of data points in raw 3IU
IZERO data vector; specified number
of cells. IZERO when greater
than zero sets the lowest cell
boundary to 0.0.
FNKI ).FN2( I ) Test of two footnotes 20AU
PAR1 thru Used as an extra blank line; 8AU/11
PARS/ IJKL inputs UKL which designates
the number of digits to the
right of the decimal point
TV Designates the known/ or 'true' F10.0
value of the sample for which
this test is run
BRKI) Text printing the true value for 20AI*
the sample
-------
OUTPUT VARIABLES
UNACCEPTABLE DATA LIST
Variable Purpose
KOR(I)
KDER(I)
ANSA(I)
Numerical identification of laboratory
Numerical identification of analyst
Raw data element
Symbol: D = Different method
Blank = Official method of test
Format
13
Al
F8.2
Al
HEADING
The heading is determined and printed by the subroutine,
THEAD
ACCEPTABLE DATA LIST
The acceptable data vector is calculated and printed by the
subroutine, DLIST.
STATISTICS ON RETAINED DATA
Variable
N
RANGE
COEFZ
TV
VRZ
SKEWZ
XBAR
SDZ1
NCELL
ZAVE
SZ196
ZMED
ACCZ
Purpose
Format
Number of data elements in retained 13
data vector
Range of data elements in retained Fll.5
data vector
Coefficient of variation of retained Fll.5
data vector
True, or known value of the sample F6.2
Variance of data elements of retained Fll.5
data vector
Skewness of the distribution of data Fll.5
elements of retained data vector
Mean of data elements in acceptable Fll.5
data vector
Standard deviation of data elements in Fll.5
retained data vector
Number of cells used in planning and 14
calculating the histogram
Mean of data elements on retained data Fll.5
vector
Confidence limits on single determination Fll.5
of retained data, + 95%
Median of data elements in retained data Fll.5
vector
Accuracy of the mean, on retained data Fll.5
vector, based upon the true value
-------
RETAINED DATA IN ASCENDING ORDER: HISTOGRAM
Variable Purpose Format
X(I) Data element F8.2
W(I) W = 'R1, data element rejected by t-test Al
alpha = 0.0050; two-tailed test
W = ' ', data element retained
N Number of data elements in the acceptable 14
data vector
OUTPUT REQUIREMENTS
Variable Purpose Format
XBAR Mean of retained data F11.5
VAR Variance on retained data F11.5
VR Sample variance on retained data F11.5
SD Standard deviation on retained data F11.5
SD1 Sample standard deviation on retained F11.5
data
S196 Sample standard deviation * 1.96 F11.5
POINT(I) Midpoint of any cell in histogram F10.4
KKK Frequency of data elements in any cell 14
XIA(I) Literal element,'X's, corresponding Al
to frequency of data points in the cell
but limited to 15 or less by space limi-
limitations
C COLST
C UP TO AND INCLUDING 121 DATA POINTS
C INCLUDES T-TEST, IDENTIFICATION OF
C OUTLIERS BY THE LETTER 'R1. ACCURACY IS BASED UPON THE TRUE
C VALUE VERSUS RETAINED DATA.
C SUMMARY OF COLLABORATIVE TEST DATA/STATISTICS/HISTOGRAM
C DATA INPUT, ONE VALUE PER DATA CARD
C INPUT OF DATA THRU SUBROUTINE 'REALT1.
INTEGER ANSA(120),ANA(120)
DIMENSION X(120),NFREQ(120),GROUP(120),POINT(120),XIA(120),
1KOR(120),KDER(120),XH(120),TE(120),TF(120),V(120),W(120)
DIMENSION AR1(20),AR2(20),AR3(20),AR5(20),BR1(20),BR2(20)
DIMENSION AR41(20),AR42(20),AR43(20),AR44(20)
DIMENSION FN1(20),FN2(20)
DIMENSION Z(120),G(120)
DIMENSION NDF(120),CVT(120)
DIMENDION KUR(120),KDUR(120),ANSB(120),ANS(120)
IPUT=2
IOUT=5
READ(IPUT,7992) JOBS
READ(IPUT,7991)(NDF(I),CVT(I),1=1,120)
C INPUT SYMBOLS...BLANK,LETTER'R1
READ(IPUT,901) BLANK,ASTER
-------
C INPUT LETTER1X1
READ(IPUT,15) EX
C INPUT DATE OF EVALUATION XX/XX/XX
READ(IPUT,73) DA,TY
C INPUT TEN LITERALS CARDS
READ(IPUT,501) AR1
READ(IPUT,501) AR2
READ(IPUT,501) AR3
READ(IPUT,501) AR41
READ(IPUT,501) AR42
READ(IPUT,501) AR43
READ(IPUT,501) AR44
READ(IPUT,501) AR5
READ(IPUT,501) BR1
READ(IPUT,501) BR2
C SET IZERO = 1 FOR LOWEST CELL BOUNDARY TO BE ZERO.
