Aug 18, 1983 - Retrieving data from the WATSTORE daily values and water quality files. .... This report describes procedures in the Statistical Analysis System ...
NONPARAMETRIC TESTS FOR TRENDS IN WATER-QUALITY DATA USING THE STATISTICAL ANALYSIS SYSTEM by Charles G. Crawford, James R. Slack, and Robert M. Hirsch
U.S. GEOLOGICAL SURVEY Open-File Report 83-550
1983
U.S. DEPARTMENT OF THE INTERIOR JAMES G. WATT, Secretary GEOLOGICAL SURVEY Dallas L. Peck, Director
For additional information write to: Chief Hydrologist U.S. Geological Survey, WRD 410 National Center Restion, Virginia 22092
Copies of this report can be purchased from: Open-File Services Section Western Distribution Branch U.S. Geological Survey Box 25425, Federal Center Lakewood, Colorado 80225 (Telephone: [303] 234-5888)
TABLE OF CONTENTS
Page Abstract..................................................................
1
Introduction..............................................................
1
Retrieving data from the WATSTORE daily values and water quality files....
2
Determining the relationship between water-quality constituents and streamf1ow..............................................................
10
Plotting water-quality data as a time series..............................
44
Statistical procedures to test for trends in water-quality time series....
49
Appendix A.
PROC SEASKEN user's guide with examples......................
56
Appendix B.
PROC SEASRS user's guide with examples.......................
69
Appendix C.
Source code for SAS procedures...............................
82
References................................................................ 101 ILLUSTRATIONS
Figure 1. Example input for WATSTORE retrieval of water-quality data by the QWRETR and QWSAS procedures.................................... 4 2.--Example input for WATSTORE retrieval of streamflow data by the DVRETR and DVINPUT procedures..................................
6
3.--Example input and output of a SAS procedure to do flow adjustment regressions-abbreviated version...........................
14-21
4.--Example input and output of a SAS procedure to do flow adjustment regressions-extended version..............................
23-42
5.--Example input and output of SAS statements t plot water-quality data and regression residuals as time series................... 45-48 6. Example input and output of SAS statements to do the Seasonal Kendall test and slope estimator procedure on a water-quality data time series...............................................
51-52
7.--Example input and output of SAS statements to do the Seasonal Mann-Whitney-Wilcoxon rank sum test and slope estimator procedure on a water-quality data time series.....................
54-55
m
CONTENTS (continued) Figure Al.--Example input and output using PROC SEASKEN to test for a trend in annual mean streamflow.............................
63-64
A2.--Example input and output using PROC SEASKEN to test for trends in water-quality constituents..........................
65-68
Bl.--Example input and output using PROC SEASRS to test for a step in annual mean streamflow................................
76-77
B2.--Example input and output using PROC SEASRS to test for step trends in water-quality constituents..........................
78-81
Cl.--Parsing module for the Seasonal Kendall test and slope estimator procedure...........................................
83
C2.--Procedure module for the Seasonal Kendall test and slope estimator procedure...........................................
84-90
C3.--Parsing modeule for the Seasonal Mann-Whitney-Wilcoxon rank sum test and slope estimator procedure........................
91
C4.--Procedure module for the Seasonal Mann-Whitney-Wilcoxon rank sum test and slope estimator procedure........................ 92-100
iv
TESTING FOR TRENDS IN WATER-QUALITY DATA USING THE STATISTICAL ANALYSIS SYSTEM By Charles G. Crawford, James R. Slack, and Robert M. Hirsch ABSTRACT
Two nonparametric procedures to test for trends in water-quality data (SEASKEN AND SEASRS) have been developed for the Statistical Analysis System* (SAS).
The procedure SEASKEN tests for a monotonic trend in time by a modified
form of Kendall's tau, the Seasonal Kendall test.
The procedure SEASRS tests
for a step trend between two different periods in a time series using a modified form of the Wilcoxon (Mann-Whitney) rank sum test, the Mann-WhitneyWilcoxon rank sum test for seasonal data. two procedures.
Examples are presented using the
The source code and user's guide for each of the two procedures
are also presented. Procedures for flow adjusting water-quality data by the SAS procedures REG and SYSREG and techniques for plotting water-quality data as a time series by the SAS procedure PLOT are presented. Additionally, examples are presented to demonstrate the use of the U.S. Geological Survey procedures QWRETR, DVRETR, QWSAS, and DVINPUT to retrieve data from the Geological Survey WATSTORE system and make it available to SAS. INTRODUCTION
Increased public concern over the quality of the Nation's rivers in the past several decades has led Federal, State, and local officials to implement or greatly expand existing water-quality monitoring programs.
Examples of
such programs are the Geological Survey's Benchmark and NASQAN networks (see Briggs, 1978).
Most of these monitoring programs have as a goal the
detection of trends in water quality. * Use of brand and firm trade names in this report is for identification purposes only and does not constitute endorsement by the U.S. Geological Survey.
Techniques of trend detection in water-quality data have correspondingly received much attention recently in the literature (see, for example, Fuller and Tsokos, 1971; Lettenmaier, 1976; and Hirsch and others, 1982).
Most of
the trend detection methods presented to date are based on classical (parametric) hypothesis testing.
