1	SUB CHI0SQ &
!	500.19 - STAT11 - CHI0SQ &
!									&
!
		CHI SQUARE MODULE &
!									&
!
	RELEASED FOR SUBMISSION TO THE DECUS LIBRARY BY &
!	DEC ENGINEERING SYSTEMS GROUP AND EDUCATION PRODUCTS GROUP &
!		SEPTEMBER, 1977
2 !	COPYRIGHT (C) 1973, DIGITAL EQUIPMENT CORPORATION, &
!									&
!
			MAYNARD, MASSACHUSETTS &

3 !	THIS SOFTWARE IS FURNISHED TO PURCHASER UNDER A LICENSE FOR USE &
!	ON A SINGLE COMPUTER SYSTEM AND CAN BE COPIED (WITH INCLUSION OF &
!	DEC'S COPYRIGHT NOTICE) ONLY FOR USE IN SUCH SYSTEM, EXCEPT AS &
!	MAY OTHERWISE BE PROVIDED IN WRITING BY DEC. &

4 !	THE INFORMATION IN THIS DOCUMENT IS SUBJECT TO CHANGE WITHOUT &
!	NOTICE AND SHOULD NOT BE CONSTRUED AS A COMMITMENT BY DIGITAL &
!	EQUIPMENT CORPORATION. &

5 !	DEC ASSUMES NO RESPONSIBILITY FOR USE OR RELIABILITY OF ITS &
!	SOFTWARE ON EQUIPMENT WHICH IS NOT SUPPLIED BY DEC. &
!									&
!									&

6 !	THIS MODULE COMPUTES AND PRINTS THE CHI-SQUARED VALUE FOR THE &
!	USER'S DATA MATRIX. &
!									&

7 ! 	AUTHOR:		MICHAEL D. KNAUER &
!									&
!
	VERSION NUMBER:	001 &
!									&
!
	DATE:		OCTOBER, 1973 &
!									&
!									&

8  !	MODIFICATIONS:  MAY, 1975 &
!									&
!
	MODIFIED TO ACCEPT MISSING DATA POINTS &
!									&
!
		BY ARDOTH HASSLER WILSON &
!		   CENTRAL STATE UNIVERSITY &
!		   EDMOND, OKLAHOMA &
!									&

00009!	MODIFICATIONS:  JUNE, 1976 &
!									&
!
	CTRL/C TRAP ADDED &

10 !									&
!									&
!
	CALLING ARGUMENTS &

11 !		1) VARIABLE NAME:	F3$ &
!		   RANGE OF VALUES:	S00000.RWM - S99999.RWM &
!		   USE:			NAME OF THE 250 ROW BY 15 COLUMN &
!					DATA MATRIX. &

13 !		2) VARIABLE NAME:	F4$ &
!		   RANGE OF VALUES:	S00000.ESF - S99999.ESF &
!		   USE:			NAME OF ELEMENTARY STATISTICS FILE &

15 !		3) VARIABLE NAME:	R% &
!		   RANGE OF VALUES:	1 - 250 &
!		   USE:			NUMBER OF ROWS IN DATA MATRIX &

17 !		4) VARIABLE NAME:	C% &
!		   RANGE OF VALUES:	1 - 15 &
!		   USE:			NUMBER OF COLUMNS IN DATA MATRIX &
!									&
!									&

20 !									&
!	RETURNING ARGUMENTS &

22 !		NONE -- THIS MODULE DOES NOT ALTER OR ADD TO ANY OF THE &
!			FILES OR VARIABLES PASSED TO IT. &
!									&
!									&

30 !	DESCRIPTION OF FUNCTION &

31 !		THIS MODULE COMPUTES AND PRINTS THE CHI-SQUARED VALUE FOR &
!		THE USER'S DATA MATRIX &

32!		IF THE DATA MATRIX IS 2 BY 2, A SPECIAL FORMULA IS USED AND &
!		THE FISHER EXACT PROBABILITY CAN BE COMPUTED. &

33 !		FOR ALL OTHER MATRICES, THE CHI SQUARE AND DEGREES OF FREEDOM &
!		ARE COMPUTED AND PRINTED, AND THE NUMBER OF ROWS AND COLUMNS &
!		WITH ALL ZERO ENTRIES AND THE NUMBER OF CELLS WITH EXPECTED &
!		FREQUENCIES LESS THAN 5 ARE COUNTED AND PRINTED. &