C OTHERWISE ENTER BLANK FIELD
C NUMBER OF CELLS = SQUARE ROOT OF NR
READ(IPUT,18) NR,NCELL,IZERO
IF(NR) 402,500,402
C READ IN TWO LINES OF FOOTNOTES
402 READ(IPUT,501) FN1
READ(IPUT,501) FN2
C DATA DESCRIPTION
DO 7993 LOOP=1,JOBS
WRITE(IOUT,30)
C DIGIT CONTROL OF MANTISSA FOR DATA PRINTOUT, IJKL
READ(IPUT,8) PAR1,PAR2,PAR3,PAR4,PARS,PAR6,PAR7,PARS,IJKL
READ(IPUT,17) TV
READ(IPUT,501) BR1
C TEST FOR TOO MUCH DATA (MORE THAN 120)
IF(NR-120) 21,21,22
22 WRITE(IOUT,24)
WRITE(IOUT,30)
GO TO 500
21 AN=NR
C FOUR SIGMA SCREENING TEST TO ELIMINATE UNACCEPTABLE DATA
MAC=1
CALL THEAD(AR1,AR2,AR3,AR41,AR42,AR43,AR44,AR5,BR1,BR2,DA,TY,
1 IOUT,MAC
WRITE(IOUT,71)
CALL REALT(KOR,KDER,G,ANSA,ANSB,NR)
IF(TV) 503,500,503
C GET STATISTICS ON RAW DATA (G(I))
503 CALL COLS1(G,NR,XBAR,SS,S)
C CALCULATE 4*SIGMA
FS = S*4.0
C PRINT HEADING
WRITE(IOUT,30)
MAC=2
CALL THEAD(AR1,AR2,AR3,AR41,AR42,AR43,AR44,AR5,BR1,BR2,DA,TY,
1 IOUT,MAC
WRITE(IOUT,71)
-------
WRITE(IOUT,7011)
C ELIMINATE UNACCEPTABLE DATA, PRINT UNACCEPTABLE DATA LIST
C REVISE THE VALUE OF N
CALL COLT2(G,FS,NR,KDER,X,ANSA,ANSB,NA,IPUT,IOUT,KUR,KDUR,
1 ANA,ANB,XBAR)
C END OF FOUR SIGMA SCREENING TEST
C SUBSTITUTE ACCEPTABLE DATA COUNT, NA, FOR N
N=NA
C SAVE ACCEPTABLE DATA VECTOR IN THE ORDER READ
DO 510 1=1,N
XH(I)=X(I)
510 CONTINUE
C GET MEAN,SS,S,VR,SD1, ON ACCEPTABLE DATA
CALL COLS3(X,N,XBAR,VAR,VR,SD,SD1,S196)
C GET SKEWNESS ON DATA
CALL COLS4(X,N,XBAR,SD,SKEW)
C SORT DATA
L=N-1
DO 120 J=1,L
LL=L-J+1
DO 110 1=1,LL
LG=I+1
IF(X(I)-X(LG)) 110,111,111
111 A=X(I)
X(I)=X(LG)
X(LG)=A
A=ANSA(I)
ANSA(I)=ANSA(LG)
ANSA(LG)=A
A=ANSB(I)
ANSB(I)=ANSB(LG)
ANSB(LG)=A
110 CONTINUE
120 CONTINUE
C T-TEST ON DATA, BOTH SORTED AND UNSORTED
C OBTAIN T VALUE
TL=0.
KLM=0
DO 610 1=1,N
TE(I)=ABS( (TV-XH(I) )/SDl)
610 TF(I)=ABS((TV-X(I))/SD1)
C READ CRITICAL VALUE OF T (CVT) FROM FILE
KN=N-1
C TEST SIGNIFICANCE OF THE T VALUE
DO 621 1=1,N
IF(TE(I)-CVT(KN)) 619,619,620
619 V(I)=BLANK
GO TO 621
620 V(I)=ASTER
621 CONTINUE
C OBTAIN RETAINED DATA VECTOR AND CALCULATE ITS STATISTICS
DO 931 1=1,N
IF(TF(I)-CVT(KN)) 929,929,930
-------
929 W(I)=BLANK
TL=TL+X(I)
KLM=KLM+1
Z(KLM)=X(I)
GO TO 931
930 W(I)=ASTER
931 CONTINUE
AN=KLM
NCELL=SQRT(AN)
IF(NCELL-l) 450,450,451
450 NCELL=2
C CALCULATE RETAINED MEAN,VARIANCE AND STANDARD DEVIATION
451 CALL COLS3(Z,KLM,ZAVE,VARZ,VRZ,SDZ,SDZ1,SZ196)
C GET SKEWNESS
CALL COLS4(Z,KLM,ZAVE,SDZ,SKEWZ)
C GET MEDIAN
CALL COLS5(Z,KLM,ZMED)
C GET COEFFICIENT OF VARIATION
CALL COLS6(SDZ1,ZAVE,COEFZ)
C GET RANGE
CALL COLS7(Z,RANGE,KLM)
C GET ACCURACY
CALL COLS8(TV,ZAVE,ACCZ)
WRITE(IOUT,30)
MAC=3
CALL THEAD(AR1,AR2,AR3,AR41,AR42,AR43,AR44,AR5,BR1,BR2,DA,TY,
1 IOUT,MAC)
WRITE(IOUT,71)
WRITE(IOUT,993)
C PRINT DATA LIST MARKING REJECTED DATA 'R1
IF(N-35) 9000,9001,9002
9000 NDIF=35-N
DO 9901 1=1,N
9901 CALL DLIST(IJKL,KUR,KDUR,XH,V,ANA,ANB,I,IOUT)
DO 8901 MM=1,NDIF
8901 WRITE(IOUT,8800) BLANK
WRITE(IOUT,502) FNl
WRITE(IOUT,502) FN2
GO TO 850
C
9001 DO 9902 1=1,N
9902 CALL DLIST(IJKL,KUR,KDUR,XH,V,ANA,ANB,I,IOUT)
WRITE(IOUT,8800) BLANK
WRITE(IOUT,502) FNl
WRITE(IOUT,502) FN2
GO TO 850
C
9002 IF(N-70) 9003,9004,9005
9003 DO 9903 1=1,35
9903 CALL DLIST(IJKL,KUR,KDUR,XH,V,ANA,ANB,I,IOUT)
WRITE(IOUT,8800) BLANK
WRITE(IOUT,502) FNl
WRITE(IOUT,502) FN2