However, because of the nature of water-quality
data (typically skewed, serially correlated, and showing seasonality), many of the assumptions underlying classical hypothesis tests are not met, rendering them inappropriate.
(For a discussion of the problems associated with these
tests, the reader is referred to Smith and others, 1982.)
Recently, however,
thinking has begun to shift toward distribution-free (nonparametric) tests that have less restrictive assumptions than their classical counterparts and are therefore less sensitive to the distribution of the water-quality time series. This report describes procedures in the Statistical Analysis System (SAS) that can appropriately be used to detect trends in water-quality data.
The
report describes the use of both the standard procedures provided with SAS and two additional procedures, SEASKEN and SEASRS. the reader is assumed. U.S.
A working knowledge of SAS by
The report was written primarily for user's of the
Geological Survey's WATSTORE data base and Amdahl computer system; however,
the source code for the SAS macros and procedures are included in the appendices. The user's guide for the SEASKEN and SEASRS procedures are also included in the appendices. RETRIEVING DATA FROM THE WATSTORE DAILY VALUES AND WATER QUALITY FILES
In order to use SAS on water-quality data, it is first necessary to get the data into a SAS data set.
A SAS data set is a collection of data observations
addressable by SAS procedures. ciated with it.
Each observation has one or more variables asso-
For more information about SAS data sets, see SAS Institute, Inc. 2
(1979) or SAS Institute, Inc. (1982a).
Data can be entered into a SAS data set
from data cards in the job stream or by reading data stored on disk or tape files.
When using data from the WATSTORE file, one of the standard Survey
retrieval procedures must first be used.
One of two Survey applications programs
(PROC QWSAS or the DVINPUT macro) is then called to convert the standard retrieval output into a SAS data set.
PROC QWSAS is a SAS procedure that produces a SAS
data set from the standard water quality file retrieval procedure QWRETR. PROC QWSAS is described in detail in the WATSTORE user's guide, volume 3, chapter IV, section R.
DVINPUT is a SAS macro that converts output from the
WATSTORE daily values file retrieval, DVRETR, to a SAS 4 ata set.
Use of the
DVINPUT macro is described in the WATSTORE message SAS documentation section (member WRD06).
The standard retrieval procedures, DVRETR and QWRETR, are
discussed in the WATSTORE user's guide, volumes 1 and 3, respectively. Figure 1 shows example input using the QWRETR and QWSAS procedures.
This
example retrieves twelve parameters - two streamflow parameters (00060 & 00061) and ten water-quality constituents - for three stations from the water quality file.
Both daily mean streamflow (parameter code 00060) and instantaneous stream-
flow (00061) should be retrieved.
For purposes of this test, the mean streamflow
may be used if the instantaneous streamflow is missing.
PROC QWSAS creates a
SAS data set named DATA1 containing the station identification number and the eleven parameters requested in the QWRETR procedure.
The parameter values are
stored in variables named Pnnnnn where nnnnn is the WATSTORE parameter codes given in the retrieval list.
In addition, the variables YEAR, MONTH, DAY, DATE,
DECTIME, and SNAME were requested in the QWSAS statement.
The variable DATE is
the day on which the sample was collected, in days since January 1, 1960. DECTIME is a decimal number representing the time the sample was collected, in
25 26
Figure 1. Example input for WATSTORE retrieval of water-quality data by the QWRETR and QWSAS procedures.
/* //
DATA;SET;IF P00061=. THEN pooo6i=P0006o;oROp P00060; PROC PRINT;BY STATION; VAR YEAR MONTH DAY DECTIME DATE P00061 P00410 P00630 P00665 P00915 P00925 P009 30 P00940 P00945 P00950 P70300; DATA TREND.MONTHLY;SET;
PROC SORT;aY STATION YEAR MONTH DAY;
20
19 21 22 23 24
//F1 JOB // CLASS /*SETUP 118545/H //PROCLIB 00 DSNsWRD.PROCLIB/DISP=SHR // EXEC QWRETR/VOL1=118545 //HDR.SYSIN 00 * M3 1968100119810930 XQWSASX R000600006100410006300066500915009250093000940009450095070300 0000600006100410006300066500915009250093000940009450095070300 0 03276500 0 03374100 0 03378500 /* // EXEC WROSAS //TREND DO DSN = USERI 0.FILENAME/DISP = OLD //SYSIN DO * PROC Qh/SAS YEAR MONTH DAY DATE DECTIME SNAME;
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
years.
These two forms of sample collection time are useful in plotting the
data as time series.
Additionally, the variable DATE may be formatted in
several different ways (see SAS Institute, Inc., 1982a, p. 409).
SNAME is the
variable containing the station name. The variable DECTIME is required to use the SAS procedures SEASKEN and SEASRS.
For data sets that do not already include the variable DECTIME, it
can be easily generated using the following statement in a SAS data step: DECTIME = YEAR(DT)+(JULDATE(DT)-YEAR(DT)*1000)/365;,
(1)
where DT is the date the observation was made. An example use of this is shown in figure 2. The example in figure 1 also sorts and prints the information retrieved by station.
Finally, the data is stored as file TREND.MONTHLY in the data set
USERID.FILENAME on a direct access device for later analysis.
