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43,50466/triaov.f4
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C WESTERN MICHIGAN UNIVERSITY
C TRIAOV.F4 (FILENAME ON LIBRARY DECTAPE)
C TRIAOV, 1.9.3 (CALLING NAME, SUBLST NO.)
C THREE-WAY ANALYSIS OF VARIANCE
C PROGRAMMED BY SAM ANEMA AT WMU, LATER MODIFIED BY R.R. BARR,
C M.T. O'BRYAN, CONSULTANT - DR. M. STOLINE
C LIBRARY DECTAPE PROGS. USED: USAGE.MAC
C APLIB PROGS. USED: IO, GETFOR, CHIPRB, FISHER, NORMCV
C FORWMU PROGS. USED: TTYPTY, MINSQV, ALLCOR, PRINTS, DEVCHG,
C EXISTS
C INTERNAL SUBR. USED: MNL, BARTLT, FIT, PRINT, WEIGH, UNWEI,
C PROP
C ABOVE COMMENTS AND RIGHT ADJUSTED COMMENTS PUT IN BY WG
C
C---------------S(1) USED IN CALL MNL, LX(3) CONTAINS NO. OF LEVELS
C--------------- ON 3 FACTORS. LNAME(2) IS APPARENTLY NOT USED
DIMENSION LX(3),S(1),LNAME(2)
C
C READ IN PARAMETERS
C
99 TYPE 100
100 FORMAT('1 ---WMU 3-WAY ANALYSIS OF VARIANCE --'///)
C CALL USAGE('TRIAOV')
C---------------TTYPTY RETURNS ZERO - TTY, MINUS ONE - BATCH JOB
CALL TTYPTY(ICODE)
C---------------ODV, IDV ARE RETURNED. OTHER ARGS. ARE INPUT.
C--------------- 1 MEANS OUTPUT? PRINTS. 0 MEANS INPUT? PRINTS.
CALL IO(6,ODV,-1,-4,1,ICODE)
801 CALL IO(4,IDV,-1,-4,0,ICODE)
98 TYPE 101
101 FORMAT (' ENTER FACTOR NAMES AND NO. OF LEVELS'/)
90 ACCEPT 102,INAME,IMAX,JNAME,JMAX
102 FORMAT (A1,1X,I)
ACCEPT 108,KNAME,KMAX,NTIMES
108 FORMAT(A1,1X,2I)
IF(IMAX.LT.2.OR.JMAX.LT.2.OR.KMAX.LT.2)GO TO 60
GO TO 63
60 TYPE 64
64 FORMAT(' THE PROGRAM REQUIRES AT LEAST 2 LEVELS ON EACH
1FACTOR.'/' REENTER FACTOR NAMES AND NO. OF LEVELS.'/)
IF(ICODE.NE.0)CALL EXIT
GO TO 90
61 TYPE 62
62 FORMAT(' THE PROBLEM IS TOO LARGE.'/' REENTER FACTOR NAMES AND
1LEVELS.'/)
IF(ICODE.NE.0)CALL EXIT
GO TO 90
63 LX(1)=IMAX
LX(2)=JMAX
LX(3)=KMAX
DO 10 I=2,3
DO 11 J=1,I-1
IF(LX(I).GE.LX(J))GO TO 11
ITM=LX(I)
LX(I)=LX(J)
LX(J)=ITM
11 CONTINUE
10 CONTINUE
MX=IMAX*JMAX*KMAX
MAX=2*(MX+IMAX*JMAX+IMAX*KMAX+JMAX*KMAX)+10*LX(3)+(LX(3)+1)*
1 (LX(3)+1)+2*LX(3)*LX(2)+2+IMAX+JMAX+KMAX+MX
CALL ALLCOR(MAX,IERR,I1,S)
IF(IERR.NE.0)GO TO 61
I2=I1+MX
I3=I2+MX
I4=I3+IMAX*JMAX
I5=I4+IMAX*KMAX
I6=I5+LX(3)+1
I7=I6+LX(3)+1
I8=I7+JMAX*KMAX
I9=I8+IMAX
I10=I9+JMAX
I11=I10+KMAX
I12=I11+IMAX*JMAX
I13=I12+IMAX*KMAX
I14=I13+JMAX*KMAX
I15=I14+LX(3)
I16=I15+LX(3)
I17=I16+LX(3)
I18=I17+(LX(3)+1)*(LX(3)+1)
I19=I18+LX(3)
I20=I19+LX(3)
I21=I20+LX(3)*LX(2)
I22=I21+LX(3)*LX(2)
I23=I22+LX(3)
I24=I23+LX(3)
I25=I24+LX(3)
CALL MNL(INAME,JNAME,KNAME,
1 IMAX,JMAX,KMAX,NTIMES,S(I1),S(I2),S(I3),S(I4),S(I5),
1S(I6),S(I7),S(I8),S(I9),S(I10),S(I11),S(I12),S(I13),S(I14),S(I15)
2,S(I16),S(I17),S(I18),S(I19),S(I20),S(I21),S(I22),S(I23),S(I24),
3 S(I25),IDV)
TYPE 802
802 FORMAT(//)
GO TO 801
END
C---------------INAME, JNAME, KNAME, IMAX, JMAX, KMAX, NTIMES
C--------------- ARE INPUT. OTHER ARGS. ARE SPACES
C--------------- RESERVED BY DYN. ALLOC.
SUBROUTINE MNL(INAME,JNAME,KNAME,
1 IMAX,JMAX,KMAX,NTIMES,NIJK,XIJK,XIJ,XIK,MC,MR,XJK,
1XI,XJ,XK,NIJ,NIK,NJK,NI,NJ,NK,D,YB,XD,DF,FF,C,B,A,XXIJK,IDV)
DIMENSION NIJK(1),XIJK(1),XIJ(1),XIK(1),MC(1),MR(1),XJK(1),XI(1),
1XJ(1),XK(1),ID(5,50),FMT(48),X(50),NIJ(1),NIK(1),NJK(1),NI(1),
2NJ(1),NK(1),D(1),YB(1),XD(1),DF(1),FF(1),C(1),B(1),A(1),IAST(19)
3,IENT(17),XXIJK(1)
DATA IAST(18),IAST(19)/',0,0,','0,0,0'/
63 IF(NTIMES.EQ.0)NTIMES=1
TYPE 103
103 FORMAT (' ENTER ID IF DESIRED ELSE RETURN'/)
DO 37 J=1,NTIMES
37 ACCEPT 104, (ID(I,J),I=1,5)
104 FORMAT (16A5)
TYPE 1010
1010 FORMAT(' MEANS? ',$)
ACCEPT 1011,IFM
1011 FORMAT(A3)
C---------------FMT RETURNS USER FORMAT. ISTD=1 IF STANDARD
C--------------- FORMAT IS REQUESTED, =0 IF FORMAT TO BE USED IS IN FMT.