-------
NDIF=70-N
WRITE(TOUT,30)
CALL THEAD(AR1,AR2,AR3,AR41,AR42,AR43,AR44,AR5,BR1,BR2,DA,TY,
1 IOUT,MAC)
WRITE(IOUT,71)
WRITE(IOUT,993)
DO 9904 1=36,N
9904 CALL DLIST (IJKL,KUR,KDUR,XH,V,ANA,ANB, I, IOUT)
DO 8903 MM=1,NDIF
8903 WRITE(IOUT,8800) BLANK
WRITE(IOUT,502) FNl
WRITE(IOUT,502) FN2
GO TO 850
C
9004 DO 9905 1=1,35
9905 CALL DLIST(IJKL,KUR,KDUR,XH,V,ANA,ANB,I,IOUT)
WRITE(IOUT,8800) BLANK
WRITE(IOUT,502) FNl
WRITE(IOUT,502) FN2
WRITE(IOUT,30)
CALL THEAD(AR1,AR2,AR3,AR41,AR42,AR43,AR44,AR5,BR1,BR2,DA,TY,
1 IOUT,MAC)
WRITE(IOUT,71)
WRITE(IOUT,993)
DO 9906 1=36,70
9906 CALL DLIST(IJKL,KUR,KDUR,XH,V,ANA,ANB,I,IOUT)
WRITE(IOUT,8800) BLANK
WRITE(IOUT,502) FNl
WRITE(IOUT,502) FN2
WRITE(IOUT,30)
C
9005 IF(N-105) 9006,9007,9008
9006 DO 9907 1=1,35
9907 CALL DLIST(IJKL,KUR,KDUR,XH,V,ANA,ANB,I,IOUT)
WRITE(IOUT,8800) BLANK
WRITE(IOUT,502) FNl
WRITE(IOUT,502) FN2
WRITE(IOUT,30)
CALL THEAD(AR1,AR2,AR3,AR41,AR42,AR43,AR44,AR5,BR1,BR2,DA,TY,
1 IOUT,MAC)
WRITE(IOUT,71)
WRITE(IOUT,993)
DO 9908 1=36,70
9908 CALL DLIST(IJKL,KUR,KDUR,XH,V,ANA,ANB,I,IOUT)
WRITE(IOUT,8800) BLANK
WRITE(IOUT,502) FNl
WRITE(IOUT,502) FN2
NDIF=105-N
WRITE(IOUT,30)
CALL THEAD(AR1,AR2,AR3,AR41,AR42,AR43,AR44,AR5,BR1,BR2,DA,TY,
1 IOUT,MAC)
WRITE(IOUT,71)
WRITE(IOUT,993)
8
-------
DO 9909 1=71,N
9909 CALL DLIST(IJKL,KUR,KDUR,XH,V,ANA,ANB,I,TOUT)
DO 8904 MM=1,NDIF
8904 WRITE(IOUT,71)
WRITE(IOUT,502) FNl
WRITE(IOUT,502) FN2
GO TO 850
9007 DO 9910 1=1,35
9910 CALL DLIST(IJKL,KUR,KDUR,XH,V,ANA,ANB,I,IOUT)
WRITE(IOUT,71)
WRITE(IOUT,502) FNl
WRITE(IOUT,502) FN2
WRITE(IOUT,30)
CALL THEAD(AR1,AR2,AR3,AR41,AR42,AR43,AR44,AR5,BR1,BR2/DA,TY,
1 IOUT,MAC)
WRITE(IOUT,71)
WRITE(IOUT,993)
DO 9911 1=36,70
9911 CALL DLIST(IJKL,KUR,KDUR,XH,V,ANA,ANB,I,IOUT)
WRITE(IOUT,71)
WRITE(IOUT,502) FNl
WRITE(IOUT,502) FN2
WRITE(IOUT,30)
CALL THEAD(AR1,AR2,AR3,AR41,AR42,AR43,AR44,AR5,BR1,BR2,DA,TY,
1 IOUT,MAC)
WRITE(IOUT,71)
WRITE(IOUT,993)
DO 9912 1=71,105
9912 CALL DLIST(IJKL,KUR,KDUR,XH,V,ANA,ANB,I,IOUT)
WRITE(IOUT,71)
WRITE(IOUT,502) FNl
WRITE(IOUT,502) FN2
GO TO 850
9008 DO 9913 1=1,35
9913 CALL DLIST(IJKL,KUR,KDUR,XH,V,ANA,ANB,I,IOUT)
WRITE(IOUT,71)
WRITE(IOUT,502) FNl
WRITE(IOUT,502) FN2
WRITE(IOUT,30)
CALL THEAD(ARl,AR2,AR3,AR41,AR4 2,AR4 3,AR4 4,AR5,BR1,BR2,DA,TY,
1 IOUT,MAC)
WRITE(IOUT,71)
WRITE(IOUT,993)
DO 9914 1=36,70
9914 CALL DLIST(IJKL,KUR,KDUR,XH,V,ANA,ANB,I,IOUT)
WRITE(IOUT,71)
WRITE(IOUT,502) FNl
WRITE(IOUT,502) FN2
WRITE(IOUT,30)
CALL THEAD(ARl,AR2,AR3,AR41,AR4 2,AR4 3,AR4 4,AR5,BRl,BR2,DA,TY,
1 IOUT,MAC)
WRITE(IOUT,71)
WRITE(IOUT,993)
-------
DO 9915 1=71,105
9915 CALL DLIST(IJKL,KUR,KDUR,XH,V,ANA,ANB,I,IOUT)
WRITE(IOUT,71)
WRITE(IOUT,502) FNl
WRITE(IOUT,502) FN2
WRITE(IOUT,30)
CALL THEAD (ARl, AR2, AR3 , AR41, AR4 2, AR4 3 , AR4 4 , AR5 , BRl, BR2, DA, TY,
1 IOUT,MAC)
WRITE(IOUT,71)
WRITE(IOUT,993)
DO 9916 1=106,N
9916 CALL DLIST(IJKL,KUR,KDUR,XH,V,ANA,ANB,I,IOUT)
NDIF=140-N
DO 8905 MM=1,NDIF
8905 WRITE(IOUT,71)
WRITE(IOUT,502) FNl
WRITE(IOUT,502) FN2
C
850 WRITE(IOUT,71)
C GETREMAINDER OF STATISTICS ON ACCEPTABLE DATA
C RANGE, MEDIAN, COEFFICIENT OF VARIATION
CALL COLS5(X,N,XMED)
CALL COLS6(SD1,XBAR,COEFV)
CALL COLS7(X,RANGZ,N)
C CALCULATE CELL BOUNDARIES, FREQUENCIES AND MIDPOINTS
IF(NCELL) 113,112,113