Line 16 describes
the existing file to be used for data storage, and line 24 copies the data to the disk file.
For information on creating disk data sets on the USGS Amdahl
computer system, see the USGS Computer Users Manual, Chapter 5. To adapt this example input to a specific application, the user will need to (1) substitute the six digit volume number of the appropriate water quality back file tape for 118545 in lines 3 and 5; (2) substitute the appropriate retrieval dates on the master control card on line 7; (3) change the retrieval and output list as desired on lines 9 and 10; (4) substitute the desired station numbers in lines 11 through 13 (and delete or add D cards as required); (5) substitute an appropriate data set name in the DSN = field on line 16; and (6) change the variables list in lines 22 and 23 to agree with the parameters listed in the retrieval list and PROC QWSAS optional variables.
// EXEC WRDSAS,MACRO=DV*DSNs'&&8KREC',DSNl=NULLFILE,DSN2=NULLFILE //TREND DD DSN=USERID.FILENAME*DISP=OLD //SYSIN DD * DVINPUT _SNAME DATA DATAA|T| for parameters in the model.
The R-square and Prob >|T| for the
function of Q in the model correspond to the R 2 and p value in the Smith and others (1982) flow-adjustment procedure.
Plots of streamflow versus sulfate,
in both arithmetic and log form, are shown in figure 3. Figure 4 shows a listing and output of a sample SAS job that does the flow-adjustment procedure using the macro REGMAC (line 44).
In addition to
providing R 2 and p for each model, the program provides several diagnostic
22
^ 00
LNDEPVAR=LOG(DEPVAR); *GET LOG OF THE FLOW;
L00061=LOG(P00061>; *3ETA = THE INTEGER PORTION OF THE BASE 10 LOG OF THE MEAN FLOW/' BETA=INT(LOb10(M00061)); *dN=DIFFERENT VALUES USED IN THE HYPERBOLIC FUNCTIONS; Bl=10**; HYPERB2U = 1/ (1+b2*P00061); HYPERB3Q=1/(1+d3*P00061); HYPERtJ4Q = 1 / (1+84*P00061 ); HYPERB5Q=1/(1+d5*P00061); HYPERB6Q=1/(1+B6*P00061); HYPERd7Q=1/(1+67*P00061>; HYPERU8U=1/(1+38*P00061); *INVQ= THE INVERSE OF THE FLOW;
INVQ=1/P00061;
*U2=SQUARE OF Q2=P00061**2;
*LQ2=SQUAR6 OF THE LOG OF THE FLOW; LQ2=L00061**2; PROC SORT 0 AT A = I NPDAT A; 3Y STATION/' % MACRO REGMAC OPTIONS NOMACROGEN NOOVP/* PROC REG 0ATA = INPDAT A;BY STATION; ID P00061; TITLE OUTPUT FROM MODLABEL: Y = FLOW/' MOOLAbEL:MODEL Y = FLOW / R;
16 17 18 19 20 21 22 23 24 25
26 27 28 29 30 31 32 33 34 35 3b 37
38
39 40
41 42 43 44 45 4b 47 48 49 50
FLOW;
Figure 4.--Example input and output of a SAS procedure to do flow adjustment regressions extended version.
THE
*GET LOG OF DEPENDENT VARIABLE;
14 15
13
OPTIONS NOMACROGEN;
PROC MEANS DAT A=F ILENAME NOPRINT MEAN/'BY STATION/'VAR P00061/' OUTPUT OUT=MEANQ MEAN=M00061; PROC SORT DATA=MEANU;BY STATION; DATA INPDATA;MERGE MEANQ FILENAME^Y STATION;
9 10 11 12
MACRO REGDATA
//F4 JOB // CLASS> //PROCLIB DD DSN=WRD.PROCLIB*DISP=SHR //A EXfcC WKDSAS,DSN1=NULLFILE*DSN2=NULLFILE //TREND DD DSN=USERID.FILENAME,DISP=OLD //SYSIN DD *
8
7
1 2 3 4 5 6
62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79
MACRO FILENAME DATAAX MACRO OEPVAR P00945/. MACRO LNDEPVAR L00945X REGDATA MACRO MOOLABEL LINEARX MACRO Y DEPv/AR/. MACRO FLOW P00061X REGMAC MACRO MODLAdEL LOGLINX MACRO Y DEPVARX MACRO FLOW L00061X REGMAC MACRO MOOLABEL LOGLOGX MACRO Y LNOEPVARX MACRO FLOW L00061X REGMAC /* //
;
KEEP STATION SNAME P00945 P00061/* PROC soRTr-av STATION;
60 61
IF STATIONS' 03374100
DATA DATAA;SET TRENO.MONTHLY;
5a
59