34 !		THE TABLE OF EXPECTED FREQUENCIES WILL BE PRINTED IF THE &
!		USER WANTS. &

35 !		CONTROL IS ALWAYS SURRENDERED TO STATCM AT THE END OF THE &
!		CHI SQUARED ANALYSIS. &

90 !									&
!	Modifications: August,1981					&
!									&
!	COMMON (STAT) MODULE$ = 6%, LINE%, SAV.F$ = 127%		&
!	added to replace core common and also to let STTMGR know	&
!	who to chain to (MODULE$).  Once i MODULE$, LINE% indicates	&
!	line to begin execution.					&
!									&
\	COMMON (STAT)	MODULE$ = 6%, LINE%, SAV.F$ = 127%		&

100 !									&
!	THIS NEXT LINE RETRIEVES THE CALLING ARGUMENTS FROM COMMON &

110	ON ERROR GOTO 9000 &
\	GOSUB 10000 &
\	!F$=SYS(CHR$(7%)) &
\	F$=SAV.F$
112	A9$=MID(F$,62%,9%) &
\	A9$=LEFT(A9$,INSTR(5%,A9$,"]")) &
\	H9=.9E-38
115 !									&
!									&
!
	FOLLOWING IS A FACTORIAL FUNCTION USED TO HELP COMPUTE THE FISHER &
!	EXACT PROBABILITY FOR A 2 BY 2 ARRAY. &
!									&
!									&

120	DEF FNF(M)
130	IF M=1 THEN FNF=1 ELSE FNF=M*FNF(M-1)
140	FNEND
144 !									&
!									&
!									&
!	THIS CODE OPENS THE DATA MATRIX, ELEMENTARY STATISTICS, AND TEMPORARY &
!	WORK FILES. NOTE THAT THE EXPECTED FREQUENCY FILE (E(250%,15%)) IS &
!	CREATED AS A TEMPORARY VIRTUAL MATRIX AND IS DELETED UPON EXIT FROM &
!	THIS MODULE. &
!									&
!									&

145	L5%=0%
150	R%=VAL(MID(F$,46%,5%))
160	C%=VAL(MID(F$,51%,5%))
170	F3$=MID(F$,31%,15%)
180	F4$=LEFT(F3$,6%)+".ESF"
190	F5$=LEFT(F3$,6%)+".TMP"
200	OPEN F3$ FOR INPUT AS FILE 3, VIRTUAL
210	DIM #3,G(250%,15%)
220	OPEN F4$ FOR INPUT AS FILE 4, VIRTUAL
230	DIM #4,S(10%,15%)
240	OPEN F5$ AS FILE 5, VIRTUAL
250	DIM #5,E(250%,15%)
299 !									&
!									&
!									&
!	THIS SECTION COMPUTES AND PRINTS THE CHI SQUARE FOR A 2 BY 2 ARRAY &
!									&
!									&

300	IF R%<>2% GOTO 1000
310	IF C%<>2% GOTO 1000
320	A=G(1%,1%) &
\	B=G(1%,2%)
330	C=G(2%,1%) &
\	D=G(2%,2%)
332	A9%=A &
\	B9%=B &
\	C9%=C &
\	D9%=D
334	IF A9%<>A OR B9%<>B OR C9%<>C OR D9%<>D THEN GOTO 1000
336	IF A9%<1% OR B9%<1% OR C9%<1% OR D9%<1% THEN GOTO 1000
340	N=A+B+C+D
350	C1=N*(ABS(A*D-B*C))^2
360	C1=C1/((A+B)*(C+D)*(A+C)*(B+D))
370	PRINT
380	PRINT "CHI-SQUARE..........";
385	PRINT USING " ###.#####",C1
390	PRINT "DEGREES OF FREEDOM..         1"
392	PRINT
395	C2=N*(ABS(A*D-B*C)-N/2)^2 &
\	C2=C2/((A+B)*(C+D)*(A+C)*(B+D))
397	PRINT "CHI-SQUARE (CORRECTED)...."; &
\	PRINT USING " ###.#####",C2 &
\	PRINT "DEGREES OF FREEDOM........         1" &
\	PRINT
399 !									&
!									&
!									&
!	IF THE USER WANTS, THIS SECTION COMPUTES AND PRINTS (FOR 2 BY 2 &
!	ARRAYS ONLY) THE FISHER EXACT PROBABILITY. IT IS COMPUTED ON LINES &
!	450 AND 460 AND IS MERELY A PRODUCT OF SEVERAL DIFFERENT FACTORIALS &
!									&
!									&