112 NCELL = 15
113 DO 130 1=1,NCELL
130 NFREQ(I) = 0
IF(IZERO-l) 141,140,140
141 WIDTH = RANGE/(NCELL-1)
WIDTH = WIDTH + .00001
RIDPT = WIDTH/2
GROUP(1) = Z(l) + RIDPT
POINT (1) = Z(l)
GO TO 150
140 WIDTH = (Z(KLM)-0.)/(NCELL-0.5)
WIDTH = WIDTH + .00001
GROUP(1) = 0.0 + WIDTH
POINT(1) = GROUP(l)/2
150 DO 160 1=2,NCELL
160 GROUP(I) = GROUP(1-1) + WIDTH
DO 190 1=1,KLM
DO 170 M=l,NCELL
IF(Z(I) - GROUP(M)) 180,180,170
170 CONTINUE
180 NFREQ(M) = NFREQ (M) -I- 1
190 CONTINUE
DO 200 1=2,NCELL
200 POINT(I) = POINT(1-1) + WIDTH
C PRINT HEADING
WRITE(IOUT,30)
MAC=4
10
-------
CALL THEAD(AR1,AR2,AR3,AR41,AR42,AR43,AR44,AR5,BR1,BR2,DA,TY,
1 IOUT,MAC)
WRITE(IOUT,71)
C PRINT STATISTICS
WRITE(IOUT,40) N,RANGE,COEFZ
IF(IJKL-l) 910,911,919
919 IF(IJKL-S) 912,913,914
910 WRITE(IOUT,410) TV
GO TO 950
911 WRITE(IOUT,411) TV
GO TO 950
912 WRITE(IOUT,412) TV
GO TO 950
913 WRITE(IOUT,413) TV
GO TO 950
914 WRITE(IOUT,414) TV
GO TO 950
950 WRITE(IOUT,50) VRZ,SKEWZ
WRITE(IOUT,60) XBAR,SDZl,NCELL
WRITE(IOUT,62) ZAVE,SZ196
WRITE(IOUT,63) ZMED
WRITE(IOUT,65) ACCZ
WRITE(IOUT,71)
WRITE(IOUT,66)
WRITE(IOUT,71)
MAX = NFREQ(l)
DO 250 I = 2,NCELL
IF(MAX - NFREQ(I)) 245,250,250
245 MAX = NFREQ(I)
250 CONTINUE
LL = 0
LM = 35
LN = 70
LP = 105
DO 320 I=1,NCELL
LL = LL+1
LM = LM+1
LN = LN+1
LP - LP+1
K = NFREQ(I)
KKK = NFREQ(I)
IF(NFREQ(I)) 322,321,322
322 IF(NFREQ(I) - 15) 323,323,324
324 NFREQ(I) = 15
K = 15
323 DO 329 KIX=1,K
XIA(KIX)=EX
329 CONTINUE
C
CALL COL1(IJKL,X,W,LL,IOUT)
IF(N-LM) 326,1325,1325
1325 CALL COL2(IJKL,X,W,LM,IOUT)
IF(N-LN) 326,325,325
11
-------
325 CALL COLS(IJKL,X,W,LN,IOUT)
IF(N-LP) 326,927,927
927 CALL COL4(IJKL,X,W,LP,IOUT)
326 WRITE(IOUT,96) POINT(I),KKK,(XIA(KIX),KIX=1,K)
GO TO 320
321 CALL COL1(IJKL,X,W,LL,IOUT)
IF(N-LM) 328,1327,1327
1327 CALL COL2(IJKL,X,W,LM,IOUT)
IF(N-LN) 328,327,327
327 CALL COL3(IJKL,X,W,LN,IOUT)
IF(N-LP) 328,928,928
928 CALL COL4(IJKL,X,W,LP,IOUT)
328 WRITE(IOUT,96) POINT(I),KKK
320 CONTINUE
J=LL+1
DO 1120 I=J,35
K=I+35
L=I+70
M=H-105
IF(N-I) 1120,1121,1121
1121 CALL COL1(IJKL,X,W,I,IOUT)
IF(N-K) 1120,1123,1123
1123 CALL COL2(IJKL,X,W,K,IOUT)
IF(N-L) 1120,1126,1126
1126 CALL COL3(IJKL,X,W,L,IOUT)
IF(N-M) 1120,1129,1129
1129 CALL COL4(IJKL,X,W,M,IOUT)
1120 CONTINUE
WRITE(IOUT,30)
7993 CONTINUE
C FORMAT STATEMENTS
8 FORMAT(8A4,II)
15 FORMAT(Al)
17 FORMAT(F10.0)
18 FORMAT(314)
24 FORMAT(1H ,•INCORRECT SAMPLE SIZE TERMINATE JOB'////////)
30 FORMAT(1H1)
40 FORMATUH , 'N,ALL DATA' ,I3,8X, 'RANGE1 ,7X,F11.5,5X,
1'COEF. VAR. ' -1Y.F-M ,*\
.'COEF. VAR. f ,1X,F11.5)
FORMAT (1H-I-,21X, • VARIANCE1 ,4X,F11.5, 5X, 'SKEWNESS' ,3X,F11.5)
FORMAT(1H ,'MEAN,ALL1,F11.5,2X,'STD. DEV.',3X,F11.5,5X,
1'NO. OF CELLS',14)
62 FORMAT(1H ,'MEAN,RET.',F10.5,2X,'CONF. LIM.',2X,F11.5,IX,
I1(95 PCT)')
63 FORMAT(1H ,'MEDIAN1,2X,F11.5)
65 FORMAT(1H ,'ACCURACY',F11.5,2X,
I1PCT RELATIVE ERROR, RETAINED DATA1)
66 FORMAT(1H ,'ACCEPTABLE DATA IN ASCENDING ORDER',3X,
1'MIDPOINT',2X,IFREQ.',4X,'HISTOGRAM'/1H ,42X,
2'RETAINED DATA ONLY')
71 FORMAT(1H )
73 FORMAT(2A4)
96 FORMAT(1H+,35X,F10.4,2X,I4,4X,15A1)
12
-------
C NOTE: ALTER 'F1 SPECS ACCORDING TO EDITORIAL REQUIREMENTS
410 FORMAT(1H ,'TRUE VAL.',F8.0)
411 FORMAT(1H ,'TRUE VAL.',F8.1)
412 FORMAT(1H ,'TRUE VAL.',F8.2)