CALL GETFOR(-1,-4,FMT,ISTD,48,4)
96 TYPE 2191
2191 FORMAT(' WHICH METHOD OF DATA ENTRY? (1 OR 2) ',$)
ACCEPT 2192,NWHICH
2192 FORMAT(I)
IF(IDV.NE.'TTY')GO TO 97
TYPE 95
95 FORMAT(' ENTER DATA'/)
GO TO 94
97 TYPE 93
93 FORMAT(' DATA IS BEING READ'/)
C
C INITIALIZE
C
94 NTI=0
80 NTI=NTI+1
N=0
MX= IMAX*JMAX*KMAX
DO 200 I=1,MX
NIJK(I)=0
XXIJK(I)=0
200 XIJK(I)=0.0
MX= IMAX*JMAX
DO 201 I=1,MX
NIJ(I)=0
201 XIJ(I)=0.0
MX=JMAX*KMAX
DO 202 I=1,MX
NJK(I)=0
202 XJK(I)=0.0
MX=IMAX*KMAX
DO 203 I=1,MX
NIK(I)=0
203 XIK(I)=0.0
DO 204 I=1,IMAX
NI(I)=0
204 XI(I)=0.0
DO 205 I=1,JMAX
NJ(I)=0
205 XJ(I)=0.0
DO 206 I=1,KMAX
NK(I)=0
206 XK(I)=0.0
SSTOT=0.0
SUM=0.0
C
C READ IN DATA
C
IF(NWHICH.EQ.2)GO TO 5364
IF(ISTD.EQ.0)GO TO 1
FMT(1)='(3I,F'
FMT(2)=') '
1 READ(4,FMT,END=300)I,J,K,(X(L),L=1,NTIMES)
IF(I.EQ.0)GO TO 300
IF(I.GT.IMAX.OR.J.GT.JMAX.OR.K.GT.KMAX)GO TO 40
IF(I.LT.1.OR.J.LT.1.OR.K.LT.1)GO TO 40
IJK=I+(J-1+(K-1)*JMAX)*IMAX
84 FORMAT(I)
N=N+1
NIJK(IJK)=NIJK(IJK)+1
XIJK(IJK)=XIJK(IJK)+X(NTI)
XXIJK(IJK)=XXIJK(IJK)+X(NTI)*X(NTI)
SUM=SUM+X(NTI)
10 SSTOT=SSTOT+X(NTI)**2
GO TO 1
5364 IF(ISTD.EQ.0)GO TO 3197
FMT(1)='(10F)'
3197 READ(4,3198,END=300)(IENT(I),I=1,17)
3198 FORMAT(A1,15A5,A4)
ENCODE(80,3198,IAST)(IENT(I),I=1,17)
IF(IENT(1).EQ.'*')GO TO 3199
IF(I.EQ.0)GO TO 3191
DECODE(95,FMT,IAST)(X(L),L=1,NTIMES)
N=N+1
NIJK(IJK)=NIJK(IJK)+1
XIJK(IJK)=XIJK(IJK)+X(NTI)
XXIJK(IJK)=XXIJK(IJK)+X(NTI)*X(NTI)
SUM=SUM+X(NTI)
SSTOT=SSTOT+X(NTI)**2
GO TO 3197
3199 DECODE(95,3140,IAST)I,J,K
3140 FORMAT(1X,3I)
IF(I.EQ.0)GO TO 300
IF(I.GT.IMAX.OR.J.GT.JMAX.OR.K.GT.KMAX)GO TO 3191
IF(I.LT.1.OR.J.LT.1.OR.K.LT.1)GO TO 3191
IJK=I+(J-1+(K-1)*JMAX)*IMAX
GO TO 3197
3191 TYPE 3192
3192 FORMAT( ' INDEX OUT OF RANGE USING METHOD 2. CANNOT CONTINUE!'/)
CALL EXIT
40 TYPE 41
41 FORMAT(' INDEX OUT OF RANGE. OBSERVATION DELETED.'/)
GO TO 1
300 CONTINUE
70 FORMAT('1',16A5)
WRITE(6,70)(ID(I,NTI),I=1,5)
C
C CALCULATE TOTAL AND WITHIN SS
C
KIND=0
MX=IMAX*JMAX*KMAX
CT=SUM**2/N
C
SSTOT=SSTOT-CT
C
SUMM=0.0
SSC=0.0
NEM=0
DO 91 I=1,MX
IF(NIJK(I).EQ.0)GO TO 42
SSC=SSC+XIJK(I)**2/NIJK(I)
GO TO 91
42 NEM=NEM+1
91 CONTINUE
SSC=SSC-CT
SSABC=SSC
SSW=SSTOT-SSC
IF((N-MX).EQ.0)KIND=1
C
C CALCULATE ACTUAL MARGINAL SUMS
C
DO 900 I=1,IMAX
DO 900 J=1,JMAX
IJ=I+(J-1)*IMAX
DO 900 K=1,KMAX
IJK=I+(J-1+(K-1)*JMAX)*IMAX
C**** WMU-AM: #1.9.3, MOD=1, MTO, 19-OCT-77 ****
IF(NIJK(IJK).GT.0)XXIJK(IJK)=XXIJK(IJK)-
1 XIJK(IJK)*XIJK(IJK)/NIJK(IJK)
C**** END = MNL, #900-4 ****
XIJ(IJ)=XIJ(IJ)+XIJK(IJK)
NIJ(IJ)=NIJ(IJ)+NIJK(IJK)
XI(I)=XI(I)+XIJK(IJK)
900 NI(I)=NI(I)+NIJK(IJK)
DO 903 J=1,JMAX
DO 903 K=1,KMAX
JK=J+(K-1)*JMAX
DO 903 I=1,IMAX
IJK=I+(J-1+(K-1)*JMAX)*IMAX
IF(NIJK(IJK).GT.1)XXIJK(IJK)=XXIJK(IJK)/(NIJK(IJK)-1)
NJK(JK)=NJK(JK)+NIJK(IJK)
XJK(JK)=XJK(JK)+XIJK(IJK)
XJ(J)=XJ(J)+XIJK(IJK)
903 NJ(J)=NJ(J)+NIJK(IJK)
DO 906 K=1,KMAX
DO 906 I=1,IMAX
IK=I+(K-1)*IMAX
DO 906 J=1,JMAX
IJK=I+(J-1+(K-1)*JMAX)*IMAX
XIK(IK)=XIK(IK)+XIJK(IJK)
NIK(IK)=NIK(IK)+NIJK(IJK)
XK(K)=XK(K)+XIJK(IJK)
906 NK(K)=NK(K)+NIJK(IJK)
IF(IFM.EQ.'YES')CALL PRINT(IMAX,JMAX,KMAX,XI,XJ,XK,XIJ,XJK,XIK,
1XIJK,NI,NJ,NK,NIJ,NJK,NIK,NIJK,SUM,N,INAME,JNAME,KNAME,XXIJK)
CALL BARTLT(IMAX,JMAX,KMAX,NIJK,XXIJK,BART)
IDEG=IMAX*JMAX*KMAX-1
IF(BART.LT.0)GO TO 9127
C---------------CBART, IDEG INPUT AND YPROB RETURNED.