400	IF N>33.0 GOTO 2000     !   NOTE--FLOATING POINT ERROR &
!		OCCURS FOR N>33
410	IF A>5 AND B>5 AND C>5 AND D>5 GOTO 2000
420	INPUT "DO YOU WISH TO COMPUTE THE FISHER EXACT PROBABILITY ";A$
425	PRINT
430	IF A$="YES" OR LEFT(A$,1%)="Y" GOTO 450
435	IF A$="NO" OR LEFT(A$,1%)="N" OR A$="" GOTO 2000
440	PRINT "YOU MUST ANSWER EITHER YES OR NO"
445	GOTO 420
450	P1 = FNF(A+B)*FNF(C+D)/FNF(N)
460	P1 = P1 * FNF(A+C) * FNF(B+D) / (FNF(A) *FNF(B) *FNF(C)*FNF(D))
470	PRINT "THE FISHER EXACT PROBABILITY...";
475	PRINT USING " ###.#####",P1
480	PRINT
490	GOTO 2000
999 !									&
!									&
!									&
!	THIS SECTION COMPUTES THE CHI SQUARE AND RELATED STATISTICS FOR OTHER &
!	THAN 2 BY 2 ARRAYS.   &
!									&
!									&

1000	X2=0.0  &
\	N=0.0
1005 !		N IS THE GRAND SUM OF ALL OBSERVATIONS
1010	N=N+S(3%,I%) FOR I%=1% TO C%
1020	FOR J%=1% TO R%
1030	T=0.0
1035 !		T IS THE SUM OF THE OBSERVATIONS IN EACH ROW.
1038	FOR I%=1% TO C% &
\	IF G(J%,I%)<>H9 THEN T=T+G(J%,I%)
1040	NEXT I%
1042	IF T<>0 GOTO 1050
1044	L7%=L7%+1%
1050	FOR K%=1% TO C%
1057	IF S(3%,K%)<>0 GOTO 1060
1058	L6%=L6%+1%
1059 !		THE E(J%,K%)'S ARE THE EXPECTED FREQUENCIES FOR EACH CELL.
1060	E(J%,K%)=(T*S(3%,K%))/N
1064	IF E(J%,K%)=0 OR G(J%,K%)=H9 GOTO 1080
1065	IF E(J%,K%)<5 THEN L5%=L5%+1%
1069 !		X2 IS THE CHI SQUARE
1070	X2=X2+(G(J%,K%)-E(J%,K%))^2/E(J%,K%)
1080	NEXT K%
1090	NEXT J%
1094 !		L6% IS THE SUM OF THE NUMBER OF ROWS AND THE NUMBER OF &
!		COLUMNS THAT HAVE ALL ZERO ENTRIES.
1095	L6%=L6%/R%+L7%
1099 !		D% IS THE DEGREES OF FREEDOM
1100	D%=(R%-1%)*(C%-1%)
1104 !									&
!									&
!									&
!	HERE THE TABLE OF EXPECTED FREQUENCIES IS PRINTED IF THE USER WANTS. &
!	NOTE THAT THE TABLE WILL BE PRINTED IN TWO PARTS IF THERE ARE MORE  &
!	THAN SIX COLUMNS IN THE DATA MATRIX. &
!									&
!									&

