FOUR-WAY LAYOUT WITH 1 OBS/CELL - YOUR NAME 1 USING MATRICES TO ANALYZE a 2^4 DESIGN 19:54 Friday, February 8, 2008 THE DATA AS SAS SEES IT NORMAL AND P-P PLOTS ARE GIVEN BELOW Obs II K T P C KT KP KC TP TC PC KTP KTC KPC TPC KTPC Yield 1 1 -1 -1 -1 -1 1 1 1 1 1 1 -1 -1 -1 -1 1 70 2 1 1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 -1 -1 60 3 1 -1 1 -1 -1 -1 1 1 -1 -1 1 1 1 -1 1 -1 89 4 1 1 1 -1 -1 1 -1 -1 -1 -1 1 -1 -1 1 1 1 81 5 1 -1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 1 -1 69 6 1 1 -1 1 -1 -1 1 -1 -1 1 -1 -1 1 -1 1 1 62 7 1 -1 1 1 -1 -1 -1 1 1 -1 -1 -1 1 1 -1 1 88 8 1 1 1 1 -1 1 1 -1 1 -1 -1 1 -1 -1 -1 -1 81 9 1 -1 -1 -1 1 1 1 -1 1 -1 -1 -1 1 1 1 -1 60 10 1 1 -1 -1 1 -1 -1 1 1 -1 -1 1 -1 -1 1 1 49 11 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 88 12 1 1 1 -1 1 1 -1 1 -1 1 -1 -1 1 -1 -1 -1 82 13 1 -1 -1 1 1 1 -1 -1 -1 -1 1 1 1 -1 -1 1 60 14 1 1 -1 1 1 -1 1 1 -1 -1 1 -1 -1 1 -1 -1 52 15 1 -1 1 1 1 -1 -1 -1 1 1 1 -1 -1 -1 1 -1 86 16 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 79 FOUR-WAY LAYOUT WITH 1 OBS/CELL - YOUR NAME 2 USING MATRICES TO ANALYZE a 2^4 DESIGN 19:54 Friday, February 8, 2008 ENTERING PROC IML TO CALCULATE PARAMETER ESTIMATES USING 16x16 MATRICES TO ANALYZE A 2^4 DESIGN: The response data and the design matrix are YIELD EQ XX EFFECTS 70 = 1 -1 -1 -1 -1 1 1 1 1 1 1 -1 -1 -1 -1 1 I 60 = 1 1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 -1 -1 1 89 = 1 -1 1 -1 -1 -1 1 1 -1 -1 1 1 1 -1 1 -1 2 81 = 1 1 1 -1 -1 1 -1 -1 -1 -1 1 -1 -1 1 1 1 3 69 = 1 -1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 1 -1 4 62 = 1 1 -1 1 -1 -1 1 -1 -1 1 -1 -1 1 -1 1 1 12 88 = 1 -1 1 1 -1 -1 -1 1 1 -1 -1 -1 1 1 -1 1 13 81 = 1 1 1 1 -1 1 1 -1 1 -1 -1 1 -1 -1 -1 -1 14 60 = 1 -1 -1 -1 1 1 1 -1 1 -1 -1 -1 1 1 1 -1 23 49 = 1 1 -1 -1 1 -1 -1 1 1 -1 -1 1 -1 -1 1 1 24 88 = 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 1 34 82 = 1 1 1 -1 1 1 -1 1 -1 1 -1 -1 1 -1 -1 -1 123 60 = 1 -1 -1 1 1 1 -1 -1 -1 -1 1 1 1 -1 -1 1 124 52 = 1 1 -1 1 1 -1 1 1 -1 -1 1 -1 -1 1 -1 -1 134 86 = 1 -1 1 1 1 -1 -1 -1 1 1 1 -1 -1 -1 1 -1 123 79 = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1234 XX`*XX=Const*I_16 IMPLIES THAT XX IS 'ALMOST ORTHOGONAL' XXPXX 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 SOLVING THE DESIGN MATRIX EQUATION FOR PARAMETER VALUES: (See the PARM column in the next table:) MSE USING MSE FROM AVERAGE OF THE LAST 5 SS VALUES BELOW = 1.2 FOUR-WAY LAYOUT WITH 1 OBS/CELL - YOUR NAME 3 USING MATRICES TO ANALYZE a 2^4 DESIGN 19:54 Friday, February 8, 2008 ENTERING PROC IML TO CALCULATE PARAMETER ESTIMATES PARAMETER ESTIMATES (ALL T STATISTICS HAVE