OJTPUT UUT = REGOAT1 P = P R=R STODENT = SR COOKO = COOKD/* PROC SORT D A ' A = R EGDA T 1 /'BY STATION/* PROC PLOT i)ATA=-REGOAT1 /'BY STATION/* PLOT P*LOOU61='P' Y*L00061='0' / OVERLAY/* PLOT R*P / \/REF = 0/* PROC UNIVARIATE OATA = REGOAT1 PLOT NORMAL/'VAR R/* X
51 52 53 54 55 56 57
Ul
ID
12799.97 55899.89 28399.94 9299 .98 15299.97 31399.93 5989.99 3029.99 2250.00 2600.00 6360.00 14799.96 22500.00 33599.93 37000.00 14100.00 11700.00 4740.00 7979.98 11300.00 14299.96 23199.95 20299.95 3B999.92 18099.96 45299.91 14899.97 9709. 9B 6549.99 9PO.OO
08S
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 1
INTERCEP P00061
5P.OOO 46.000 49.000 59.000 45.000 17.000 53.000 68.000 67.000 73.000 58.000 57.000 61.000 42.000 44.000 4 P. 000 59.000 61.000 . 41 .000 45.000 45.000 48.000 35.000 50.000 36.000 64.000 53.000 56.000 60.000
ACTUAL
60.288824 -0.0005675
53.025 28.566 44.172 55.011 51.606 42.469 56.890 58.569 59.012 58.813 56.680 51.890 47.520 41.221 39.291 52.287 53.649 57.599 55.760 53.876 52.174 47.123 48.769 3P.156 50.017 34.581 51.833 54.778 56.572 59.733
PREDICT VALUE
0 .0001 0 .0001
42.49? -B.453
4.975 1.037 17.434 2.962 .388 4.R2B .068 3. 989 .031 -6.606 -25.469 .531 .179 -3.890 9.431 .267 7.988 .319 14.187 .305 .167 1.320 .030 5.110 13.4BO .161 .643 0.779120 4.709 .826 -4.287 .030 .047 5.351 .222 3.401 .120 . -12.876 .053 -7.174 .030 -2.123 .1P3 .100 -.768611 .939 -3.156 .05fl -.017103 3.4 1*> .3Gfl .030 12.167 -1.778 .ono .161 -.571709 .374 0.?67??5
10.144 9.757 10.102 10.139 10.145 10.0R1 10.129 10.115 10.111 10.113 10.130 10.145 10.131 10.064 19.032 10.145 10.143 10.123 . 10.142 10.145 10.128 10.137 10.011 10.142 9.932 10.145 10.140 10.131 10.104
VARIABLE LABEL
0.490 1.787 0.478 0.393 -0.651 -2.526 -0.3R4 0.932 0.790 1.403 0.130 0.504 1.331 0.077 0.469 -0.423 0.528 0.336 . -1.270 -0.707 -0.210 -0.076 -0.315 -0.002 0.344 1.199 -0.175 -0.056 0.026
** *
*****! 1 1* 1* 1** 1 1* 1**
1 |*** 1 1 *|
**
*
16:06 THURSDAY, AUGUST
0 .001 0 .147 0 .002 0 .001 0 .002 0 .074 0 .001 0 .007 0 .005 0 .016 0 .000 0 .001 0 .012 0 .000 0 .004 0 .001 0 .001 0 .001 . 0 .009 0 .003 0 .000 0 .000 0 .002 0 .000 0 .003 0 .007 0 .000 0 .000 0 .000
COOK»S D
INSTANTANEOUS (CFSI
-2-1-0 1 2
INTERCEPT STREAMFLOH,
STD ERR STP FPR STUDENT PREDICT RESIDUAL RESIDUAL RESIDUAL
1.418811 .00006713385
STANDARD ERROR
PARAMETER ESTIMATE
DF
VARIABLE
PROB > |T|
0.4267 0.4207
R-SQUARF ADJ R-SO
10.196942 52.040815 19.59412
ROOT MSE DEP MEAN C.V.
0 .0001
PROB>F
T FOR HOS PARAMETER-0
71.459
7429. 9P3 1D3.978
7429.983 9981.852 17411.835
MODEL ERROR C TOTAL
1 96 97
DF
SOURCE F VALUE
(MG/L AS
MFAN SQUARE
SULFATE DISSOLVED
SUM OF SQUARES
MODEL: LINEAR OEP VARIABLE: P00945
OUTPUT FROM LINEAR: P00945- P000f> 1 STATION IDENTIFICATION NUMBER-03374100 18, 1983
CTl
ID
23?0.00 1860.00 2930.00 8379.^8 11099.97 46600.00 46599.91 12699.97 3759.99 4899.99 3709.99 4099.99 1040.00 2790.00 19PO.OO 514.00 574.00 25000.00 31200.00 8090.00 3100.00 3099.99 3440.00 16PO.OO 1810.00 9860.00 2840.00 33800.00 10700.00 5620.00 9220.00 19000.00 17000.00 7320.00 8290.00 11000.00 3770.00 3180.00 31600.00 32200.00 8600.00 76000.00 30400.00 13700.00 9350.00 6R20.00 6000.00 68400.00 41100.00 7410.00 10200.00 54900.00 5440.00
DBS
31 3? 33 3* 35 36 37 38 39 40 41 42 43 44 45 46 47 46 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83
65.000 56.000 56.000 42.000 66.000 37.000 54.000 64.000 63.000 51.000 57.000 63.000 69.000 33.000 35.000 62.000 . 36.000 54.000 30.000 41.000 50.000 50.000 45.000 49.000 26.000 34.000 45.000 42.000 31.000 40.000