CALL CHIPRB(BART,IDEG,YPROB)
IF(IERR.NE.99)WRITE(6,9128)YPROB
9128 FORMAT(5X,'WITH CHI-SQUARE PROBABILITY=',T39,F5.3)
IF(IERR.EQ.99)WRITE(6,9129)
9129 FORMAT(5X,'NO PROBABILITY CALC. DF OR BARTLETT OUTSIDE LIMITS')
9127 KON=NIJK(1)
DO 1012 I=2,IMAX*JMAX*KMAX
IF(NIJK(I).NE.KON)GO TO 1014
1012 CONTINUE
GO TO 1020
C**** WMU-AM: #1.9.3, MOD=1, MTO, 19-SEP-77 ****
1014 DO 2000 I=1,IMAX
DO 2000 J=1,JMAX
DO 2000 K=1,KMAX
IJK=I+(J-1+(K-1)*JMAX)*IMAX
IF(NIJK(IJK).NE.NI(I)*NJ(J)*NK(K)/(N*N))GOTO 1018
2000 CONTINUE
CALL PROP(IMAX,JMAX,KMAX,XI,XJ,XK,XIJ,XIK,XJK,XIJK,
1 NI,NJ,NK,NIJ,NJK,NIK,NIJK,
2 SSTOT,SSW,N,CT,SSC)
1018 CALL FIT(IMAX,JMAX,KMAX,XI,XJ,XK,NI,NJ,NK,XIJ,XJK,XIK,
1NIJ,NJK,NIK,NIJK,D,DF,XD,FF,YB,A,B,C,MC,MR,SUM,SSW,N,SSTOT,NEM,
2SSABC,INAME,JNAME,KNAME,SSINT,CT)
C**** END = MNL, #1016-2 ****
DO 1016 I=1,IMAX*JMAX*KMAX
IF(NIJK(I).EQ.0)GO TO 1017
1016 CONTINUE
CALL WEIGH(IMAX,JMAX,KMAX,NIJK,XIJK,INAME,JNAME,KNAME,A,B,C,YB,XD,
1DF,SSINT,SSTOT,SSW,N)
WRITE(6,1021)
1021 FORMAT(///,20X,'UNWEIGHTED MEANS ANOVA')
GO TO 1023
1020 WRITE(6,1022)
1022 FORMAT(///,20X,'ANALYSIS OF VARIANCE')
1023 CALL UNWEI(IMAX,JMAX,KMAX,XI,XJ,XK,XIJ,XJK,XIK,XIJK,NI,NJ,NK,NIJ,
1NJK,NIK,NIJK,SSTOT,SSW,N,INAME,JNAME,KNAME)
1017 IF(NTI.NE.NTIMES)GO TO 81
RETURN
81 REWIND 5
GO TO 80
END
C
C BARTLETTS TEST FOR HOMOGENEITY
C
C---------------IMAX, JMAX, KMAX, NIJK, XXIJK ARE INPUT; CS RETURNED
SUBROUTINE BARTLT(IMAX,JMAX,KMAX,NIJK,XXIJK,CS)
DIMENSION NIJK(1),XXIJK(1)
V=0
VI=0
SPSQ=0
CS=0
WRITE(6,3)
3 FORMAT(///,2X,'BARTLETT''S TEST STATISTIC FOR TESTING ',
1 'HOMOGENEITY OF CELL VARIANCES')
DO 1 I=1,IMAX
DO 1 J=1,JMAX
DO 1 K=1,KMAX
IJK=I+(J-1+(K-1)*JMAX)*IMAX
IF(NIJK(IJK).LT.2)GO TO 99
V=V+(NIJK(IJK)-1)
VI=VI+1./(NIJK(IJK)-1)
CS=CS+(NIJK(IJK)-1)*ALOG(XXIJK(IJK))
1 SPSQ=SPSQ+XXIJK(IJK)*(NIJK(IJK)-1)
SPSQ=SPSQ/V
IJKMAX=IMAX*JMAX*KMAX
ID=IJKMAX-1
CS=(V*ALOG(SPSQ)-CS)/(1.+(VI-1./V)/(3.*ID))
WRITE(6,4)IJKMAX,CS,ID
4 FORMAT(/5X,'NUMBER OF CELL VARIANCES='I4,/,
1 5X,'BARTLETT''S STATISTIC=',F12.3,5X,'DF=',I4)
RETURN
99 WRITE(6,5)
5 FORMAT(' IS NOT POSSIBLE SINCE AT LEAST ONE SAMPLE SIZE',
1 ' IS EITHER 0 OR 1')
CS=-1
RETURN
END
C
C CUMULATIVE CHI SQUARE SUBROUTINE
C
C SOURCE-CHARLES A. NAGY
C
C CUMULATIVE CHI SQUARE SUBROUTINE
C
C SOURCE-CHARLES A. NAGY
C
C FITTING CONSTANTS
C
C**** WMU-AM: #1.9.3, MOD=1, MTO, 23-SEP-77 ****
C---------------IMAX, JMAX, KMAX, XI, XJ, XK, NI, NJ, NK, XIJ, XJK,
C---------------XIK, NIJ, NJK, NIK, NIJK, INAME, JNAME, KNAME, SSTOT, SSW,
C--------------- N, CT, NEM, SSABC ARE INPUT. D, DF, XD, FF, YB,
C--------------- A, B, C, SSINT ARE RETURNED. SPACE FOR MC, MR IS RESERVED
C--------------- BY ALLCOR AND USED BY MINVSQ BUT NOT NEEDED ELSEWHERE
SUBROUTINE FIT(IMAX,JMAX,KMAX,XI,XJ,XK,NI,NJ,NK,XIJ,XJK,XIK,
1NIJ,NJK,NIK,NIJK,D,DF,XD,FF,YB,A,B,C,MC,MR,SUM,SSW,N,SSTOT,NEM,
2SSABC,INAME, JNAME,KNAME,SSINT,CT)
DIMENSION XI(1),XJ(1),XK(1),NI(1),NJ(1),NK(1),XIJ(1),XJK(1),XIK(1)
DIMENSION NIJ(1),NJK(1),NIK(1),NIJK(1),D(1),DF(1),FF(1),YB(1)
DIMENSION XD(1),A(1),B(1),C(1),MC(1),MR(1)
C**** END = FIT, #1104-10 ****
JM1=JMAX+1
DO 1100 I=1,JM1
DO 1100 J=1,JM1
IJ=I+(J-1)*JM1
IF(I.EQ.JM1.OR.J.EQ.JM1)GO TO 1103
XNTL=0.0
DO 1104 K=1,IMAX
LM1=K+(I-1)*IMAX
LM2=K+(J-1)*IMAX
XNTL=XNTL+FLOAT(NIJ(LM1)*NIJ(LM2))/FLOAT(NI(K))
1104 CONTINUE
IF(I.EQ.J)GO TO 1102
D(IJ)=-XNTL
GO TO 1100
1102 D(IJ)=NJ(J)-XNTL
GO TO 1100
1103 D(IJ)=1.0
IF(I.EQ.J)D(IJ)=0.0
1100 CONTINUE
CALL MINVSQ(D,JM1,1.0,MC,MR,JM1,-1,2,DET,IEXP)
DO 1105 J=1,JMAX
XNTL=0.0
DO 1106 I=1,IMAX