1105	INPUT "DO YOU WISH TO PRINT EXPECTED FREQUENCIES";P$ &
\	PRINT
1107	IF P$="YES" OR LEFT(P$,1%)="Y" GOTO 1115
1109	IF P$="NO" OR LEFT(P$,1%)="N" OR P$="" GOTO 1500
1111	PRINT "YOU MUST ANSWER EITHER YES OR NO"
1113	GOTO 1105
1115	PRINT "  EXPECTED FREQUENCY IN EACH CELL"  &
\	PRINT
1120	C1%=1%  &
\	C2%=C%
1125	K%=C1%+5% &
\	IF K%>C% THEN K%=C%-C1%+1% ELSE K%=6%
1130	PRINT "ROW/COL";
1135	PRINT TAB(1%+K1%*11%);C1%+K1%-1%; FOR K1%=1% TO K%
1140	PRINT
1150	FOR J%=1% TO R%
1160	PRINT J%;TAB(5%);
1170	FOR K%=C1% TO C1%+5%
1175	IF K%>C% GOTO 1190
1180	PRINT USING " #####.####",E(J%,K%);
1190	NEXT K%
1200	PRINT
1210	NEXT J%
1220	PRINT
1230	IF C2%<=6% GOTO 1500
1240	C2%=C2%-6%
1250	C1%=C1%+6%
1260	GOTO 1125
1499 !									&
!									&
!									&
!	THIS SECTION PRINTS THE PREVIOUSLY COMPUTED CHI SQUARE AND RELATED &
!	STATISTICS. &
!									&
!
1500	PRINT
1501	IF L5%<=0% GOTO 1505
1502	PRINT L5%;" CELLS HAVE AN EXPECTED FREQUENCY"
1503	PRINT "GREATER THAN 0 AND LESS THAN 5."
1504	PRINT "THE COMPUTED CHI-SQUARE THEREFORE MAY NOT BE MEANINGFUL"
1505	IF L6%=0% GOTO 1509
1506	PRINT "(";L6%;" ROWS AND/OR COLUMNS HAVE ALL 0 ENTRIES"
1507	PRINT "AND HAVE BEEN DISREGARDED IN THIS CALCULATION)"
1509	PRINT
1510	PRINT "CHI-SQUARE..........";
1515	PRINT USING " ###.#####",X2
1520	PRINT "DEGREES OF FREEDOM..";
1525	PRINT USING "     #####",D%
1530	PRINT
1535	IF L5%<=0% AND L6%<=0% GOTO 1999
1537	PRINT "WOULD YOU LIKE TO COMPUTE CHI-SQUARE USING YATES"; &
!	" CORRECTION"; &
\	INPUT Y9$ &
\	IF LEFT(Y9$,1%)<>"Y" GOTO 1999
1540	X2=0 &
\	FOR J%=1% TO R% &
\	FOR K%=1% TO C% &
\	IF	E(J%,K%)=0 OR G(J%,K%)=H9 &
	THEN	GOTO 1550
1545	X2=X2+(ABS(G(J%,K%)-E(J%,K%))-0.5)^2/E(J%,K%)
1550	NEXT K% &
\	NEXT J%
1560	PRINT &
!	 &
\	PRINT "CHI-SQUARE (CORRECTED)...."; &
!	 &
\	PRINT USING " ###.#####",X2
1565	PRINT "DEGREES OF FREEDOM........"; &
\	PRINT USING "    ######",D%
1570	PRINT
1999 !									&
!									&
!									&
!	HERE CONTROL IS RETURNED TO STATCM. NOTE THAT IT DOESN'T ASK IF &
!	YOU WANT TO COMPUTE MORE CHI SQUARE, SINCE THE CHI SQUARE IS COMPUTED &
!	FOR THE WHOLE DATA MATRIX. &
!									&
!									&

2000	PRINT 
2010	CLOSE 3,4,5
2020	KILL EDIT$(F5$,-1%) + ";0"
2030	!R$=SYS(CHR$(8)+F$) &
\	SAV.F$ = F$
2040	!CHAIN "STATCM"+A9$						&
\	MODULE$= "STATCM"						&
\	LINE% = 0%							&
\	SUBEXIT								&

09000	IF ERR=28% THEN GOSUB 10000 &
!\	RESUME 2000 &
\	MODULE$ = "FINISH" &
\	GOTO 32750
09010	ON ERROR GOTO 0
10000	V0%=CTRLC ! SYS(CHR$(6%)+CHR$(-7%)) &
\	RETURN	! CTRL/C TRAP
32750	SUBEND