CALL SEQUENCE... ftest SDX SDY FRATIO KVALU DVALU MASK INPUT OUTPUT \ [ -a VAL1 -lx VAL2 -ly VAL3 -kind VAL4 ] DESCRIPTION... ftest - CONDUCT AN EQUALITY OF VARIANCE TEST (F-TEST). AUTHORS - F. ZWIERS, F. MAJAESS, November 28/1984. LAST REVISION: $Header: /home/cvs/RMNLIB/utils/rdiag/lspgm/ftest.ptn,v 4.16 2014/09/25 20:20:48 dugas Exp $ PURPOSE - CONDUCT AN EQUALITY OF VARIANCES TEST ( AN F-TEST ) AND REPORT THE 'F-VALUE' IN FRATIO, AS WELL AS RETURNING THE K-VALUE AND D-VALUE WHICH ARE RESPECTIVELY THE TRANSFORMED SIGNIFICANCE LEVELS AND THE ACCEPTANCE/REJECTION FLAG. NOTE: 1 - TESTS ARE NOT PERFORMED WHEN EITHER OF THE VARIANCES IS APPROXIMATELY EQUAL TO THE NOISE INDUCED BY THE PACKING ALGORITHM. 2 - INTERPRETATION OF SDX AND SDY FILES IS CONTROLLED BY INPUT PARAMETER ISTD (SEE INPUT CARD PARAMETERS DESCRIPTION BELOW). 3 - ALSO, MASK FILE NEED NOT BE SPECIFIED IN THE PROGRAM CALLING SEQUENCE. INPUT FILES... (IF (ISTD.EQ.0) THEN (SDX = FIELDS OF THE STANDARD DEVIATION OF THE X-VARIABLE. ( SQRT(SUM(X(I)-XBAR)**2/(NX-1)), I=1,...,NX. (OTHERWISE, (SDX = FIELDS OF THE VARIANCE OF THE X-VARIABLE. ( SUM(X(I)-XBAR)**2/NX, I=1,...,NX. SDY = AS SDX EXCEPT FOR THE Y-VARIABLE. OUTPUT FILES... FRATIO = FIELDS OF F-VALUES COMPUTED AS : F=SX**2/SY**2 WHERE, SX AND SY ARE THE STANDARD DEVIATIONS OF X AND Y RESPECTIVELY. KVALU = FIELDS OF K-VALUES OF TRANSFORMED SIGNIFICANCE LEVELS COMPUTED AS K IN: P=ALPHA/(5**(K-1)) OR K=LOG (ALPHA/P)+1 5 WHICH INDICATES THAT THE OBSERVED STATISTIC IS SIGNIFICANT AT THE ALPHA/(5**(K-1)) SIGNIFICANCE LEVEL. THUS K=1 INDICATES THAT THE OBSERVED STATISTIC IS JUST SIGNIFICANT AT THE ALPHA SIGNIFICANCE LEVEL. IF PLOTTED WITH UNIT CONTOUR INTERVALS, SUCCESSIVE CONTOURS WILL ENCLOSE REGIONS WHERE LOCALLY IT IS FIVE TIMES AS UNLIKELY THAT VALUES OF THE OBSERVED STATISTICS ARE CONSISTENT WITH THE NULL HYPOTHESIS THAN IN REGIONS OUTSIDE THE NEXT LOWER CONTOUR. DVALU = FIELDS OF D-VALUES COMPUTED AS: __ ! 0 IF THE NULL HYPOTHESIS IS ACCEPTED D = ! ! 1 IF THE NULL HYPOTHESIS IS REJECTED -- MASK = FIELDS OF MASK-VALUES COMPUTED AS: __ ! 1 IF THE TEST WAS CONDUCTED MASK = ! ! 0 IF THE TEST WAS NOT CONDUCTED -- THE MASK FILE IS NOT RETURNED IF THE PROGRAM IS NOT CALLED WITH OUTPUT FILE MASK. INPUT PARAMETERS... ALPHA (a) = THE SIGNIFICANCE LEVEL OF THE TEST. ANX (lx) = THE NUMBER OF OBSERVATIONS IN THE X-VARIABLE DATA SET, ANY (ly) = THE NUMBER OF OBSERVATIONS IN THE Y-VARIABLE DATA SET. THE ACTUAL VALUE USED ARE RATHER NX AND NY DEFINED AS NX = INT( ANX ) AND NY = INT( ANY ). IF NX > 1 AND NY > 1 THEN NX AND NY READ FROM THE INPUT CARD ARE USED IN THE COMPUTATION OF THE NUMBER OF DEGREES OF FREEDOM. OTHERWISE, THE NX AND NY VALUES NEEDED IN THE COMPUTATION ARE OBTAINED FROM THE RECORD LABELS OR FROM THE IP3 DESCRIPTORS, DEPENDING ON THE FILE TYPE OF THE FILES SDX AND SDY. ISTD (kind) = A FLAG USED TO DETERMINE THE CONTENTS OF THE SDX AND SDY FILES. THAT IS : IF (ISTD.EQ.0) THEN SDX AND SDY FILES CONTAIN THE UNBIASED ESTIMATES OF THE STANDARD DEVIATIONS OF X AND Y RESPECTIVELY. OTHERWISE, SDX AND SDY FILES CONTAIN THE VARIANCES OF X AND Y, RESPECTIVELY. READ(LIGNE,5010) ALPHA,ANX,ANY,ISTD 5010 FORMAT(10X,E10.0,2F5.0,I5) EXAMPLE OF INPUT CARD... *FTEST. 5.E-2 10. 5. 1 0123456789012345678901234567890123456789012345678901234567890 1 2 3 4 5 6 7 EXIT CONDITIONS... 0 NO PROBLEMS FATAL CONDITIONS... 1 PREMATURE EOF ON UNIT 5 2 PREMATURE EOF ON UNIT 1 AND/OR 2 3 INITIAL ILLEGAL DATA TYPE OR SDX/SDY NOT COMPATIBLE 4 CANNOT READ FIRST RECORD IN SDX 5 PARAMETER NX TOO SMALL 6 CANNOT READ FIRST RECORD IN SDY 7 PARAMETER NY TOO SMALL 8 MORE THAN ONE SIZE IN SDX AND/OR SDY NON-FATAL CONDITIONS... 101 VERY SMALL VALUES FOUND IN SDX OR SDY 102 NAMEL MISMATCH BETWENN SDX AND SDY