53.000 65.000 50.000 46.000 60.000 63.000 70.000 82.000 BP.OOO 83.000 35.000 3P.OOO 50.000 56.000
65.000 77.000 66.000 60.000 51.000 33.000
ACTUAL
58.972 *9.233 5P.626 55.533 53.990 33.843 33.843 53.082 58.155 57.508 5P.1B3 57.962 59.699 5R.706 59.165 59.997 59.963 46.101 42.583 55.698 58.530 5R.530 5P.337 59.335 59.262 54.693 5P.677 41.107 54.217 57.099 55.056 49.506 50.641 56.135 55.590 54.046 58.149 5P.484 42.356 42.015 55.408 17.159 43.037 52.514 54.983 50.15
9B 1.016F-1? 10?. 906 0.660651 9981.85 1.0247? 1 C.P06838
-0 4443333333322222211110000
0 55555556667777778899 0 1112223333444
1 1223334
LEAF B 33 578
PROB>D
STD MEAN PPOn>|T| PRPBXSI
ess
SUM WGTS SUM VARIANCE KURTOSIS
RESIDUALS
MOMENTS
9P 1.037E-14 10. 1*4? -0.130921 9981.85 9.7P4E+16 1.012E-14 69.5 9P 0.0652879
STEM 2 2 1
TSMEAN'O SCN RANK NUM t* 0 DtNORMAL
cv
MEAN STD DEV SKFHNESS U5S
M
VARIABLES
I
BOXPLOT 0 I I I
I
54.99 11.5392 -26.9872
5 4.85
27.5**
27.5+
MISSING VALUE COUNT X COUNT/MOBS
RANGE 03-01 MODE
-26.9872
MAX 28.0029 03 6.34615 MED -0.149089 -5.19306 01
0* MIN
100JC 75* 50? 25*
LOWEST -26.9872 -25.4694 -23.1493 -21.5194 -21.0463
NORMAL PROBABILITY PLOT
28.0029 17.4509 12.B9R -12.7116 -21.07 -26.9872
-2
* -1
«0
«1
*2
* *
EXTREMES
HIGHFST 17.4343 17. 7*67 22.B34B 23.0369 28.0029
16:06 THURSDAY, AUGUST IB, 19P3
4****** ******* 4***** ******* ****** *****4 ***** * ***
5* 1*
99* 95* 90* 10*
OUAMTILES(nEF«4)
UNIVARIATE
OUTPUT FROM LINEAR: poo?45* POOOSI
7.495376 0.821471
136.455 -9.317384
ID
12799.97 55899.89 28399.94 9299 .9B 15299.97 31399.93 59P9.99 3029.99 2250.00 2600.00 6360.00 14799.96 22500.00 33599.93 37000.00 14100.00 11700.00 4740.00 7979.98 11300.00 14299.96 23199.95 20299.95 38999.92 18099.96 45299.91 14899.97 9 709 .98 6549.99 980.00
DBS
1 2 3 * 5 6 7 B 9 10 11 12 13 14 15 16 17 IB 19 20 21 22 23 24 25 26 27 28 29 30
1 1
1NTERCFP 1 00061 ,
5P.OOO 46.000 49.000 59.000 45.000 17.000 53.000 68 .000 67.000 73.000 58.000 57.000 61.000 42.000 44.000 4 P. 000 59.000 61.000 . 41.000 45.000 45.000 48.000 35.000 50.000 38.000 64.000 53.000 56.000 60.000
48.339 34.604 40.913 51.315 46.677 39.978 55.414 *1.764 64.537 63.190 54.856 46.986 43.083 39.347 38.449 47.438 49.176 57.595 52.741 49.500 47.306 42.798 44.042 37.958 45.111 36.563 46.923 50.913 54.581 72.281
18.205 -11.342
T FOR HO: PARAHETER«0
0.5727 0.5682
128. 64B
F VALUE
(MG/L AS SO*)
0.0001 0.0001
PROB > |Tl
0.0001
PROB>F
0.947318 9.661 1.776 11.396 8. 086 1.324 7. 685 0.891618 -1.677 1.007 -22.978 1.3B6 -2.414 0.937731 1.235 6.236 1.416 2.463 9.810 1.326 3.144 0.923297 10.014 0.994729 17.917 1.189 1.429 2.653 5.551 1.492 0.977546 C. 562374 9.824 0.9244BP 3.405 1.015 . 0.891462 -8.500 0.917094 -2.306 D.9P2405 .206 2.202 3.958 .135 -2.95R .527 4.889 .079 1.437 .629 17.077 0.997220 2.087 D. 8«?4859 1.419 0.917093 -i?.?ni 1.994
B.753 B.623 B.704 B.759 B.746 9. 6*4 B.754 B.717 S.699 B.703 8.755 9.747 8.723 8.697 B.676 B.749 9.755 8.745 . 8.7*6 B.7«9 8.721 B.730 8.670 B.737 S.652 9.747 9.7«* 8.7*6 9.575
VARIABLE LAB^L
1.104 1.322 0.929 0.877 -0.192 -2.643 -0.276 0.715 0.283 1.127 0.359 1.145 2.054 0.305 0.640 0.064 1.122 0.3B9 . -0.971 -0.264 0.253 0.453 -0.341 0.560 0.166 1.952 0.238 0.162 -1.432
2
*l 1 1 1 1 1* 1 |*** 1 1 *+|
+++*+! 1 1* 1 1** 1 1** 1**** 1 1* 1 1** 1
1** 1** 1* 1* 1
-2-1-0 1
INTERCEPT
STD ERR STD ERR STUDENT PRFDICT RFSIDUAL RESIDUAL RESIDUAL
STANDARD ERROR
PARAHFTFR ESTIMATE
OF
VARIABLE
PREDICT VALUE
R-SQUAFF ADJ R-SO
8. 803812 52.040815 16.91713
ROOT MSE OEP MEAN C.V.