DEGF=5): NOTE THAT PARMS IS EXACTLY THE SAME AS IN FOURFAC.SAS ESTIMATING ERROR VARIANCE FROM THE LAST FIVE TERMS EFFECTS BOOKPARMS PARMS TSTAT PROBGRT FNOTES I 72.25 72.250 263.82 0.0000 (***) 1 -8.00 -4.000 -14.61 0.0000 (***) 2 24.00 12.000 43.82 0.0000 (***) 3 -0.25 -0.125 -0.46 0.6672 4 -5.50 -2.750 -10.04 0.0002 (***) 12 1.00 0.500 1.83 0.1275 13 0.75 0.375 1.37 0.2292 14 0.00 0.000 0.00 1.0000 23 -1.25 -0.625 -2.28 0.0713 24 4.50 2.250 8.22 0.0004 (***) 34 -0.25 -0.125 -0.46 0.6672 123 -0.75 -0.375 . . 123 124 0.50 0.250 . . 124 134 -0.25 -0.125 . . 134 123 -0.75 -0.375 . . 123 1234 -0.25 -0.125 . . 1234 (***) P<0.001 (**) P<0.01 (*) P<0.05 Note that the `BOOKPARMS' column is identical with the Estimates column in Table 5.11 in the text p200, and the P-values are identical with P-values in proc reg output in FourFac.sas FOUR-WAY LAYOUT WITH 1 OBS/CELL - YOUR NAME 4 USING MATRICES TO ANALYZE a 2^4 DESIGN 19:54 Friday, February 8, 2008 QUITTING PROC IML AND RE-ENTERING PLAIN SAS: THE EXPORTED DATA SET (NEWPARMDAT) AS SAS SEES IT Obs EFFECTS BOOKPARMS PARMS TSTAT 1 1 -8.00 -4.000 -14.6059 2 2 24.00 12.000 43.8178 3 3 -0.25 -0.125 -0.4564 4 4 -5.50 -2.750 -10.0416 5 12 1.00 0.500 1.8257 6 13 0.75 0.375 1.3693 7 14 0.00 0.000 0.0000 8 23 -1.25 -0.625 -2.2822 9 24 4.50 2.250 8.2158 10 34 -0.25 -0.125 -0.4564 11 123 -0.75 -0.375 . 12 124 0.50 0.250 . 13 134 -0.25 -0.125 . 14 123 -0.75 -0.375 . 15 1234 -0.25 -0.125 . FOUR-WAY LAYOUT WITH 1 OBS/CELL - YOUR NAME 5 USING MATRICES TO ANALYZE a 2^4 DESIGN 19:54 Friday, February 8, 2008 NORMAL PROBABILITY PLOT (PROBPLOT IN SAS) „ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ† 25 ‰ ‚ ‚ + ‚ ‚ ‚ ‚ ‚ ‚ ‚ 20 ‰ ‚ ‚ ‚ ‚ ‚ ‚ ‚ ‚ ‚ 15 ‰ ‚ ‚ ‚ ‚ ‚ ‚ ‚ B ‚ ‚ O 10 ‰ ‚ O ‚ ‚ K ‚ ‚ P ‚ ‚ A ‚ ‚ R 5 ‰ + ‚ M ‚ ‚ S ‚ ‚ ‚ ‚ ‚ + + + ‚ 0 ‰ + + + + + ‚ ‚ + + + ‚ ‚ ‚ ‚ ‚ ‚ ‚ -5 ‰ + ‚ ‚ ‚ ‚ ‚ ‚ + ‚ ‚ ‚ -10 ‰ ‚ Š…ƒƒƒƒƒƒƒƒ…ƒƒƒƒ…ƒƒƒƒƒƒƒ…ƒƒƒƒƒƒƒƒ…ƒƒƒƒƒƒƒƒ…ƒƒƒƒƒƒƒ…ƒƒƒƒ…ƒƒƒƒƒƒƒƒ…Œ 1 5 10 25 50 75 90 95 99 Normal Percentiles FOUR-WAY LAYOUT WITH 1 OBS/CELL - YOUR NAME 6 USING MATRICES TO ANALYZE a 2^4 DESIGN 19:54 Friday, February 8, 2008 NORMAL P-P PLOT (PPPLOT IN SAS) „ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ† C 1.0 ‰ +‚ u ‚ NN ‚ m ‚ + NN ‚ u ‚ NN ‚ l ‚ NN ‚ a ‚ + NN ‚ t ‚ NN ‚ i 0.8 ‰ + N ‚ v ‚ NN ‚ e ‚ + NN ‚ ‚ NN ‚ D ‚ NN ‚ i ‚ + NN ‚ s ‚ NN ‚ t 0.6 ‰ + N ‚ r ‚ NN ‚ i ‚ NN ‚ b ‚ NN ‚ u ‚ NN ‚ t ‚ NN ‚ i ‚ NN ‚ o 0.4 ‰ N ‚ n ‚ NN ‚ ‚ NN + ‚ o ‚ NN ‚ f ‚ NN ‚ ‚ NN ‚ B ‚ NN ‚ O 0.2 ‰ N + ‚ O ‚ NN ‚ K ‚ NN + ‚ P ‚ NN ‚ A ‚ NN ‚ R ‚ NN + ‚ M ‚ NN ‚ S 0 ‰N ‚ Š…ƒƒƒƒƒƒƒƒƒƒƒƒ…ƒƒƒƒƒƒƒƒƒƒƒƒ…ƒƒƒƒƒƒƒƒƒƒƒƒ…ƒƒƒƒƒƒƒƒƒƒƒƒ…ƒƒƒƒƒƒƒƒƒƒƒƒ…Œ 0 .2 .4 .6 .8 1 Normal(Mu=0.9 Sigma=6.9852)