C KRAN 10
C ..................................................................KRAN 20
C KRAN 30
C SUBROUTINE KRANK KRAN 40
C KRAN 50
C PURPOSE KRAN 60
C TEST CORRELATION BETWEEN TWO VARIABLES BY MEANS OF KENDALL KRAN 70
C RANK CORRELATION COEFFICIENT KRAN 80
C KRAN 90
C USAGE KRAN 100
C CALL KRANK(A,B,R,N,TAU,SD,Z,NR) KRAN 110
C KRAN 120
C DESCRIPTION OF PARAMETERS KRAN 130
C A - INPUT VECTOR OF N OBSERVATIONS FOR FIRST VARIABLE KRAN 140
C B - INPUT VECTOR OF N OBSERVATIONS FOR SECOND VARIABLE KRAN 150
C R - OUTPUT VECTOR OF RANKED DATA OF LENGTH 2*N. SMALLEST KRAN 160
C OBSERVATION IS RANKED 1, LARGEST IS RANKED N. TIES KRAN 170
C ARE ASSIGNED AVERAGE OF TIED RANKS. KRAN 180
C N - NUMBER OF OBSERVATIONS KRAN 190
C TAU - KENDALL RANK CORRELATION COEFFICIENT (OUTPUT) KRAN 200
C SD - STANDARD DEVIATION (OUTPUT) KRAN 210
C Z - TEST OF SIGNIFICANCE OF TAU IN TERMS OF NORMAL KRAN 220
C DISTRIBUTION (OUTPUT) KRAN 230
C NR - CODE, 0 FOR UNRANKED DATA IN A AND B, 1 FOR RANKED KRAN 240
C DATA IN A AND B (INPUT) KRAN 250
C KRAN 260
C REMARKS KRAN 270
C SD AND Z ARE SET TO ZERO IF N IS LESS THAN TEN KRAN 280
C KRAN 290
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED KRAN 300
C RANK KRAN 310
C TIE KRAN 320
C KRAN 330
C METHOD KRAN 340
C DESCRIBED IN S. SIEGEL, 'NONPARAMETRIC STATISTICS FOR THE KRAN 350
C BEHAVIORAL SCIENCES', MCGRAW-HILL, NEW YORK, 1956, KRAN 360
C CHAPTER 9 KRAN 370
C KRAN 380
C ..................................................................KRAN 390
C KRAN 400
SUBROUTINE KRANK(A,B,R,N,TAU,SD,Z,NR) KRAN 410
DIMENSION A(1),B(1),R(1) KRAN 420
C KRAN 430
SD=0.0 KRAN 440
Z=0.0 KRAN 450
FN=N KRAN 460
FN1=N*(N-1) KRAN 470
C KRAN 480
C DETERMINE WHETHER DATA IS RANKED KRAN 490
C KRAN 500
IF(NR-1) 5, 10, 5 KRAN 510
C KRAN 520
C RANK DATA IN A AND B VECTORS AND ASSIGN TIED OBSERVATIONS KRAN 530
C AVERAGE OF TIED RANKS KRAN 540
C KRAN 550
5 CALL RANK (A,R,N) KRAN 560
CALL RANK (B,R(N+1),N) KRAN 570
GO TO 40 KRAN 580
C KRAN 590
C MOVE RANKED DATA TO R VECTOR KRAN 600
C KRAN 610
10 DO 20 I=1,N KRAN 620
20 R(I)=A(I) KRAN 630
DO 30 I=1,N KRAN 640
J=I+N KRAN 650
30 R(J)=B(I) KRAN 660
C KRAN 670
C SORT RANK VECTOR R IN SEQUENCE OF VARIABLE A KRAN 680
C KRAN 690
40 ISORT=0 KRAN 700
DO 50 I=2,N KRAN 710
IF(R(I)-R(I-1)) 45,50,50 KRAN 720
45 ISORT=ISORT+1 KRAN 730
RSAVE=R(I) KRAN 740
R(I)=R(I-1) KRAN 750
R(I-1)=RSAVE KRAN 760
I2=I+N KRAN 770
SAVER=R(I2) KRAN 780
R(I2)=R(I2-1) KRAN 790
R(I2-1)=SAVER KRAN 800
50 CONTINUE KRAN 810
IF(ISORT) 40,55,40 KRAN 820
C KRAN 830
C COMPUTE S ON VARIABLE B. STARTING WITH THE FIRST RANK, ADD 1 KRAN 840
C TO S FOR EACH LARGER RANK TO ITS RIGHT AND SUBTRACT 1 FOR EACH KRAN 850
C SMALLER RANK. REPEAT FOR ALL RANKS. KRAN 860
C KRAN 870
55 S=0.0 KRAN 880
NM=N-1 KRAN 890
DO 60 I=1,NM KRAN 900
J=N+I KRAN 910
DO 60 L=I,N KRAN 920
K=N+L KRAN 930
IF(R(K)-R(J)) 56,60,57 KRAN 940
56 S=S-1.0 KRAN 950
GO TO 60 KRAN 960
57 S=S+1.0 KRAN 970
60 CONTINUE KRAN 980
C KRAN 990
C COMPUTE TIED SCORE INDEX FOR BOTH VARIABLES KRAN1000
C KRAN1010
KT=2 KRAN1020
CALL TIE(R,N,KT,TA) KRAN1030
CALL TIE(R(N+1),N,KT,TB) KRAN1040
C KRAN1050
C COMPUTE TAU KRAN1060
C KRAN1070
IF(TA) 70,65,70 KRAN1080
65 IF(TB) 70,67,70 KRAN1090
67 TAU=S/(0.5*FN1) KRAN1100
GO TO 80 KRAN1110
70 TAU=S/((SQRT(0.5*FN1-TA))*(SQRT(0.5*FN1-TB))) KRAN1120
C KRAN1130
C COMPUTE STANDARD DEVIATION AND Z IF N IS 10 OR LARGER KRAN1140
C KRAN1150
80 IF(N-10) 90,85,85 KRAN1160
85 SD=(SQRT((2.0*(FN+FN+5.0))/(9.0*FN1))) KRAN1170
Z=TAU/SD KRAN1180
90 RETURN KRAN1190
END KRAN1200