ACTUAL
9971 .154 77.507101
9971.154 7440.682 17411.835
MPDEL FRROR C TOTAL
1 96 97
OF
SCURCE
ME />N SOUAPE
SULFATE DISSDIVED
SUM OF SQUARES
MODEL: LOGLIN Dfp VARIABLE: P00945
IDENTIFICATION NUHBFR=03374100
OUTPUT FROM LOGLIN: poo94*= STATION
0.007 0.037 0.010 0.004 0.000 O.OB9 0.000 0.005 0.001 0.015 0.001 O.ODB 0.039 0.001 0.006 0.000 0.007 0.001 . 0.005 0.000 0.001 0.002 0.002 0.002 0.000 0.0?5 0.000 0.000 0.055
COOK'S 0
16:06 THURSDAY, AUGUST
IB, 1983
ID
2320.00 1860.00 2930.00 8379 .9B 11099.97 46600.00 46599.91 12699.07 3759.99 4899.99 3709.99 4099.99 1040.00 2790.00 1960.00 514.00 574.00 25000.00 31200.00 8090.00 3100.00 3099.99 3440.00 16BO.OO 1810.00 9860.00 2840.00 33000.00 10700.00 5620.00 9220.00 19000.00 17000.00 7320.00 8280.00 11000.00 3770.00 3180.00 31600.00 32200.00 8600.00 76000.00 30400.00 13700.00 9350.00 6820.00 6000.00 68400.00 41100.00 7410.00 10200.00 54900.00 5440.00
DBS
31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 5B 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83
65.000 77.000 66.000 60.000 51.000 33.000 . 53.000 65.000 50.000 46.000 60.000 63.000 70.000 B2.000 86.000 83.000 35.000 38.000 50.000 56.000 » 65.000 56.000 56.000 42.000 66.000 37.000 54.000 64.000 63.000 51.000 57.000 63.000 69.000 33.000 35.000 62.000 . 36.000 54.000 30.000 41.000 50.000 50.000 45.000 49.000 26.000 34.000 45.000 42.000 31 .000 40.000
ACTUAL
64.252 66.311 62.077 52.286 49.667 36.299 36.299 4P.412 59.753 57.286 59.878 58.946 71.728 62.533 65.728 76.294 77.265 42.102 40.037 52.614 61.551 61.551 60.582 67.259 66.565 50.770 62.368 39.292 50.009 56.008 51.396 44.659 45.695 53.546 52.398 49.751 59.728 61.314 39.919 39.743 52.044 31.742 40.279 47.706 51.265 54.205 55.399 32.724 37.470 53.432 50.454 34.772 56.311
PREDICT VALUE .396 0.74P136 .541 10.609 .255 3.923 0.8 F95P1 7.714 0.9 3621 1.333 .648 -3.299 .64P . 0.9 5116 4.508 .119 5.247 .002 -7.2B6 .126 -13.B7B .078 1.054 .950 -8.72B .283 7.467 .499 16.272 .400 9.706 .395 5.735 .249 -7.102 .382 -2.037 O.B 0753 -2.614 .222 -5.551 .222 , 4.418 .165 .610 -11.259 .559 -10.565 -8.770 0 .8 6346 .273 3.632 -2.292 .433 0.9071R9 3.991 0.955634 7.992 O.B91137 11.604 6.341 1.102 11.305 1.051 9.454 0.899163 16.602 O.BP9875 -16.751 0.911947 -24.72B I. IIP 1.206 0.686054 1.390 . -3.743 1.402 1.956 0.8P9319 -1.742 1.99P 1.366 0.720620 2.294 0.9f7970 -1.265 0.891945 -9.205 0.9C955B -6.399 0.937297 -6.724 1.921 -3.470 1.5t2 -0.432 0.897737 -P. 454 0.9002T>0 -3.772 1.763 -16.311 0.96*742 0.524 0.601 -O.B33 -1.5B9 0.121 -1.017 0.857 1.876 1.149 0.677 -0.815 -0.234 -0.298 -0.637 . 0.506 -1.301 -1.219 -1.001 0.417 -0.264 0.456 0.913 1.325 0.726 1.293 1.080 1.896 -1.913 -2.832 0.079 . -0.431 0.223 -0.203 0.093 0.262 -0.144 -1.051 -0.731 -0.783 -0.400 -0.963 -0.965 -0.437 -1.P64
8.753 8.732 8.747 B.731 B.73P 8.5P5 8.710 B.675 8.447 8.472 9.715 8.695 8.759 9.719 B.726 8.655 8.665 8.75B 8.711 9.696 9.757 9.752 8.759 B.735 8.741 B.75B B.759 8.756 8.733 8.721 . B.691 B.759 8.574 B.697 8.750 9.759 B.757 fl.754 8.592 B.664 B.75P 8.75P 8.625 9.751