413 FORMAT(1H ,'TRUE VAL.',F8.3)
414 FORMAT(1H ,'TRUE VAL.',F8.4)
501 FORMAT(20A4)
502 FORMAT(1H r20A4)
901 FORMAT(2A1)
993 FORMATUH ,24X,'NUMBER OF SAMPLE'/lH ,23Xf
1'LAB/ANALYST RECOVERY1/1H ,38X,
2'BY LAB.1/)
7011 FORMAT(1H ,'UNACCEPTABLE DATA LIST'///)
7991 FORMAT(13,5X,F6.0)
7992 FORMAT(14)
8800 FORMAT(1H ,A1)
500 CALL EXIT
END
13
-------
SUBROUTINE THEAD
This subroutine provides for the print of the heading upon demand by
the main program. The input consists of a library of literal cards and
a date card to be used in forming the specific heading. The actual
format of the heading is controlled by an integer variable which
activates a computed go to statement.
INPUT REQUIREMENTS
Variable Purpose
AR1(I) Literal card
AR2(I) Literal card
DA,TY Date card
BR2(I) Literal card
AR3(I) Literal card
MAC Integer Variable assigned to select literal line
specific for the current text.
AR4KI) Literal card
AR42(I) Literal card
AR43(I) Literal card
AR44(I) Literal card
AR5(I) Literal card
BR2(I) Literal card
BR1(I) Literal card
SUBROUTINE THEAD(ARl,AR2,AR3,AR41,AR42,AR43,AR44,AR5,BR1,BR2,
1 DA,TY,IOUT,MAC)
DIMENSION AR1(20),AR2(20),AR3(20),AR5(20),BR1(20),BR2(20)
DIMENSION AR41(20),AR42(20),AR43(20),AR44(20)
WRITE(IOUT,502) ARl
WRITE(IOUT,502) AR2
WRITE(IOUT,72) DA,TY
WRITE(IOUT,502) BR2
WRITE(IOUT,502) AR3
GOTO (10,20,30,40),MAC
10 WRITE(IOUT,502) AR41
GO TO 50
20 WRITE(IOUT,502) AR42
GO TO 50
30 WRITE(IOUT,502) AR43
GO TO 50
40 WRITE(IOUT,502) AR44
50 WRITE(IOUT,502) AR5
WRITE(IOUT,502) BR2
WRITE(IOUT,502) BR2
502 FORMAT(1H ,20A4)
72 FORMAT(1H ,8OX,'EVALUATION DATE = ',2A4)
RETURN
END
14
-------
SUBROUTINE REALT
The purpose of this subroutine is to screen the raw data as punched.
The raw data may consist of censored data or blanks instead of data in
valid form for this analysis. The number of data cards may be unknown.
A card with numbers other than zero punched in card column 80 follows
the data deck. Testing of fields such as censor sign or the absence of
a decimal point is accomplished through character comparison. A valid
raw data vector is created by this subroutine. This raw data vector is
printed followed by count of input data and a count of output data.
Subroutine CONV2 is used to convert the validated raw data into a real
data vector, T.
INPUT REQUIREMENTS
Variable Purpose Format
ALAB(I) Numerical identification of laboratory 13
NNYL(I) Numerical identification of analyst Al
L(I) Data censor (Greater than or less than) Al
J(I) Integer portion of data element 14
M(I) Decimal point of data element Al
K(I) Decimal portion of data element 12
AN(I) Symbol: D = Different method Al
Blank = Official method of test
ST(I) Unused literal field A2
KOUNT(I) Field used for 'stop' card 12
OUTPUT REQUIREMENTS
Variable Purpose Format
AL(I) Numerical identification of laboratory 13
NN(I) Numerical identification of analyst Al
T(I) Element of the raw data vector F10.2
ANA(I) Method type, all blank A2
SUBROUTINE REALT(AL,NN,T,ANA,ANB,NR)
INTEGER AL(120),ALAB(120),AN(120),ANA(120)
DIMENSION NNYLU20) ,L(120) ,J(120) ,M(120) ,K(120) ,ST(120) ,
1 NN(120),JJ(120),KK(120),T(120),KOUNT(120),ANB(120)
C FOR TRACE METAL DATA ANALYSIS...UNKNOWN CARD COUNT.
C PLACE 9'S CARD AFTER EACH INDIVIDUAL DATA DECK.