IJ=I+(J-1)*IMAX
1106 XNTL=XNTL+FLOAT(NIJ(IJ))*XI(I)/FLOAT(NI(I))
1105 YB(J)=XNTL
DO 1107 J=1,JMAX
XNTL=0.0
DO 1108 K=1,JMAX
JK=J+(K-1)*JM1
1108 XNTL=XNTL+D(JK)*(XJ(K)-YB(K))
1107 XD(J)=XNTL
DO 1109 J=1,JMAX
DO 1110 K=1,KMAX
XNTL=0.0
JK=J+(K-1)*JMAX
DO 1111I=1,IMAX
IJ=I+(J-1)*IMAX
IK=I+(K-1)*IMAX
1111 XNTL=XNTL+FLOAT(NIJ(IJ)*NIK(IK))/FLOAT(NI(I))
1110 DF(JK)=FLOAT(NJK(JK))-XNTL
1109 CONTINUE
DO 1112 J=1,JMAX
DO 1113 K=1,KMAX
XNTL=0.0
JK=J+(K-1)*JMAX
DO 1114 L=1,JMAX
JL=J+(L-1)*JM1
LK=L+(K-1)*JMAX
1114 XNTL=XNTL+D(JL)*DF(LK)
1113 FF(JK)=XNTL
1112 CONTINUE
DO 1115 K=1,KMAX
XNTL=0.0
DO 1116 I=1,IMAX
IK=I+(K-1)*IMAX
1116 XNTL=XNTL+FLOAT(NIK(IK))*XI(I)/FLOAT(NI(I))
YNTL=0.0
DO 1117 J=1,JMAX
JK=J+(K-1)*JMAX
1117 YNTL=YNTL+DF(JK)*XD(J)
1115 YB(K)=XK(K)-XNTL-YNTL
KM1=KMAX+1
DO 1118 K=1,KM1
DO 1118 KK=1,KM1
KKK=K+(KK-1)*KM1
IF(K.EQ.KM1)GO TO 1119
IF(KK.EQ.KM1)GO TO 1119
XNTL=0.0
DO 1120 I=1,IMAX
IK=I+(K-1)*IMAX
IKK=I+(KK-1)*IMAX
1120 XNTL=XNTL+FLOAT(NIK(IK)*NIK(IKK))/FLOAT(NI(I))
YNTL=0.0
DO 1122 J=1,JMAX
JK=J+(K-1)*JMAX
JKK=J+(KK-1)*JMAX
1122 YNTL=YNTL+DF(JK)*FF(JKK)
IF(K.EQ.KK)GO TO 1121
D(KKK)=-XNTL-YNTL
GO TO 1118
1121 D(KKK)=NK(K)-XNTL-YNTL
GO TO 1118
1119 D(KKK)=1.0
IF(K.EQ.KK)D(KKK)=0.0
1118 CONTINUE
CALL MINVSQ(D,KM1,1.0,MC,MR,KM1,-1,2,DET,IEXP)
CTERM=0.0
DO 1123 K=1,KMAX
XNTL=0.0
DO 1124 KK=1,KMAX
KKK=K+(KK-1)*KM1
1124 XNTL=XNTL+D(KKK)*YB(KK)
C(K)=XNTL
1123 CTERM=CTERM+C(K)*XK(K)
BTERM=0.0
DO 1125 J=1,JMAX
XNTL=0.0
DO 1126 K=1,KMAX
JK=J+(K-1)*JMAX
1126 XNTL=XNTL+FF(JK)*C(K)
B(J)=XD(J)-XNTL
1125 BTERM=BTERM+B(J)*XJ(J)
ZNTL=0.0
DO 1127 I=1,IMAX
XNTL=0.0
DO 1128 J=1,JMAX
IJ=I+(J-1)*IMAX
1128 XNTL=XNTL+FLOAT(NIJ(IJ))*B(J)
YNTL=0.0
DO 1129 K=1,KMAX
IK=I+(K-1)*IMAX
1129 YNTL=YNTL+FLOAT(NIK(IK))*C(K)
A(I)=(XI(I)-XNTL-YNTL)/FLOAT(NI(I))
1127 ZNTL=ZNTL+A(I)
XMU=ZNTL/FLOAT(IMAX)
ATERM=0.0
DO 1130 I=1,IMAX
1130 ATERM=ATERM+(A(I)-XMU)*XI(I)
RABC=XMU*SUM+ATERM+BTERM+CTERM-CT
SSINT=SSABC-RABC
ZNTL=0.0
DO 1140 I=1,IMAX
XNTL=0.0
DO 1141 J=1,JMAX
IJ=I+(J-1)*IMAX
XNTL=XNTL+FLOAT(NIJ(IJ))*XD(J)/FLOAT(NI(I))
1141 CONTINUE
YB(I)=XI(I)/FLOAT(NI(I))-XNTL
ZNTL=ZNTL+YB(I)
1140 CONTINUE
ZNTL=ZNTL/FLOAT(IMAX)
RAB=ZNTL*SUM-CT
DO 1142 I=1,IMAX
RAB=RAB+(YB(I)-ZNTL)*XI(I)
1142 CONTINUE
DO 1143 J=1,JMAX
RAB=RAB+XD(J)*XJ(J)
1143 CONTINUE
RC=RABC-RAB
KM1=KMAX+1
DO 1144 K=1,KM1
DO 1144 L=1,KM1
KL=K+(L-1)*KM1
IF(K.EQ.L)GO TO 1145
IF(K.EQ.KM1)GO TO 1146
IF(L.EQ.KM1)GO TO 1146
XNTL=0.0
DO 1147 I=1,IMAX
IK=I+(K-1)*IMAX
IL=I+(L-1)*IMAX
XNTL=XNTL+FLOAT(NIK(IK)*NIK(IL))/FLOAT(NI(I))
1147 CONTINUE
D(KL)=-XNTL
GO TO 1144
1145 IF(K.EQ.KM1)GO TO 1245
XNTL=0.0
DO 1244 I=1,IMAX
IK=I+(K-1)*IMAX
XNTL=XNTL+FLOAT(NIK(IK))**2/FLOAT(NI(I))
1244 CONTINUE
D(KL)=FLOAT(NK(K))-XNTL
GO TO 1144
1245 D(KL)=0.0
GO TO 1144
1146 D(KL)=1.0
1144 CONTINUE
CALL MINVSQ(D,KM1,1.0,MC,MR,KM1,-1,2,DET,IEXP)
DO 1148 K=1,KMAX
XNTL=0.0
DO 1149 I=1,IMAX
IK=I+(K-1)*IMAX
XNTL=XNTL+FLOAT(NIK(IK))*XI(I)/FLOAT(NI(I))
1149 CONTINUE
YB(K)=XNTL
1148 CONTINUE
DO 1150 K=1,KMAX
XNTL=0.0
DO 1151 KK=1,KMAX
KKK=K+(KK-1)*KM1
XNTL=XNTL+D(KKK)*(XK(KK)-YB(KK))
1151 CONTINUE
XD(K)=XNTL
1150 CONTINUE
ZNTL=0.0
DO 1152 I=1,IMAX
XNTL=0.0
DO 1153 K=1,KMAX
IK=I+(K-1)*IMAX
XNTL=XNTL+FLOAT(NIK(IK))*XD(K)/FLOAT(NI(I))
1153 CONTINUE
YB(I)=XI(I)/FLOAT(NI(I))-XNTL
ZNTL=ZNTL+YB(I)
1152 CONTINUE
ZNTL=ZNTL/FLOAT(IMAX)
RAC=ZNTL*SUM-CT
DO 1154 I=1,IMAX
RAC=RAC+(YB(I)-ZNTL)*XI(I)
1154 CONTINUE
DO 1155 K=1,KMAX
RAC=RAC+XD(K)*XK(K)
1155 CONTINUE
RB=RABC-RAC
DO 1156 K=1,KM1
DO 1157 L=1,KM1
KL=K+(L-1)*KM1
IF(K.EQ.L)GO TO 1158