0.086 1.233 0.450 O.BB1 0.152 -0.382
B.692 B.66B fl.714 8.759 9.756 9.648
STD ERR STD EPR STUDENT PREDICT RESIDUAL RESIDUAL RESIDUAL
*** j
* *
** * *
+**( *****! 1
i* i»* i* i** i** i*++
r i* i i i* i* *i *** i **i i* i*++ i** i* *i i i *i i* ** i »* **
1 |**
-2-1-0 I
2
OUTPUT FROM LOGLIN: P00945= LOOOM STATION IDENTIFICATION NUMBFS=03374100
0.000 0.024 0.002 0.004 0.000 0.003 . 0.002 0.003 0.005 0.021 0.000 0.027 0.009 0.053 0.057 0.018 0.007 0.001 0.000 0.004 . 0.002 0.029 0.024 0.005 0.002 0.001 0.001 0.005 0.009 0.004 0.012 0.006 0.019 0.020 0.066 0.000 . 0.002 0.000 0.001 0.000 0.000 0.000 0.006 0.003 0.015 0.003 0.005 0.005 0.004 0.021
COPK'S D
16806 THURSDAY, AUGUST 1R, 1993
CO CO
IB ICO. 00 49800.00 16500.00 14800.00 9500.00 6000.00 7580.00 3200.00 2500.00 2050.00 3170.00 1650.00 14600.00 5780.00 12POO.OO 24100.00 11200.00 8160.00 4880.00 2860.00
84 85 86 87 88 89 90 91 9? 93 9* 95 96 97 98 99 100 101 102 103
46.000 35.000 45.000 39.000 45.000 . 29.000 56.000 71.000 64.000 67.000 74.000 44.000 54.000 48.000 45.000 40.000 62.000 36.000 61.000
ACTUAL
SUM OF RESIDUALS SUM OF SQUARED RESIDUALS
in
DBS 1.079 2.BB9 1.695 -.680576 1.038 -.973067 0.994730 -7.986 0.893042 -6.117 0.937297 0.9953B1 -24.221 -5.256 1.2D5 7.444 1.350 1.476 -1.405 5.657 1.210 6.573 1.622 0.9P9773 -3.113 -1.747 0.947437 0.947319 -.338893 2.557 1.228 -9. 583 0.915338 O.B903BO 9.466 -21.324 1.D04 -1.302 1.269
8.737 8.639 9.742 9.7*7 B.75P . 8.758 8.721 8.700 B.679 8.720 B.653 B.74B 8.753 9.753 8. 718 B.756 B.759 8.746 B.712 0.331 -0.079 -0.111 -0.913 -0.698 . -2.765 -0.603 O.B56 -0.162 0.649 0.760 -0.356 -0.200 -0.039 0.293 -1.093 1.08] -2.43B -0.149
STP ERR STD ERR STUDENT PREDICT RESIDUAL RESIDUAL RESIDUAL
2.07905E-11 7440 .682
45.111 35.681 45.973 46.986 51.117 55.399 53.221 61.255 63.556 65.405 61.343 67.427 47.113 55.747 48.339 42.443 49.583 52.534 57.324 62.302
PREDICT VALUE
#*#+*| *l 1* | 1* 1* 1 1 1 1 »*| 1** *+*+( 1
1 1 1 *l *l
-2-1-0 1
2
OUTPUT FROM LOGL1N: POfW5= IOOOM STATION IDENTIFICATION NUMBER *03374100
0.040 0.003 0.009 0.000 0.004 0.010 0.031 O.OOD 0.000 0.001 0.007 0.006 0.039 0.000
0.001 0.000 0.000 0.005 0.003
COOK'S D
16:06 THURSDAY, AUGUST IB. 19R3
u> -Pa
NOTE:
5.0
-4--
0 *
10
?0
30 *
V A 40 I U E
P R 60 F 0 I C T 50 E 0
70
80
90
6.0 6.5
-.4..
5 DBS HAD MISSING VALUES
5.5
P P
0
DBS HIDOFN
.-4 -. 7.0
PP
o
o
n o oo
7.5
.-4-.
,
PPPO
L00061
P.O
.-4-
0
ppp
0 0
0
00 00
0
8.5
.. 4
on 00 0 0
PPP 0 OOPPPPP 000 PP P 0 00 0 CIPPPP
PP
0
SYMBOL USED IS P SYMBOL USFD IS 0
PPPP 0 00 OPPPP
00
PP
0
PLOT PF P*L00061 PLOT OF P009*5*L00061
OUTPUT FROM LOGLIN: POOM5 = L00061 STATION 1DFNT1F1CATION NUKPER=03374100
9.5
0
10.5
. -4--
4-. 11.0
0 0 PPPPP 0 OPPP 0 0 00 PPP 0 0 PP 0
PPP
10.0
0 0 0 P PP 00 OPPPPP 0 PP P
o n
16:06 THURSDAY, AUGUST IB, 19S3
fj
n
P P
10
to
-5
-30
-25
-20
-15
A L S -10
1 0
R E 5
10
15
A
A
A
AA
A
A
A A
A A
A A
A
A
A
A
A
AA A
A
PLOT OF R*P
A A
A
A A
A A
A
A
A A
A
A
A
A A
A
A
A
A
A
A
A A
A A
A
AA
A
AA
LEGEND: A = i DBS, B = ? DBS, ETC.
