CALL SEQUENCE... ttesta XBAR VX YBAR VY MDIF TVALUE KVALUE DVALUE MASK \ INPUT OUTPUT [ -a VAL1 -lx VAL2 -ly VAL3 -kind VAL4 [VAL5] [VAL6] ] DESCRIPTION... ttesta - CONDUCT AN "APPROXIMATE" DIFFERENCE OF MEANS TEST. AUTHORS - F.Zwiers, JAN 25/85, LAST REVISION: $Header: Correction-a-la-doc-pour-la-taille-des-echantillons @ 2018-03-26 17:16:00 -0400 (dugas) $ PURPOSE - CONDUCT A DIFFERENCE OF MEANS TEST. THE TEST WHICH IS CONDUCTED IS THE 'APPROXIMATE T-TEST' WHICH MAKES NO ASSUMPTION ABOUT THE EQUALITY OF VARIANCES. HOWEVER, ALL THE OTHER ASSUMPTIONS USUALLY MADE WHEN CONDUCTING A T-TEST (I.E., INDEPEDENT OBSERVATIONS FROM NORMAL POPULATIONS IN EACH SAMPLE, INDEPENDENT SAMPLES) MUST STILL BE SATISFIED. UPON RETURN, THE PROGRAM REPORTS THE COMPUTED T-TEST VALUES IN TVALUE 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 THE "POOLED VARIANCE" IS APPROXIMATELY EQUAL TO THE NOISE INDUCED BY THE PACKING ALGORITHM. 2) INTERPRETATION OF VX AND VY FILES IS CONTROLED BY INPUT PARAMETER IVAR. 3) MASK FILE NEED NOT BE SPECIFIED IN THE PROGRAM CALLING SEQUENCE.(SEE OUTPUT FILES SECTION BELOW). INPUT FILES... XBAR = FIELDS OF MEANS OF THE 'X-CONTROL' VARIABLE. (IF (IVAR.EQ.0) THEN (VX = FIELDS OF THE VARIANCE OF X. ( SUM(X(I)-XBAR)**2/NX, I=1,...,NX. (OTHERWISE, (VX = FIELDS OF THE STANDARD DEVIATION OF X. ( SQRT(SUM(X(I)-XBAR)**2/(NX-1)), I=1,...,NX. YBAR = SAME AS XBAR EXCEPT FOR THE 'Y-EXPERIMENT' VARIABLE. VY = SAME AS VX EXCEPT FOR THE 'Y-EXPERIMENT' VARIABLE. OUTPUT FILES... MDIF = FIELDS OF MEAN DIFFERENCES COMPUTED AS D=(YBAR-XBAR). TVALUE = FIELDS OF 'T-VALUES' GIVEN BY T = (YBAR-XBAR)/SDIF SDIF = SQRT( AXT+AYT ) AXT = VX/(NX-1) AYT = VY/(NY-1) WHERE, VX AND VY ARE THE VARIANCES OF X AND Y VARIABLES RESPECTIVELY. NOTE - THE APPROPRIATE NUMBER OF DEGREES OF FREEDOM, (NDF), ARE ESTIMATED FROM THE OBSERVATIONS AS FOLLOWS: (SEE FOR EXAMPLE, PROB AND STATS FOR ENGINEERS AND SCIENTISTS BY WALPOLE AND MYERS). NDF = MAX( 1,INT( ANUM/ADEN+0.5 ) ) ANUM = ( AXT+AYT )**2 ADEN = AXT**2/(NX-1) + AYT**2/(NY-1) WHERE, AXT AND AYT ARE AS DEFINED ABOVE. KVALUE = 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 (I.E. EQUALITY OF MEANS) THAN IN REGIONS OUTSIDE THE NEXT LOWER CONTOUR. DVALUE = 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 -- NOTE - 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 CONTROL DATA SET, ANY (ly) = THE NUMBER OF OBSERVATIONS IN THE EXPERIMENT DATA SET. THE ACTUAL VALUE USED ARE RATHER NX AND NY DEFINED AS NX = INT( ANX ) AND NY = INT( ANY ). IF NX >= 1 , NY >= 1 THEN NX AND NY 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 SAMPLE SIZE CODING THAT IS PRESENT IN THE FILE DESCRIPTORS, DEPENDING ON THE FILE TYPE OF THE XBAR AND YBAR FILES. KIND (kind/1) = -1, REJECT THE NULL HYPOTHESIS IF P > 1 - ALPHA (IE - CONDUCT A ONE TAILED TEST AND REJECT IF THE TEST STATISTIC IS UNUSUALLY SMALL). = 0, INDICATES A TWO TAILED TEST (REJECT IF P > 1 - ALPHA/2 OR IF P < ALPHA/2) (IE - REJECT IF THE TEST STATISTIC IS UNUSUALLY SMALL OR LARGE). = 1, REJECT THE NULL HYPOTHESIS IF P < ALPHA (IE - CONDUCT A ONE TAILED TEST AND REJECT IF THE TEST STATISTIC IS UNUSUALLY LARGE). IVAR (kind/2) = A FLAG USED TO DETERMINE THE CONTENTS OF THE VX AND VY FILES. THAT IS : IF (IVAR.EQ.0) THEN THE VX AND VY FILES CONTAIN THE VARIANCES OF X AND Y, RESPECTIVELY. OTHERWISE, VX AND VY FILES CONTAIN THE UNBIASED ESTIMATES OF THE STANDARD DEVIATIONS OF X AND Y, RESPECTIVELY. MATCH(kind/3) = A FLAG USED TO DETERMINE IF THE VARIABLE NAMES IN XBAR AND YBAR *MUST* BE MATCHED. In this case, An unmatched variables will generate an error abort. THE DEFAULT BEHAVIOUR IS NOT TO CHECK THIS (=NO). READ(5,5010) ALPHA,ANX,ANY,KIND,IVAR 5010 FORMAT(10X,E10.0,2F5.0,2I5) EXAMPLE OF INPUT CARD... *TTESTA. 5.E-2 10. 5. 0 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 3 3 INITIAL ILLEGAL DATA TYPE OR SDX/SDY NOT COMPATIBLE 4 CANNOT READ FIRST RECORD IN XBAR 5 PARAMETER NX TOO SMALL 6 CANNOT READ RECORD IN VX 7 MORE THAN ONE SIZE IN XBAR AND/OR VX 8 CANNOT READ FIRST RECORD IN YBAR 9 PARAMETER NY TOO SMALL 10 CANNOT READ RECORD IN VY 11 MORE THAN ONE SIZE IN YBAR AND/OR VY 12 MORE THAN ONE SIZE IN XBAR AND/OR YBAR 13 MEMORY ALLOCATION PROBLEM NON-FATAL CONDITIONS... 101 VERY SMALL VALUES FOUND IN VX OR VY 102 NAMES OF MEAN FIELDS DO NOT MATCH