IF(K.EQ.KM1)GO TO 1159
IF(L.EQ.KM1)GO TO 1159
XNTL=0.0
DO 1160 J=1,JMAX
JK=J+(K-1)*JMAX
JL=J+(L-1)*JMAX
XNTL=XNTL+FLOAT(NJK(JK)*NJK(JL))/FLOAT(NJ(J))
1160 CONTINUE
D(KL)=-XNTL
GO TO 1157
1158 IF(K.EQ.KM1)GO TO 1161
XNTL=0.0
DO 1162 J=1,JMAX
JK=J+(K-1)*JMAX
XNTL=XNTL+FLOAT(NJK(JK))**2/FLOAT(NJ(J))
1162 CONTINUE
D(KL)=FLOAT(NK(K))-XNTL
GO TO 1157
1161 D(KL)=0.0
GO TO 1157
1159 D(KL)=1.0
1157 CONTINUE
1156 CONTINUE
CALL MINVSQ(D,KM1,1.0,MC,MR,KM1,-1,2,DET,IEXP)
DO 1163 K=1,KMAX
XNTL=0.0
DO 1164 J=1,JMAX
JK=J+(K-1)*JMAX
XNTL=XNTL+FLOAT(NJK(JK))*XJ(J)/FLOAT(NJ(J))
1164 CONTINUE
YB(K)=XNTL
1163 CONTINUE
DO 1165 K=1,KMAX
XNTL=0.0
DO 1166 L=1,KMAX
KL=K+(L-1)*KM1
XNTL=XNTL+D(KL)*(XK(L)-YB(L))
1166 CONTINUE
XD(K)=XNTL
1165 CONTINUE
ZNTL=0.0
DO 1167 J=1,JMAX
XNTL=0.0
DO 1168 K=1,KMAX
JK=J+(K-1)*JMAX
XNTL=XNTL+FLOAT(NJK(JK))*XD(K)/FLOAT(NJ(J))
1168 CONTINUE
YB(J)=XJ(J)/FLOAT(NJ(J))-XNTL
ZNTL=ZNTL+YB(J)
1167 CONTINUE
ZNTL=ZNTL/FLOAT(JMAX)
RBC=ZNTL*SUM-CT
DO 1171 J=1,JMAX
RBC=RBC+(YB(J)-ZNTL)*XJ(J)
1171 CONTINUE
DO 1169 K=1,KMAX
RBC=RBC+XD(K)*XK(K)
1169 CONTINUE
RA=RABC-RBC
WRITE(6,100)
100 FORMAT(///,17X,'PRELIMINARY ANOVA - FITTING CONSTANTS')
WRITE(6,101)
101 FORMAT(/5X,'SOURCE',5X,'SUM OF SQUARES',3X,'DF',4X,'MEAN SQUARE',
14X,'F',4X,'PROB')
IDF=IMAX*JMAX*KMAX-1
C**** WMU-AM: #1.9.3, MOD=1, MTO, 19-SEP-77 ****
DO 201 I=1,IMAX
DO 201 J=1,JMAX
DO 201 K=1,KMAX
IJK=I+(J-1+(K-1)*JMAX)*IMAX
201 IF(NIJK(IJK).EQ.0) IDF=IDF-1
C**** WMU-AM: #1.9.3, MOD=1, MTO, 7-OCT-77 ****
XMS=SSABC/FLOAT(IDF)
KDF=(IMAX*JMAX*KMAX-1)-IDF
C**** END = FIT, #202-6 ****
IDW=N-IDF-1
IF(IDF.GT.0.AND.IDW.GT.0) GOTO 202
TYPE 2001
2001 FORMAT (' NOT ENOUGH DATA TO CARRY OUT AN ANOVA.')
WRITE (6,2001)
RETURN
202 SMW=SSW/FLOAT(IDW)
C**** END = FIT, #102-3 ****
F=XMS/SMW
PROB=FISHER(IDF,IDW,F)
WRITE(6,102)SSABC,IDF,XMS,F,PROB
102 FORMAT(/5X,'SUBCLASS',2X,F15.2,I5,F15.2,F7.2,F6.3)
IDF=IMAX+JMAX+KMAX-3
WRITE(6,103)RABC,IDF
103 FORMAT(/3X,'MAIN EFFECTS',F15.2,I5)
IDF=IMAX*JMAX*KMAX-IMAX-JMAX-KMAX+2-NEM
C**** WMU-AM: #1.9.3, MOD=1, MTO, 10-OCT-77 ****
IF(IDF.GT.0) GOTO 204
WRITE(6,2002)
2002 FORMAT (' TOO MANY MISSING CELLS TO OBTAIN AN INTER-'/
1 ' ACTION TEST.'//)
GOTO 205
204 XMS=SSINT/FLOAT(IDF)
F=XMS/SMW
PROB=FISHER(IDF,IDW,F)
WRITE(6,104)SSINT,IDF,XMS,F,PROB
104 FORMAT(/4X'INTERACTION',F15.2,I5,F15.2,F7.2,F6.3)
205 WRITE(6,105)SSW,IDW,SMW
C**** END = FIT, #105-1 ****
105 FORMAT(/6X,'WITHIN',3X,F15.2,I5,F15.2)
IDF=N-1
WRITE(6,106)SSTOT,IDF
106 FORMAT(/6X,'TOTAL',4X,F15.2,I5)
WRITE(6,107)
107 FORMAT(///,20X,'FINAL ANOVA - FITTING CONSTANTS')
WRITE(6,108)
108 FORMAT(/7X,'SOURCE',8X,'SUM OF SQUARES DF MEAN SQUARE F'
13X,'PROB')
IDT=IMAX+JMAX+KMAX-3
WRITE(6,109)RABC,IDT
109 FORMAT(//4X,'MAIN EFFECTS',4X,F15.2,I5)
IDF=IDT-(IMAX-1)
WRITE(6,110)JNAME,KNAME,INAME,RBC,IDF
110 FORMAT(//1X,A1,' & ',A1,' IGNORING ',A1,3X,F15.2,I5)
IDF=IMAX-1
XMS=RA/FLOAT(IDF)
F=XMS/SMW
PROB=FISHER(IDF,IDW,F)
WRITE(6,111)INAME,JNAME,KNAME,RA,IDF,XMS,F,PROB
111 FORMAT(/1X,A1,' ELIMINATING ',A1,' & ',A1,F15.2,
1 I5,F15.2,F7.2,F6.3)
IDF=IDT-(JMAX-1)
WRITE(6,110)INAME,KNAME,JNAME,RAC,IDF
IDF=JMAX-1
XMS=RB/FLOAT(IDF)
F=XMS/SMW
PROB=FISHER(IDF,IDW,F)
WRITE(6,111)JNAME,INAME,KNAME,RB,IDF,XMS,F,PROB
IDF=IDT-(KMAX-1)
WRITE(6,110)INAME,JNAME,KNAME,RAB,IDF
IDF=KMAX-1
XMS=RC/FLOAT(IDF)
F=XMS/SMW
PROB=FISHER(IDF,IDW,F)
WRITE(6,111)KNAME,INAME,JNAME,RC,IDF,XMS,F,PROB
WRITE(6,112)SSW,IDW,SMW
112 FORMAT(//7X,'WITHIN',7X,F15.2,I5,F15.2)
RETURN
END
C
C PRINT OUT MEANS
C
C---------------ALL ARGUMENTS ARE INPUT.