OUTPUT FROM LOGLIN: P00945* L00061 STATION IDENTIFICATION NUMBFR=0337«100
A
A A
70
7?
U>:06 THURSDAY1 . AUGUST 18,
19P3
11
en
CO
P:NORMAL
SCN RANK HUM ^.= 0
T:HEAN*O
N MEAN STO DEV SKEWNESS USS CV
-20 3 -22 0 -2* 72
4.
«4
073*6 01557788 236*577 00*692677 012356791*69 677713** 777*33073 87531064330 63 317*1 628755*0 36 93
-1* -16 R3 -18
-12
-6 -8 -10
2 0 -0 -2 -*
10 8 6 *
12
4
PRQB>0
4
STO MEAM PROB>|T| PRDB>IS|
ess
SUM WGTS SUM VARIANCE KURTOSIS
RESIDUALS
FOMENTS
98 2.121E-13 P. 758 31 -0.5973*fi 7**0.6fi *.128E*15 2.39PE-13 167.5 9P 0.07B2*36
STEM LEAF 16 3619 1*
VARIABLES
2
1 1
2
5 8 7 9 12 8 9 11 2 5 8 2 2
0.1*3
9B 2.079E-11 76.7081 0.62*17* 7*40.68 O.B8*723 1 0.554
I I 4
I *
4 4 I I 4
I *
4
BDXPLOT
MAX 03 HED 01 HIM 42.64*5 11.1894 -24.72P2
17.916B 5.85993 0.9008P6 -5.32948 -24.7282
4
-25*+
-11
3
17*
HISSING VALUE COUNT * COUNT/NOBS
RANGE 03-01 MODE
lOOt 75* 50K 25* OT
4 -2
*
5 4.85
»
-4-
**
*«
-16.9796 -24.72P2
-10.63*2
17.9161 I1.B377 9.9*287
-* -1
**»
.-4. *0
** + ***** **+ + **«***« *»*
**** ****
4+ *+***+
-* *2
**
-24.7292 -2*.2206 -22.9778 -21.3236 -16.7509
LOHFST
EXTREMES
12
HIGHEST 11.60** 16.2716 16.602* 17.0765 17.9168
lfc:06 THURSDAY, AUGUST 18, 1983
NORMAL PROBABILITY PLOT
*** **-»
1*
5*
99* 95* 90* 10*
OUANT1LES(DEF=4)
UNIVARIATE
OUTPUT EPOM LPGL1N: P0094** L00061
STANDARD ERROR
PARAMETER ESTIMATE
ID
12799.97 55899. *9 28399.9* 9299. 9fl 15299.97 31399.93 5989.99 3029.99 2250.00 2600.00 6360.00 14799.96 22500.00 33599.93 37000.00 14100.00 11700.00 4740.00 7979. 9B 11300.00 14299.96 23199.9*5 20299. 95 38999.92 18099.96 45299.91 14899.97 9709.98 6549.99 9RO.OO
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 1
INTERCFP L 00061
OBS
OF
VARIABLE
4.060 3.B29 3.89? 4.078 3.807 2.833 3.970 .220 .205 .290 .060 .043 111 3.738 3.784 3.871 4.078 4.111 . 3.714 3.807 3.807 3.871 3.555 3.912 3.638 4.159 3.970 4.025 4 .094
ACTUAL
VALUE
|T|
0.0001 0.0001
PROS >
0.0001
PROP>F
0.020771 0.03F941 0.029033 0.019550 0.022095 0.030397 0.020561 0.027084 0.031045 0.029065 0.020244 0.021810 O.D2607B 0.031343 0.032720 0.021434 0.020270 0.022260 0.019546 0.020138 0.021540 0.07M4P 0.024886 0.033486 0.02365P 0.035713 0.021865 0.019621 0.02010B 0.1PB017
-1.178
0.217170 0.191911 1.132 0.256444 0.1B9064 1.356 0.195096 0.190P36 1.022 0.175524 0.192040 0.914 -.003804 0.191765 -0.020 -.845044 0.190624 -4.433 -.012619 0.191934 -0.066 0.111270 0. 191123 0.582 0.041724 0.190519 0.219 0.154078 0.190B32 0.807 0.088554 0.191968 0.461 0.226475 0.191796 1.181 0.371328 0.191263 1.941 0.071865 0.190471 0.377 0.136111 0.190239 0.715 0.045716 0.191839 0.238 0.217741 0.191965 1.134 0.084923 0.191744 0.443 ... -.152621 0.191982 -0.795 -.016233 0.191B27 -0.085 0.072750 0.191212 0.380 0.112733 0.191421 0.589 -.063050 0.190106 -0.437 0.132461 0.191577 0.691 C. 026724 0. 199700 0.141 0.343546 0.1917