IPUT=2
IOUT=5
C INPUT DATA
1=0
NR=0
19 1=1+1
NG=I-1
15
-------
READ(IPUT,1) ALAB(I) ,NNYL(I) ,L(I),J(I),M(I),K(I) ,AN(I) ,ST(I) ,
1 KOUNT(I)
IF(KOUNT(I)) 10,10,99
10 IF(L(I)-16448) 19,11,19
11 IF(M(I)-16448) 21,19,21
21 IF(AN(I)-16448) 19,20,19
20 NR=NR+1
AL(NR) = ALAB(I)
NN(NR) » NNYL(I)
JJ(NR) = J(I)
KK(NR) - K(I)
ANA(NR) = AN (I)
ANB(NR) - ST(I)
GO TO 19
C
99 WRITE(IOUT,71)
DO 40 1=1,NR
CALL CONV2(JJ,KK,T,NR)
WRITE(IOUT,31) AL(I),NN(I),T(I),ANA(I)
40 CONTINUE
WRITE(IOUT,32) NG,NR
C FORMAT STATEMENTS
1 FORMAT(I3,A1,1X,I4,A1,I2,A1,62X,A2,I2)
31 FORMAT(1H ,I3,A1,5X,F10.2,A1)
32 FORMAT(1HO,5X,'INPUT DATA COUNT - ',14,' WITH NULL VALUES'/1H ,
1 5X,'OUTPUT DATA COUNT = ',14,' CONSOLIDATED REAL DATA1///)
71 FORMAT(1H )
RETURN
END
16
-------
SUBROUTINE CONV2
The purpose of this subroutine is to convert a validated input number,
entered as an integer variable followed by a literal character (the
decimal point) and followed by a second integer number. The data were
entered by this format, I4,A1,I2, for the purpose of screening the
data. Censored data and missing data were removed from the gross input
data vector. This subroutine takes the two integers and converts these
to the decimal number.
INPUT REQUIREMENTS
Variable Purpose
J(I) Integer to the left of the decimal point
K(I) Integer to the right of the decimal point
OUTPUT REQUIREMENTS
Variable Purpose
T(I) Output valid data vector
N Number of data elements to be converted
SUBROUTINE CONV2(J,K,T,N)
DIMENSION J(120),K(120),T(120)
DO 10 1=1,N
A - J(I)
B= (FLOAT(K(I)))/100.
T(I) = A + B
10 CONTINUE
RETURN
END
17
-------
SUBROUTINE COLS1
This subroutine calculates the sample statistics on a set of data
points. Up to and including 120 data points may be accommodated.
The following computations are made:
Sample Mean = Sum/N where Sample Mean = mean of the data points
Sum = sum of the data points
N = number of data points
Total = sum of (A(I)-Sample Mean)**2
and
Sample Variance = Total/(N-l)
Sample Standard Deviation = Square root of the Sample Variance
INPUT REQUIREMENTS
Variable Purpose
A(I) Data element
N Number of data elements
OUTPUT REQUIREMENTS
Variable Purpose
XBAR Sample mean
SS Sample variance
S Sample standard deviation
SUBROUTINE COLS1(A,N,XBAR,SS,S)
DIMENSION A(120)
TOTAL =0.0
DO 10 1=1,N
TOTAL = TOTAL + A(I)
10 CONTINUE
AN = N
BN = N-l
XBAR = TOTAL/AN
T = 0.0
DO 20 1=1,N
T = T + (A(I)-XBAR)**2
20 CONTINUE
SS = T/BN
S = SQRT(SS)
RETURN
END
18
-------
SUBROUTINE COLT2
This subroutine performs the four sigma screening test. Data are
arbitrarily considered to be unacceptable if their difference from the
mean is greater than four standard deviations from the mean. The test
is performed on each data element. An unacceptable data list is
printed, the acceptable data vector is stored and returned to the main
program.
INPUT REQUIREMENTS
Variable Purpose
G(I) Raw data element
XBAR Mean on raw data
FSD Value of four standard deviations of raw data vector
M Number of raw data elements
KOR(I) Numerical identification of laboratory
KDER(I) Numerical identification of analyst
ANSA(I) Symbol: D = Different method
Blank = Official method of test
ANSB(I) Spare field, unused at this time
OUTPUT REQUIREMENTS
Variable Purpose
X(I) Data element, acceptable data vector
NA Number of acceptable data elements
IPUT Input device number
IOUT Output device number
KUR(I) Numerical identification of laboratory
KDUR(I) Numerical identification of analyst
ANA(I) Symbol: D = Different method
Blank = Official method of test
ANB(I) Spare field, unused at this time
SUBROUTINE COLT2(G,FSD,M,KOR,KDER,X,ANSA,ANSB,NA,IPUT,IOUT,KUR,
1 KDUR,ANA,ANB,XBAR)
INTEGER ANSA(120),ANA(120)
DIMENSION G(120),KOR(120),KDER(120),X(120),KUR(120),KDUR(120),
1 ANSB(120),ANB(120)
N=M
NA=0
DO 10 1=1,N
AMAA = ABS(G(I)-XBAR)
IF(AMAA-FSD) 20,20,30
30 WRITE(IOUT,2) KOR(I),KDER(I),G(I),ANSA(I)
GO TO 10
20 NA=NA+1
19
-------
X(NA) =
KUR(NA) = KOR(I)
KDUR(NA) = KDER(I)
ANA(NA) = ANSA(I)
ANB(NA) = ANSB(I)
10 CONTINUE
2 FORMATCLH , 13,3X, Al,F10.2 ,2X,A1)
RETURN
END
20
-------
SUBROUTINE COLS3
This subroutine calculates sample statistics and population statistics
on a set of data points. The population standard deviation is used in
the calculation of skewness. The following computations are made:
Mean = Sum/N where Mean = mean of the data points;
Sum = sum of data points; N = number of data points