SUBROUTINE PRINT(IMAX,JMAX,KMAX,XI,XJ,XK,XIJ,XJK,XIK,XIJK,NI,
1NJ,NK,NIJ,NJK,NIK,NIJK,SUM,N,INAME,JNAME,KNAME,XXIJK)
DIMENSION XI(1),XJ(1),XK(1),XIJ(1),XJK(1),XIK(1),XIJK(1),NI(1)
1,NJ(1),NK(1),NIJ(1),NJK(1),NIK(1),NIJK(1),XXIJK(1)
311 GMEAN=SUM/FLOAT(N)
WRITE(6,601)INAME,JNAME ,KNAME
601 FORMAT(///,10X,A1,3X,A1,3X,A1,6X,'MEAN',13X,'STD DEV',5X,'N'/)
DO 602 I=1,IMAX
DO 602 J=1,JMAX
DO 602 K=1,KMAX
IND=I+(J-1+(K-1)*JMAX)*IMAX
IF(NIJK(IND).EQ.0)GO TO 667
STDV=SQRT(XXIJK(IND))
XX=XIJK(IND)/FLOAT(NIJK(IND))
WRITE(6,603)I,J,K,XX,STDV,NIJK(IND)
603 FORMAT(9X,I3,1X,I3,1X,I3,G,F15.7,I5)
GO TO 602
667 WRITE(6,668)I,J,K,NIJK(IND)
668 FORMAT(9X,I3,1X,I3,1X,I3,30X,I5)
602 CONTINUE
DO 604 I=1,IMAX
DO 604 J=1,JMAX
IND=I+(J-1)*IMAX
XX=XIJ(IND)/FLOAT(NIJ(IND))
604 WRITE(6,605)I,J,XX,NIJ(IND)
605 FORMAT(9X,I3,1X,I3,1X,' .',G,15X,I5)
DO 606 I=1,IMAX
DO 606 K=1,KMAX
IND=I+(K-1)*IMAX
XX=XIK(IND)/FLOAT(NIK(IND))
606 WRITE(6,607)I,K,XX,NIK(IND)
607 FORMAT(9X,I3,1X,' .',1X,I3,G,15X,I5)
DO 608 J=1,JMAX
DO 608 K=1,KMAX
IND=J+(K-1)*JMAX
XX=XJK(IND)/FLOAT(NJK(IND))
608 WRITE(6,609)J,K,XX,NJK(IND)
609 FORMAT(9X,' .',1X,I3,1X,I3,G,15X,I5)
DO 610 I=1,IMAX
XX=XI(I)/FLOAT(NI(I))
610 WRITE(6,611)I,XX,NI(I)
611 FORMAT(9X,I3,1X,' .',1X,' .',G,15X,I5)
DO 612 J=1,JMAX
XX=XJ(J)/FLOAT(NJ(J))
612 WRITE(6,613)J,XX,NJ(J)
613 FORMAT(9X,' .',1X,I3,1X,' .',G,15X,I5)
DO 614 K=1,KMAX
XX=XK(K)/FLOAT(NK(K))
614 WRITE(6,615)K,XX,NK(K)
615 FORMAT(9X,' .',1X,' .',1X,I3,G,15X,I5)
WRITE(6,616)GMEAN,N
616 FORMAT(9X,' .',1X,' .',1X,' .',G,15X,I5)
RETURN
END
C
C WEIGHTED MEANS ANALYSIS
C
C---------------YS, XN1, XN2, XN3, YT, YR ARE RETURNED OTHER ARGS.
C--------------- ARE INPUT.
SUBROUTINE WEIGH(IMAX,JMAX,KMAX,NIJK,XIJK,INAME,JNAME,KNAME,
1XN1,XN2,XN3,YR,YS,YT,SSINT,SSTOT,SE,N)
DIMENSION NIJK(1),XIJK(1),XN1(1),XN2(1),XN3(1),YR(1),YS(1),YT(1)
XN=0.0
XD=0.0
DO 1 I=1,IMAX
XNTL=0.0
ZNTL=0.0
DO 2 J=1,JMAX
DO 3 K=1,KMAX
IJK=I+(J-1+(K-1)*JMAX)*IMAX
XNTL=XNTL+1.0/FLOAT(NIJK(IJK))
ZNTL=ZNTL+XIJK(IJK)/NIJK(IJK)
3 CONTINUE
2 CONTINUE
XN1(I)=FLOAT(JMAX*JMAX*KMAX*KMAX)/XNTL
YR(I)=ZNTL/FLOAT(JMAX*KMAX)
XN=XN+XN1(I)*YR(I)
XD=XD+XN1(I)
1 CONTINUE
CCR=XN/XD
XN=0.0
XD=0.0
DO 4 J=1,JMAX
ZNTL=0.0
XNTL=0.0
DO 5 I=1,IMAX
DO 6 K=1,KMAX
IJK=I+(J-1+(K-1)*JMAX)*IMAX
XNTL=XNTL+1.0/FLOAT(NIJK(IJK))
ZNTL=ZNTL+XIJK(IJK)/FLOAT(NIJK(IJK))
6 CONTINUE
5 CONTINUE
XN2(J)=FLOAT(IMAX*IMAX*KMAX*KMAX)/XNTL
YS(J)=ZNTL/FLOAT(IMAX*KMAX)
XN=XN+XN2(J)*YS(J)
XD=XD+XN2(J)
4 CONTINUE
CCS=XN/XD
XN=0.0
XD=0.0
DO 7 K=1,KMAX
ZNTL=0.0
XNTL=0.0
DO 8 I=1,IMAX
DO 9 J=1,JMAX
IJK=I+(J-1+(K-1)*JMAX)*IMAX
XNTL=XNTL+1.0/FLOAT(NIJK(IJK))
ZNTL=ZNTL+XIJK(IJK)/FLOAT(NIJK(IJK))
9 CONTINUE
8 CONTINUE
XN3(K)=FLOAT(IMAX*IMAX*JMAX*JMAX)/XNTL
YT(K)=ZNTL/FLOAT(IMAX*JMAX)
XN=XN+XN3(K)*YT(K)
XD=XD+XN3(K)
7 CONTINUE
CCT=XN/XD
SSR=0.0
DO 10 I=1,IMAX
10 SSR=SSR+XN1(I)*((YR(I)-CCR)**2)
SSS=0.0
DO 11 J=1,JMAX
11 SSS=SSS+XN2(J)*((YS(J)-CCS)**2)
SST=0.0
DO 12 K=1,KMAX
12 SST=SST+XN3(K)*((YT(K)-CCT)**2)
WRITE(6,100)
100 FORMAT(///,22X,'THREE WAY WEIGHTED MEANS ANOVA')
WRITE(6,101)
101 FORMAT(/4X,'SOURCE',9X,'SUM OF SQUARES DF',4X,'MEAN SQUARE',5X,
1'F PROB')
IDF=IMAX-1
XMS=SSR/FLOAT(IDF)
IDW=N-IMAX*JMAX*KMAX
SMW=SE/FLOAT(IDW)
F=XMS/SMW
PROB=FISHER (IDF,IDW,F)
WRITE(6,102)INAME,SSR,IDF,XMS,F,PROB
102 FORMAT(/6X,A1,10X,F15.2,I5,F15.2,F7.2,F6.3)
IDF=JMAX-1
XMS=SSS/FLOAT(IDF)
F=XMS/SMW
PROB=FISHER(IDF,IDW,F)
WRITE(6,102)JNAME,SSS,IDF,XMS,F,PROB
IDF=KMAX-1
XMS=SST/FLOAT(IDF)
F=XMS/SMW
PROB=FISHER(IDF,IDW,F)
WRITE(6,102)KNAME,SST,IDF,XMS,F,PROB
IDF=IMAX*JMAX*KMAX-IMAX-JMAX-KMAX+2
XMS=SSINT/FLOAT(IDF)
F=XMS/SMW
PROB=FISHER(IDF,IDW,F)
WRITE(6,103)SSINT,IDF,XMS,F,PROB
103 FORMAT(/3X,'INTERACTION',3X,F15.2,I5,F15.2,F7.2,F6.3)
WRITE(6,104)SE,IDW,SMW
104 FORMAT(/5X,'WITHIN',6X,F15.2,I5,F15.2)
IDF=N-1
WRITE(6,105)SSTOT,IDF
105 FORMAT(/5X,'TOTAL',7X,F15.2,I5)
RETURN
END
C
C UNWEIGHTED MEANS ANALYSIS
C
C---------------XI, XJ, XK, XIJ, XJK, XIK ARE MODIFIED. OTHER
C--------------- ARGS. ARE INPUT WITHOUT MODIFICATION.
