C MPAI 10
C ..................................................................MPAI 20
C MPAI 30
C SUBROUTINE MPAIR MPAI 40
C MPAI 50
C PURPOSE MPAI 60
C PERFORM THE WILCOXON MATCHED-PAIRS SIGNED-RANKS TEST, GIVEN MPAI 70
C TWO VECTORS OF N OBSERVATIONS OF THE MATCHED SAMPLES. MPAI 80
C MPAI 90
C USAGE MPAI 100
C CALL MPAIR (N,A,B,K,T,Z,P,D,E,L,IE) MPAI 110
C MPAI 120
C DESCRIPTION OF PARAMETERS MPAI 130
C N - NUMBER OF OBSERVATIONS IN THE VECTORS A AND B MPAI 140
C A - INPUT VECTOR OF LENGTH N CONTAINING DATA FROM THE FIRST MPAI 150
C SAMPLE MPAI 160
C B - INPUT VECTOR OF LENGTH N CONTAINING DATA FROM THE SECONDMPAI 170
C SAMPLE MPAI 180
C K - OUTPUT VARIABLE CONTAINING THE NUMBER OF PAIRS OF THE MPAI 190
C MATCHED SAMPLES WHOSE DIFFERENCES ARE NON ZERO (0) MPAI 200
C T - OUTPUT VARIABLE CONTAINING THE SUM OF THE RANKS OF PLUS MPAI 210
C OR MINUS DIFFERENCES, WHICHEVER IS SMALLER MPAI 220
C Z - VALUE OF THE STANDARDIZED NORMAL SCORE COMPUTED FOR THE MPAI 230
C WILCOXON MATCHED-PAIRS SIGNED-RANKS TEST MPAI 240
C P - COMPUTED PROBABILITY OF OBTAINING A VALUE OF Z AS MPAI 250
C EXTREME AS THE ONE FOUND BY THE TEST MPAI 260
C D - WORKING VECTOR OF LENGTH N MPAI 270
C E - WORKING VECTOR OF LENGTH N MPAI 280
C L - WORKING VECTOR OF LENGTH N MPAI 290
C IE- 1, IF SAMPLES A AND B ARE IDENTICAL. MPAI 300
C 0 OTHERWISE. IF IE=1, THEN T=P=0, AND Z=-10**75 MPAI 310
C MPAI 320
C REMARKS MPAI 330
C THE COMPUTED PROBABILTY IS FOR A ONE-TAILED TEST. MPAI 340
C MULTIPLYING P BY 2 WILL GIVE THE VALUE FOR A TWO-TAILED MPAI 350
C TEST. MPAI 360
C MPAI 370
C SUBROUTINES AND FUNCTIONS SUBPROGRAMS REQUIRED MPAI 380
C RANK MPAI 390
C NDTR MPAI 400
C MPAI 410
C METHOD MPAI 420
C REFER TO DIXON AND MASSEY, AN INTRODUCTION TO STATISTICAL MPAI 430
C ANALYSIS (MC GRAW-HILL, 1957) MPAI 440
C MPAI 450
C ..................................................................MPAI 460
C MPAI 470
SUBROUTINE MPAIR (N,A,B,K,T,Z,P,D,E,L,IE) MPAI 480
C MPAI 490
DIMENSION A(1),B(1),D(1),E(1),L(1) MPAI 500
C MPAI 510
IE=0 MPAI 520
K=N MPAI 530
C MPAI 540
C FIND DIFFERENCES OF MATCHED-PAIRS MPAI 550
C MPAI 560
BIG=0.0 MPAI 570
DO 55 I=1,N MPAI 580
DIF=A(I)-B(I) MPAI 590
IF(DIF) 10, 20, 30 MPAI 600
C MPAI 610
C DIFFERENCE HAS A NEGATIVE SIGN (-) MPAI 620
C MPAI 630
10 L(I)=1 MPAI 640
GO TO 40 MPAI 650
C MPAI 660
C DIFFERENCE IS ZERO (0) MPAI 670
C MPAI 680
20 L(I)=2 MPAI 690
K=K-1 MPAI 700
GO TO 40 MPAI 710
C MPAI 720
C DIFFERENCE HAS A POSITIVE SIGN (+) MPAI 730
C MPAI 740
30 L(I)=3 MPAI 750
C MPAI 760
40 DIF= ABS(DIF) MPAI 770
IF(BIG-DIF) 45, 50, 50 MPAI 780
45 BIG=DIF MPAI 790
50 D(I)=DIF MPAI 800
C MPAI 810
55 CONTINUE MPAI 820
IF(K) 57,57,59 MPAI 830
57 IE=1 MPAI 840
T=0.0 MPAI 850
Z=-1.7E38 MPAI 860
P=0 MPAI 870
GO TO 100 MPAI 880
C MPAI 890
C STORE A LARGE VALUE IN PLACE OF 0 DIFFERENCE IN ORDER TO MPAI 900
C ASSIGN A LARGE RANK (LARGER THAN K), SO THAT ABSOLUTE VALUES MPAI 910
C OF SIGNED DIFFERENCES WILL BE PROPERLY RANKED MPAI 920
C MPAI 930
59 BIG=BIG*2.0 MPAI 940
DO 65 I=1,N MPAI 950
IF(L(I)-2) 65, 60, 65 MPAI 960
60 D(I)=BIG MPAI 970
65 CONTINUE MPAI 980
C MPAI 990
CALL RANK (D,E,N) MPAI1000
C MPAI1010
C FIND SUMS OF RANKS OF (+) DIFFERENCES AND (-) DIFFERENCES MPAI1020
C MPAI1030
SUMP=0.0 MPAI1040
SUMM=0.0 MPAI1050
DO 80 I=1,N MPAI1060
IF(L(I)-2) 70, 80, 75 MPAI1070
70 SUMM=SUMM+E(I) MPAI1080
GO TO 80 MPAI1090
75 SUMP=SUMP+E(I) MPAI1100
80 CONTINUE MPAI1110
C MPAI1120
C SET T = SMALLER SUM MPAI1130
C MPAI1140
IF(SUMP-SUMM) 85, 85, 90 MPAI1150
85 T=SUMP MPAI1160
GO TO 95 MPAI1170
90 T=SUMM MPAI1180
C MPAI1190
C COMPUTE MEAN, STANDARD DEVIATION, AND Z MPAI1200
C MPAI1210
95 FK=K MPAI1220
U=FK*(FK+1.0)/4.0 MPAI1230
S= SQRT((FK*(FK+1.0)*(2.0*FK+1.0))/24.0) MPAI1240
Z=(T-U)/S MPAI1250
C MPAI1260
C COMPUTE THE PROBABILITY OF A VALUE AS EXTREME AS Z MPAI1270
C MPAI1280
CALL NDTR (Z,P,BIG) MPAI1290
C MPAI1300
100 RETURN MPAI1310
END MPAI1320