C POIN 10
C ..................................................................POIN 20
C POIN 30
C SUBROUTINE POINT POIN 40
C POIN 50
C PURPOSE POIN 60
C TO COMPUTE THE POINT-BISERIAL CORRELATION COEFFICIENT POIN 70
C BETWEEN TWO VARIABLES, WHEN ONE OF THE VARIABLES IS A BINARYPOIN 80
C VARIABLE AND ONE IS CONTINUOUS. THIS IS A SPECIAL CASE OF POIN 90
C THE PEARSON PRODUCT-MOMENT CORRELATION COEFFICIENT. POIN 100
C POIN 110
C USAGE POIN 120
C CALL POINT (N,A,B,HI,ANS,IER) POIN 130
C POIN 140
C DESCRIPTION OF PARAMETERS POIN 150
C N - NUMBER OF OBSERVATIONS POIN 160
C A - INPUT VECTOR OF LENGTH N CONTAINING THE CONTINUOUS POIN 170
C VARIABLE POIN 180
C B - INPUT VECTOR OF LENGTH N CONTAINING THE DICHOTOMOUS POIN 190
C (BINARY) VARIABLE POIN 200
C HI - INPUT NUMERICAL CODE TO INDICATE THE HIGHER CATEGORY. POIN 210
C ANY VALUE OF THE BINARY VARIABLE NOT LESS THAN HI WILLPOIN 220
C BE CLASSIFIED IN THE HIGHER OF THE TWO CATEGORIES. POIN 230
C ANS - OUTPUT VECTOR OF LENGTH 9 CONTAINING THE FOLLOWING POIN 240
C RESULTS POIN 250
C ANS(1)- MEAN OF VARIABLE A POIN 260
C ANS(2)- STANDARD DEVIATION OF VARIABLE A POIN 270
C ANS(3)- NUMBER OF OBSERVATIONS IN THE HIGHER POIN 280
C CATEGORY OF VARIABLE B POIN 290
C ANS(4)- NUMBER OF OBSERVATIONS IN THE LOWER POIN 300
C CATEGORY OF VARIABLE B POIN 310
C ANS(5)- MEAN OF VARIABLE A FOR ONLY THOSE POIN 320
C OBSERVATIONS IN THE HIGHER CATEGORY OF POIN 330
C VARIABLE B POIN 340
C ANS(6)- MEAN OF VARIABLE A FOR ONLY THOSE POIN 350
C OBSERVATIONS IN THE LOWER CATEGORY OF POIN 360
C VARIABLE B POIN 370
C ANS(7)- POINT-BISERIAL CORRELATION COEFFICIENT POIN 380
C ANS(8)- T-TEST FOR THE SIGNIFICANCE OF THE POIN 390
C DIFFERENCE BETWEEN THE MEANS OF VARIABLE A POIN 400
C FOR THE HIGHER AND LOWER CATEGORIES POIN 410
C RESPECTIVELY. POIN 420
C ANS(9)- DEGREES OF FREEDOM FOR THE T-TEST POIN 430
C IER- 1, IF ALL ELEMENTS OF B ARE NOT LESS THAN HI. POIN 440
C -1, IF ALL ELEMENTS OF B ARE LESS THAN HI. POIN 450
C 0, OTHERWISE. IF IER IS NON-ZERO, ANS(I), I=5,...,9, POIN 460
C IS SET TO 10**75. POIN 470
C POIN 480
C REMARKS POIN 490
C THE SYMBOLS USED TO IDENTFY THE VALUES OF THE TWO CATEGORIESPOIN 500
C OF VARIABLE B MUST BE NUMERIC. ALPHABETIC OR SPECIAL POIN 510
C CHARACTERS CANNOT BE USED. POIN 520
C THE T-TEST(ANS(8)) IS A TEST OF WHETHER THE POINT-BISERIAL POIN 530
C COEFFICIENT DIFFERS SIGNIFICANTLY FROM ZERO. POIN 540
C POIN 550
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED POIN 560
C NONE POIN 570
C POIN 580
C METHOD POIN 590
C REFER TO P. HORST, 'PSYCHOLOGICAL MEASUREMENT AND POIN 600
C PREDICTION', P. 91 (WADSWORTH, 1966). POIN 610
C POIN 620
C ..................................................................POIN 630
C POIN 640
SUBROUTINE POINT (N,A,B,HI,ANS,IER) POIN 650
C POIN 660
DIMENSION A(1),B(1),ANS(1) POIN 670
C POIN 680
C COMPUTE MEAN AND STANDARD DEVIATION OF VARIABLE A POIN 690
C POIN 700
IER=0 POIN 710
SUM=0.0 POIN 720
SUM2=0.0 POIN 730
DO 10 I=1,N POIN 740
SUM=SUM+A(I) POIN 750
10 SUM2=SUM2+A(I)*A(I) POIN 760
FN=N POIN 770
ANS(1)=SUM/FN POIN 780
ANS(2)=(SUM2-ANS(1)*SUM)/(FN-1.0) POIN 790
ANS(2)= SQRT(ANS(2)) POIN 800
C POIN 810
C FIND NUMBERS OF CASES IN THE HIGHER AND LOWER CATEGORIES POIN 820
C POIN 830
P=0.0 POIN 840
SUM=0.0 POIN 850
SUM2=0.0 POIN 860
DO 30 I=1,N POIN 870
IF(B(I)-HI) 20, 25, 25 POIN 880
20 SUM2=SUM2+A(I) POIN 890
GO TO 30 POIN 900
25 P=P+1.0 POIN 910
SUM=SUM+A(I) POIN 920
30 CONTINUE POIN 930
C POIN 940
Q=FN-P POIN 950
ANS(3)=P POIN 960
ANS(4)=Q POIN 970
IF (P) 35,35,40 POIN 980
35 IER=-1 POIN 990
GO TO 50 POIN1000
40 ANS(5)=SUM/P POIN1010
IF (Q) 45,45,60 POIN1020
45 IER=1 POIN1030
50 DO 55 I=5,9 POIN1040
55 ANS(I)=1.7E38 POIN1050
GO TO 65 POIN1060
60 ANS(6)=SUM2/Q POIN1070
C POIN1080
C COMPUTE THE POINT-BISERIAL CORRELATION POIN1090
C POIN1100
R=((ANS(5)-ANS(1))/ANS(2))* SQRT(P/Q) POIN1110
ANS(7)=R POIN1120
C POIN1130
C COMPUTE T RATIO USED TO TEST THE HYPOTHESIS OF ZERO CORRELATIONPOIN1140
C POIN1150
T=R* SQRT((FN-2.0)/(1.0-R*R)) POIN1160
ANS(8)=T POIN1170
C POIN1180
C COMPUTE DEGREES OF FREEDOM POIN1190
C POIN1200
ANS(9)=FN-2 POIN1210
C POIN1220
65 RETURN POIN1230
END POIN1240