SUBROUTINE UNWEI(IMAX,JMAX,KMAX,XI,XJ,XK,XIJ,XJK,XIK,XIJK,
1NI,NJ,NK,NIJ,NJK,NIK,NIJK,SSTOT,SSW,N,INAME,JNAME,KNAME)
DIMENSION XI(1),XJ(1),XK(1),XIJ(1),XJK(1),XIK(1),XIJK(1),NI(1),
1NJ(1),NK(1),NIJ(1),NJK(1),NIK(1),NIJK(1)
MX=IMAX*JMAX*KMAX
XN=0.0
DO 100 I=1,MX
XN=XN+1.0/FLOAT(NIJK(I))
100 XIJK(I)=XIJK(I)/FLOAT(NIJK(I))
XN=XN/FLOAT(MX)
KIND=0
IF(N.EQ.MX)KIND=1
SUM=0.0
DO 309 I=1,MX
309 SUM=SUM+XIJK(I)
CTT=SUM**2/MX
C
C REINITIALIZE CERTAIN VALUES
C
DO 909 I=1,IMAX
909 XI(I)=0.0
DO 910 J=1,JMAX
910 XJ(J)=0.0
DO 911 K=1,KMAX
911 XK(K)=0.0
DO 912 I=1,IMAX*JMAX
912 XIJ(I)=0.0
DO 913 I=1,JMAX*KMAX
913 XJK(I)=0.0
DO 914 I=1,IMAX*KMAX
914 XIK(I)=0.0
SSI=0.0
SSJ=0.0
SSK=0.0
SSIJ=0.0
SSIK=0.0
SSJK=0.0
SSIJK=0.0
C
C CALCULATE MARGINAL SUMS
C
DO 301 I=1,IMAX
DO 301 J=1,JMAX
IJ=I+(J-1)*IMAX
DO 302 K=1,KMAX
IJK=I+(J-1+(K-1)*JMAX)*IMAX
XIJ(IJ)=XIJ(IJ)+XIJK(IJK)
302 XI(I)=XI(I)+XIJK(IJK)
301 CONTINUE
DO 303 J=1,JMAX
DO 304 K=1,KMAX
JK=J+(K-1)*JMAX
DO 305 I=1,IMAX
IJK=I+(J-1+(K-1)*JMAX)*IMAX
XJK(JK)=XJK(JK)+XIJK(IJK)
305 XJ(J)=XJ(J)+XIJK(IJK)
304 CONTINUE
303 CONTINUE
DO 306 K=1,KMAX
DO 307 I=1,IMAX
IK=I+(K-1)*IMAX
DO 308 J=1,JMAX
IJK=I+(J-1+(K-1)*JMAX)*IMAX
XIK(IK)=XIK(IK)+XIJK(IJK)
308 XK(K)=XK(K)+XIJK(IJK)
307 CONTINUE
306 CONTINUE
C
C COMPUTE MAIN EFFECTS AND INTERACTIONS
C
SSC=0.0
DO 500 I=1,MX
500 SSC=SSC+XIJK(I)**2
MX=IMAX*JMAX
DO 501 I=1,MX
501 SSIJ=SSIJ+XIJ(I)**2
MX=JMAX*KMAX
DO 502 I=1,MX
502 SSJK=SSJK+XJK(I)**2
MX=IMAX*KMAX
DO 503 I=1,MX
503 SSIK=SSIK+XIK(I)**2
DO 504 I=1,IMAX
504 SSI=SSI+XI(I)**2
DO 505 I=1,JMAX
505 SSJ=SSJ+XJ(I)**2
DO 506 I=1,KMAX
506 SSK=SSK+XK(I)**2
XN=1.0/XN
SSC=(SSC-CTT)*XN
SSI=(SSI/FLOAT(JMAX*KMAX)-CTT)*XN
SSJ=(SSJ/FLOAT(IMAX*KMAX)-CTT)*XN
SSK=(SSK/FLOAT(IMAX*JMAX)-CTT)*XN
SSIJ=(SSIJ/FLOAT(KMAX)-CTT)*XN-SSI-SSJ
SSJK=(SSJK/FLOAT(IMAX)-CTT)*XN-SSJ-SSK
SSIK=(SSIK/FLOAT(JMAX)-CTT)*XN-SSI-SSK
SSIJK=SSC-SSI-SSJ-SSK-SSIJ-SSIK-SSJK
C
C CALCULATE AND PRINT ANOVA
C
WRITE(6,700)XN
700 FORMAT(/20X,'H.M. CELL SIZE = ',F10.5)
IDW=N-IMAX*JMAX*KMAX
IF(KIND.EQ.1)IDW=(IMAX-1)*(JMAX-1)*(KMAX-1)
SS=SSW
IF(KIND.EQ.1)SS=SSIJK
SMW=SS/FLOAT(IDW)
WRITE(6,702)
702 FORMAT(/7X,'SOURCE',4X,'SUM OF SQUARES',4X,'DF',3X,'MEAN SQUARE',7
1X'F',5X,'PROB')
IDF=IMAX*JMAX*KMAX-1
SM=SSC/FLOAT(IDF)
F=SM/SMW
PROB=FISHER(IDF,IDW,F)
WRITE(6,703)SSC,IDF,SM,F,PROB
703 FORMAT(/4X,'SUBCLASSES',2X,F15.2,I6,F15.2,F9.3,F8.3)
IDF=IMAX-1
SM=SSI/FLOAT(IDF)
F=SM/SMW
PROB=FISHER(IDF,IDW,F)
WRITE(6,704)INAME,SSI,IDF,SM,F,PROB
704 FORMAT(/8X,A1,7X,F15.2,I6,F15.2,F9.3,F8.3)
IDF=JMAX-1
SM=SSJ/FLOAT(IDF)
F=SM/SMW
PROB=FISHER(IDF,IDW,F)
WRITE(6,704)JNAME,SSJ,IDF,SM,F,PROB
IDF=KMAX-1
SM=SSK/FLOAT(IDF)
F=SM/SMW
PROB=FISHER(IDF,IDW,F)
WRITE(6,704)KNAME,SSK,IDF,SM,F,PROB
IDF=(IMAX-1)*(JMAX-1)
SM=SSIJ/FLOAT(IDF)
F=SM/SMW
PROB=FISHER(IDF,IDW,F)
WRITE(6,705)INAME,JNAME,SSIJ,IDF,SM,F,PROB
705 FORMAT(/8X,2A1,6X,F15.2,I6,F15.2,F9.3,F8.3)
