C SIGN 10
C ..................................................................SIGN 20
C SIGN 30
C SUBROUTINE SIGNT SIGN 40
C SIGN 50
C PURPOSE SIGN 60
C TO PERFORM A NON-PARAMETRIC SIGN TEST, GIVEN TWO SETS OF SIGN 70
C MATCHED OBSERVATIONS. IT TESTS THE NULL HYPOTHESIS THAT THESIGN 80
C DIFFERENCES BETWEEN EACH PAIR OF MATCHED OBSERVATIONS HAS A SIGN 90
C MEDIAN EQUAL TO ZERO. SIGN 100
C SIGN 110
C USAGE SIGN 120
C CALL SIGNT (N,A,B,K,M,P,IE) SIGN 130
C SIGN 140
C DESCRIPTION OF PARAMETERS SIGN 150
C N - NUMBER OF OBSERVATIONS IN SETS A AND B SIGN 160
C A - INPUT VECTOR OF LENGTH N CONTAINING DATA FROM THE FIRST SIGN 170
C SAMPLE, A SIGN 180
C B - INPUT VECTOR OF LENGTH N CONTAINING DATA FROM THE SECONDSIGN 190
C SAMPLE, B SIGN 200
C K - OUTPUT VARIABLE CONTAINING THE NUMBER OF PAIRS OF SIGN 210
C OBSERVATIONS FROM THE TWO SAMPLES WHOSE DIFFERENCES ARE SIGN 220
C NON-ZERO SIGN 230
C M - OUTPUT VARIABLE CONTAINING THE NUMBER OF PLUS OR MINUS SIGN 240
C DIFFERENCES, WHICHEVER IS FEWER. SIGN 250
C P - COMPUTED PROBABILITY OF AS FEW AS M NUMBER OF PAIRS SIGN 260
C HAVING THE SAME SIGN, ASSUMING THAT THE SAMPLES CAME SIGN 270
C FROM THE SAME POPULATION. SIGN 280
C IE- 0, IF THERE IS NO ERROR. SIGN 290
C 1, IF K IS ZERO. IN THIS CASE, P IS SET TO 1.0 AND SIGN 300
C M TO 0. SIGN 310
C SIGN 320
C REMARKS SIGN 330
C IF K IS LESS THAN OR EQUAL TO 25, THE PROBABILITY WILL BE SIGN 340
C COMPUTED USING THE BINOMIAL DISTRIBUTION. IF K IS GREATER SIGN 350
C THAN 25, THE PROBABILITY WILL BE COMPUTED USING THE NORMAL SIGN 360
C APPROXIMATION TO THE BINOMIAL DISTRIBUTION. SIGN 370
C P COMPUTED IS THE PROBABILITY FOR A ONE-TAILED TEST. THUS, SIGN 380
C FOR A TWO TAILED TEST, DOUBLE THE VALUE FOR P. SIGN 390
C SIGN 400
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED SIGN 410
C NDTR SIGN 420
C SIGN 430
C METHOD SIGN 440
C REFER TO DIXON AND MASSEY, INTRODUCTION TO STATISTICAL SIGN 450
C ANALYSIS (MCGRAW-HILL, 1957). SIGN 460
C SIGN 470
C ..................................................................SIGN 480
C SIGN 490
SUBROUTINE SIGNT (N,A,B,K,M,P,IE) SIGN 500
C SIGN 510
DIMENSION A(1),B(1) SIGN 520
DOUBLE PRECISION FN,FD SIGN 530
C SIGN 540
C INITIALIZATION SIGN 550
C SIGN 560
IE=0 SIGN 570
K=0 SIGN 580
MPLUS=0 SIGN 590
MMINS=0 SIGN 600
C SIGN 610
C FIND (+) OR (-) DIFFERENCE SIGN 620
C SIGN 630
DO 40 I=1,N SIGN 640
D=A(I)-B(I) SIGN 650
IF(D) 20, 40, 30 SIGN 660
C SIGN 670
C (-) DIFFERENCE SIGN 680
C SIGN 690
20 K=K+1 SIGN 700
MMINS=MMINS+1 SIGN 710
GO TO 40 SIGN 720
C SIGN 730
C (+) DIFFERENCE SIGN 740
C SIGN 750
30 K=K+1 SIGN 760
MPLUS=MPLUS+1 SIGN 770
C SIGN 780
40 CONTINUE SIGN 790
IF(K) 41,41,42 SIGN 800
41 IE=1 SIGN 810
P=1.0 SIGN 820
M=0 SIGN 830
GO TO 95 SIGN 840
42 FK=K SIGN 850
C SIGN 860
C FIND THE NUMBER OF FEWER SIGNS SIGN 870
C SIGN 880
IF(MPLUS-MMINS) 45, 45, 50 SIGN 890
45 M=MPLUS SIGN 900
GO TO 55 SIGN 910
50 M=MMINS SIGN 920
C SIGN 930
C TEST WHETHER K IS GREATER THAN 25 SIGN 940
C SIGN 950
55 IF(K-25) 60, 60, 77 SIGN 960
C SIGN 970
C K IS LESS THAN OR EQUAL TO 25 SIGN 980
C SIGN 990
60 P=1.0 SIGN1000
IF(M) 75, 75, 65 SIGN1010
65 FN=1.0 SIGN1020
FD=1.0 SIGN1030
DO 70 I=1,M SIGN1040
FI=I SIGN1050
FN=FN*(FK-(FI-1.0)) SIGN1060
FD=FD*FI SIGN1070
70 P=P+FN/FD SIGN1080
C SIGN1090
75 P=P/(2.0**K) SIGN1100
GO TO 95 SIGN1110
C SIGN1120
C K IS GREATER THAN 25. COMPUTE MEAN, STANDARD DEVIATION, AND Z SIGN1130
C SIGN1140
77 U=0.5*FK SIGN1150
S=0.5*SQRT(FK) SIGN1160
FM=M SIGN1170
IF(FM-U) 80, 85, 85 SIGN1180
80 CON=0.5 SIGN1190
GO TO 90 SIGN1200
85 CON=0.0 SIGN1210
90 Z=(FM+CON-U)/S SIGN1220
C SIGN1230
C COMPUTE P ASSOCIATED WITH THE VALUE AS EXTREME AS Z SIGN1240
C SIGN1250
CALL NDTR (Z,P,D) SIGN1260
C SIGN1270
95 RETURN SIGN1280
END SIGN1290