Total = sum of (A(I)-Mean)**2
and
Sample variance = Total/(N-l)
Sample standardard deviation = Square root of the sample variance
Population variance = Total/N
Population standard deviation = Square root of the population
variance
INPUT REQUIREMENTS
Variable Purpose
A(I) Data element
N Number of data elements
OUTPUT REQUIREMENTS
Variable Purpose
XBAR Mean of data elements
VAR Population variance
VR Sample variance
SD Population standard deviation
SD1 Sample standard deviation
S196 Sample standard deviation X 1.96
SUBROUTINE COLS3(A,N,XBAR,VAR,VR,SD,SDlrSl96)
DIMENSION A(120)
TOTAL =0.0
DO 10 1=1,N
TOTAL = TOTAL + A(I)
10 CONTINUE
AN = N
BN = N-l
XBAR = TOTAL/AN
T - 0.0
DO 20 1=1,N
T = T + (A(I)-XBAR)**2
20 CONTINUE
VAR = T/AN
VR = T/BN
SD - SQRT(VAR)
SD1 = SQRT(VR)
S196 = SD1*1.96
RETURN
END
21
-------
SUBROUTINE COLS4
This subroutine calculates the coefficient of skewness which is a
measure of lack of symmetry of the data. The expression for this
coefficient is:
Skewness = Sum of ((A(I)-XBAR)**3/N)*SD**3
A(I) = data element
XBAR = Smple Mean of data elements
N = number of data elements
SD = population standard deviation
INPUT REQUIREMENTS
Variable Purpose
X(I) Data element
N Number of data elements
XBAR Sample Mean of data elements
SD Population standard deviation
OUTPUT REQUIREMENTS
Variable Purpose
SKEW Coefficient of skewness
SUBROUTINE COLS4(X,N,XBAR,SD,SKEW)
DIMENSION X(120)
SKW1 =0.0
DO 10 1=1,N
SKW1 = SKW1 + (X(I) - XBAR)**3
10 CONTINUE
SKW2 = N * SD**3
SKEW = SKW1/SKW2
RETURN
END
22
-------
SUBROUTINE COLS5
This subroutine calculates the median in a set of data. The median is
calculated by the following expression:
X = data element
Median = (X(J) + X(K))/2
J « (N+D/2
K = (N+2)/2
N = Number of data points
INPUT REQUIREMENTS
Variable Purpose
X(I) Data element
N Number of data elements
OUTPUT REQUIREMENTS
Variable Purpose
XMED Median of data elements
SUBROUTINE COLS5(X,N,MED)
DIMENSION X(120)
J = (N+D/2
K = (N+2)/2
XMED = (X(J) + X(K))/2.0
RETURN
END
23
-------
SUBROUTINE COLS6
This subroutine calculates the coefficient of variation of a set of
data elements. The expression for this calculation follows:
Coefficient of variation = Sample standard deviation/Mean
INPUT REQUIREMENTS
Variable Purpose
SD Sample standard deviation
XBAR Sample mean
OUTPUT REQUIREMENTS
Variable Purpose
COEFV Coefficient of variation
SUBROUTINE COLS6(SD,XBAR,COEFV)
COEFV = SD/XBAR
RETURN
END
24
-------
SUBROUTINE COLS7
This subroutine calculates the range of a set of data elements. The
range is the difference between the largest element and the smallest
element. The set of data elements have previously been sorted and
placed in ascending order.
INPUT REQUIREMENTS
Variable Purpose
X(I) Data element
N Number of data elements
OUTPUT REQUIREMENTS
Variable Purpose
RANGE Range
SUBROUTINE COLS7(X,RANGE,N)
DIMENSION X(120)
RANGE = X(N) - X(l)
RETURN
END
25
-------
SUBROUTINE COLS8
This subroutine calculates the accuracy of the mean of a set of data
elements. For the purpose of this method study, the accuracy is based
upon the known value or "true value" of the material sought in the
sample. The accuracy is expressed as percent of true value.
INPUT REQUIREMENTS
Variable Purpose
TV True value
XBAR Sample Mean of data set
OUTPUT REQUIREMENTS
Variable Purpose
ACC Accuracy
SUBROUTINE COLS8(TV,XBAR,ACC)
C
ACC = (XBAR - TV)/TV
ACC = ACC*100.0
C
RETURN
END
26
-------
SUBROUTINES COLl, COL2, COL3, COL4
These closely related subroutines provide for the printing of data
elements in columns 1, 2, 3 or 4 by subroutines COLl, COL2, COL3 or
COL4, respectively. The proper format for printing the data is
selected according to the value of the input variable, IJKL.
INPUT AND OUTPUT REQUIREMENTS
Variable Purpose
X(I) Data element
W(I) Symbol of t-test result: 'R1 = Rejected
1 ' - Retained
LL Data element counter
IJKL Integer equal to the number of digits to the right of
the decimal point
IOUT Output device number
790
791
792
793
794
1
2
3
4
5
50
790
791
792
793
794
SUBROUTINE COLl(IJKL,X,W,LL,IOUT)
DIMENSION X(120),W(120)
FORMAT(1H ,F8.0,A1)
FORMAT(1H ,F8.1,A1)
FORMAT(1H ,F8.2,A1)
FORMAT(1H ,F8.3,A1)
FORMAT(1H ,F8.4,A1)
MAA = IJKL+1
GO TO (1,2,3,4,5),MAA
WRITE(IOUT,790) X(LL),W(LL)
GO TO 50
WRITE(IOUT,791) X(LL),W(LL)
GO TO 50
WRITE(IOUT,792) X(LL),W(LL)
GO TO 50
WRITE(IOUT,793) X(LL),W(LL)
GO TO 50
WRITE(IOUT,794)