IDF=(IMAX-1)*(KMAX-1)
SM=SSIK/FLOAT(IDF)
F=SM/SMW
PROB=FISHER(IDF,IDW,F)
WRITE(6,705)INAME,KNAME,SSIK,IDF,SM,F,PROB
IDF=(JMAX-1)*(KMAX-1)
SM=SSJK/FLOAT(IDF)
F=SM/SMW
PROB=FISHER(IDF,IDW,F)
WRITE(6,705)JNAME,KNAME,SSJK,IDF,SM,F,PROB
IF(KIND.EQ.1)GO TO 710
IDF=(IMAX-1)*(JMAX-1)*(KMAX-1)
SM=SSIJK/FLOAT(IDF)
F=SM/SMW
PROB=FISHER(IDF,IDW,F)
WRITE(6,706)INAME,JNAME,KNAME,SSIJK,IDF,SM,F,PROB
706 FORMAT(/8X,3A1,5X,F15.2,I6,F15.2,F9.3,F8.3)
WRITE(6,707)SSW,IDW,SMW
707 FORMAT(/6X,'WITHIN',4X,F15.2,I6,F15.2)
GO TO 711
710 WRITE(6,706)INAME,JNAME,KNAME,SSIJK,IDW,SMW
711 RETURN
END
C**** WMU-AM: #1.9.3, MOD=1, MTO, 23-SEP-77 ****
C
C
C PROPORTIONAL ANALYSIS
C (WRITTEN BY DR. MICHAEL R. STOLINE, WMU, SEP-77)
C
C
C---------------ALL ARGS. ARE INPUT.
SUBROUTINE PROP(IMAX,JMAX,KMAX,XI,XJ,XK,XIJ,XIK,XJK,
1 XIJK,NI,NJ,NK,NIJ,NJK,NIK,NIJK,SSTOT,SSW,N,CT,SSC)
DIMENSION XI(1),XJ(1),XK(1),XIJ(1),XIK(1),XJK(1),XIJK(1),
1 NI(1),NJ(1),NK(1),NIJ(1),NJK(1),NIK(1),NIJK(1)
SSI=0.
SSJ=0.
SSK=0.
SSIJ=0.
SSIK=0.
SSJK=0.
SSIJK=0.
DO 1 I=1,IMAX
1 SSI=SSI+(XI(I)**2.)/NI(I)
SSI=SSI-CT
DO 2 J=1,JMAX
2 SSJ=SSJ+(XJ(J)**2.)/NJ(J)
SSJ=SSJ-CT
DO 3 K=1,KMAX
3 SSK=SSK+(XK(K)**2.)/NK(K)
SSK=SSK-CT
DO 4 I=1,IMAX
DO 4 J=1,JMAX
IJ=I+(J-1)*IMAX
4 SSIJ=SSIJ+(XIJ(IJ)**2.)/NIJ(IJ)
DO 5 I=1,IMAX
DO 5 K=1,KMAX
IK=I+(K-1)*IMAX
5 SSIK=SSIK+(XIK(IK)**2.)/NIK(IK)
DO 6 J=1,JMAX
DO 6 K=1,KMAX
JK=J+(K-1)*JMAX
6 SSJK=SSJK+(XJK(JK)**2.)/NJK(JK)
SSIJ=SSIJ-CT
SSIK=SSIK-CT
SSJK=SSJK-CT
SSIJ=SSIJ-SSI-SSJ
SSIK=SSIK-SSI-SSK
SSJK=SSJK-SSJ-SSK
SSIJK=SSC-SSI-SSJ-SSK-SSIJ-SSIK-SSJK
IDF=IMAX-1
JDF=JMAX-1
KDF=KMAX-1
IJDF=IDF*JDF
IKDF=IDF*KDF
JKDF=JDF*KDF
IJKDF=IJDF*KDF
MSDF=N-IMAX*JMAX*KMAX
NM1=N-1
WRITE(6,101)
WRITE(6,102)SSI,IDF,SSJ,JDF,SSK,KDF,SSIJ,IJDF,SSIK,IKDF,
1 SSJK,JKDF,SSIJK,IJKDF,SSW,MSDF,SSTOT,NM1
101 FORMAT(/'0 THE SAMPLE SIZES ARE PROPORTIONAL. THE SUMS'/
1 ' OF SQUARES ARE DECOMPOSABLE INTO MAIN EFFECTS SUMS'/
1 ' OF SQUARES AND INTERACTION SUMS OF SQUARES, AS IN'/
1 ' THE BALANCED CASE. HOWEVER, THE USUAL F-TESTS ARE'/
1 ' NOT VALID IN THE PROPORTIONAL CASE, SO THESE TESTS'/
1 ' ARE NOT GIVEN IN THE PROPORTIONAL AOV TABLE. A COM-'/
1 ' PLICATED EXACT ANALYSIS FOR PROPORTIONAL CASES IS'/
1 ' DESCRIBED IN BANCROFT, BUT IS NOT GIVEN HERE.'/
1 ' A SUITABLE APPROXIMATE ANALYSIS FOR PROPORTIONAL'/
1 ' CASES IS THE LEAST SQUARES(FITTING CONSTANTS) METHOD'/
1 ' GIVEN HERE.'///
1 20X,'PROPORTIONAL AOV TABLE'///
1 ' SOURCE',T15,'SUM OF SQUARES',T35,'DEGREES OF FREEDOM'/
1 ' ------',T15,'--------------',T35,'------------------')
102 FORMAT (' A',T15,F11.3,T35,I11/
1 ' B',T15,F11.3,T35,I11/
1 ' C',T15,F11.3,T35,I11/
1 ' AB',T15,F11.3,T35,I11/
1 ' AC',T15,F11.3,T35,I11/
1 ' BC',T15,F11.3,T35,I11/
1 ' ABC',T15,F11.3,T35,I11/
1 ' WITHIN',T15,F11.3,T35,I11/
1 1X,51('-')/
1 ' TOTAL',T15,F11.3,T35,I11//)
C**** END = PROP, NEW-ROUTINE ****
END