RETURN
END
X(LL),W(LL)
SUBROUTINE COL2(IJKL,X,W,LL,IOUT)
DIMENSION X(120),W(120)
FORMAT(1H+,11X,F8.0,A1)
FORMAT(1H+,11X,F8.1,A1)
FORMAT(1H+,11X,F8.2,Al)
FORMAT(1H+,11X,F8.3,A1)
FORMAT(1H+,11X,F8.4,A1)
MAA = IJKL+1
GO TO (1,2,3,4,5),MAA
WRITE(IOUT,790) X(LL),W(LL)
GO TO 50
27
-------
2
3
4
5
50
790
791
792
793
794
1
2
3
4
5
50
790
791
792
793
794
1
2
3
4
5
50
WRITE(IOUT,791) X(LL),W(LL)
GO TO 50
WRITE(IOUT,792) X(LL),W(LL)
GO TO 50
WRITE(IOUT,793) X(LL),W(LL)
GO TO 50
WRITE(IOUT,794) X(LL),W(LL)
RETURN
END
SUBROUTINE COL3(IJKL,X,W,LL,IOUT)
DIMENSION X(120),W(120)
FORMAT(1H+,21X,F8.0,A1)
FORMAT(1H+,21X,F8.:
FORMAT(1H+,21X,F8.:
FORMAT(1H+,2IX,F8.:
FORMAT(1H+,2IX,F8.-
MAA = IJKL+1
GO TO (1,2,3,4,5),MAA
WRITE(IOUT,790) X(LL),W(LL)
GO TO 50
WRITE(IOUT,791)
GO TO 50
WRITE(IOUT,792)
GO TO 50
WRITE(IOUT,793)
GO TO 50
WRITE(IOUT,794)
RETURN
END
X(LL),W(LL)
X(LL),W(LL)
X(LL),W(LL)
X(LL),W(LL)
SUBROUTINE COL4(IJKL,X,W,LL,IOUT)
DIMENSION X(120),W(120)
FORMAT(1H+,31X,F8.0,A1)
FORMAT(1H+,31X,F8.1,A1)
FORMAT(1H+,31X,F8.2,A1)
FORMAT(1H+,31X,F8.3,Al)
FORMAT(1H+,31X,F8.4,A1)
MAA = IJKL+1
GO TO (1,2,3,4,5),MAA
WRITE(IOUT,790) X(LL),W(LL)
GO TO 50
WRITE(IOUT791) X(LL),W(LL)
GO TO 50
WRITE(IOUT,792) X(LL),W(LL)
GO TO 50
WRITE(IOUT,793) X(LL),W(LL)
GO TO 50
WRITE(IOUT,794) X(LL),W(LL)
RETURN
END
28
-------
SUBROUTINE DLIST
This subroutine prints a data list in accordance with the number of
digits to the right of the decimal point. The following range of
decimals are allowed: xx., xx.x, x.xx, x.xxx, and x.xxxx.
INPUT REQUIREMENTS
Variable Purpose
IJKL Integer representing number of digits to the right of
the decimal point
I Count of data element in the vector
IOUT Output device number
OUTPUT REQUIREMENTS
Variable Purpose Format
KUR(I) Laboratory identification number 13
KDUR(I) Analyst identification number Al
XH(I) Unsorted vector data element F7.2
V(I) Symbol of t-test results: "R" = Rejected Al
" " = Retained
ANA(I) Method used: "D" = Different method Al
" " = Official method
ANB(I) Spare field, unused at this time A2
SUBROUTINE DLIST(IJKL,KUR,KDUR,XH,V,ANA,ANBfI,IOUT)
INTEGER ANA(120)
DIMENSION KUR(120),KDUR(120),XH(120),V(120),ANB(120)
430 FORMATUH ,23X, I3,4X,Al, 8X,F7. 0, IX, Al,Al,A2)
431 FORMAT(1H ,23X,13,4X,Al,8X,F7.1,IX,Al,Al,A2)
432 FORMATdH ,23X, 13, 4X, Al, 8X,F7.2 , IX, Al, Al,A2)
433 FORMATdH ,23X, I3,4X,Al,8X,F7. 3 ,1X,A1,A1,A2)
434 FORMATdH , 23X, 13 ,4X, Al, 8X,F7. 4 , IX, Alf Al,A2)
MAA = IJKL+1
GO TO (1,2,3,4,5),HAA
1 WRITE(IOUT,430) KUR(I),KDUR(I),XH(I),V(I),ANA(I),ANB(I)
GO TO 50
2 WRITE(IOUT,431) KUR(I),KDUR(I),XH(I),V(I),ANA(I),ANB(I)
GO TO 50
3 WRITE(IOUT,432) KUR(I),KDUR(I),XH(I),V(I),ANA(I),ANB(I)
GO TO 50
4 WRITE(IOUT,433) KUR(I),KDUR(I),XH(I),V(I),ANA(I),ANB(I)
GO TO 50
5 WRITE (IOUT,434) KUR(I) ,KDUR(I) ,XH (I) , V(I) , ANA(I) ,ANB (I)
50 RETURN
END
29
-------
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO. 2.
EPA-670/4-7S-004a
I. TITLE AND SUBTITLE
FORTRAN PROGRAMS FOR ANALYZING COLLABORATIVE
TEST DATA
PART I: GENERAL STATISTICS
'. AUTHOR(S)
Elmo C. Julian
. PERFORMING ORGANIZATION NAME AND ADDRESS
National Environmental Research Center
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, Ohio 45268
2. SPONSORING AGENCY NAME AND ADDRESS
Same as above
3 RECIPIENT'S XCCESSI ON-NO.
5. REPORT DATE
April 1975; Issuing Date
6. PERFORMING ORGANIZATION CODE
8. PERFORMING ORGANIZATION REPORT NO.
10. PROGRAM ELEMENT NO. ]_^A327
ROAP 24AEL; Task 006
11. CONTRACT/GRANT NO.
13. TYPE OF REPORT AND PERIOD COVERED
14. SPONSORING AGENCY CODE
5. SUPPLEMENTARY NOTES
See Part II, EPA-670/4-75-004b
6. ABSTRACT
A FORTRAN program for IBM 1130 is described by which general statistics on inter-
laboratory studies of chemical analytical methods may be obtained. Data screening
followed by a statistical t-test for identifying outliers is included. A
histogram of data in ascending order is provided.
'. KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
FORTRAN, Data, Statistics
i. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
b.lDENTIFIERS/OPEN ENDED TERMS
Programs, Collaborative
test
19. SECURITY CLASS (This Report)
UNCLASSIFIED
20. SECURITY CLASS (This page)
UNCLASSIFIED
c. COS AT I Field/Group
9B
21. NO. OF PAGES
47
22. PRICE
A Form 2220-1 (9-73)
39
S GOVERNMENT PRINTING OFFICE: 1975-657-592/53A9 Region No. 5-11
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