A REPLICATED HYPER-GRAECO-LATIN SQUARE for testing Cloth Wear 1 See Table 4.12 in text (Box-Hunter-Hunter) p163 THE DATA AS SAS SEES IT 11:38 Thursday, January 24, 2008 Obs Replicate Cycle Position Emory Yy Treat Holder 1 Rep1 C1 P1 al 320 A 1 2 Rep1 C1 P2 be 297 B 2 3 Rep1 C1 P3 ga 299 C 3 4 Rep1 C1 P4 de 313 D 4 5 Rep1 C2 P1 be 266 C 4 6 Rep1 C2 P2 al 227 D 3 7 Rep1 C2 P3 de 260 A 2 8 Rep1 C2 P4 ga 240 B 1 9 Rep1 C3 P1 ga 221 D 2 10 Rep1 C3 P2 de 240 C 1 11 Rep1 C3 P3 al 267 B 4 12 Rep1 C3 P4 be 252 A 3 13 Rep1 C4 P1 de 301 B 3 14 Rep1 C4 P2 ga 238 A 4 15 Rep1 C4 P3 be 243 D 1 16 Rep1 C4 P4 al 290 C 2 17 Rep2 C5 P1 ep 285 A 1 18 Rep2 C5 P2 xi 280 B 2 19 Rep2 C5 P3 th 331 C 3 20 Rep2 C5 P4 ka 311 D 4 21 Rep2 C6 P1 xi 268 C 4 22 Rep2 C6 P2 ep 233 D 3 23 Rep2 C6 P3 ka 291 A 2 24 Rep2 C6 P4 th 280 B 1 25 Rep2 C7 P1 th 265 D 2 26 Rep2 C7 P2 ka 273 C 1 27 Rep2 C7 P3 ep 234 B 4 28 Rep2 C7 P4 xi 243 A 3 29 Rep2 C8 P1 ka 306 B 3 30 Rep2 C8 P2 th 271 A 4 31 Rep2 C8 P3 xi 270 D 1 32 Rep2 C8 P4 ep 272 C 2 A REPLICATED HYPER-GRAECO-LATIN SQUARE for testing Cloth Wear 2 See Table 4.12 in text (Box-Hunter-Hunter) p163 MEANS FOR EACH LEVEL OF EACH FACTOR 11:38 Thursday, January 24, 2008 (In order of how they appear on p163 in text) Note they are the same with two exceptions: The MEANS Procedure Analysis Variable : Yy N Treat Obs Mean Std Dev ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ A 8 270.0 27.6 B 8 275.6 27.1 C 8 279.9 27.0 D 8 260.4 36.2 ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ A REPLICATED HYPER-GRAECO-LATIN SQUARE for testing Cloth Wear 3 See Table 4.12 in text (Box-Hunter-Hunter) p163 MEANS FOR EACH LEVEL OF EACH FACTOR 11:38 Thursday, January 24, 2008 (In order of how they appear on p163 in text) Note they are the same with two exceptions: The MEANS Procedure Analysis Variable : Yy N Holder Obs Mean Std Dev ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ 1 8 268.9 27.7 2 8 272.0 24.4 3 8 274.0 39.6 4 8 271.0 29.0 ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ A REPLICATED HYPER-GRAECO-LATIN SQUARE for testing Cloth Wear 4 See Table 4.12 in text (Box-Hunter-Hunter) p163 MEANS FOR EACH LEVEL OF EACH FACTOR 11:38 Thursday, January 24, 2008 (In order of how they appear on p163 in text) Note they are the same with two exceptions: The MEANS Procedure Analysis Variable : Yy N Position Obs Mean Std Dev ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ P1 8 279.0 31.1 P2 8 257.4 25.9 P3 8 274.4 31.6 P4 8 275.1 28.7 ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ A REPLICATED HYPER-GRAECO-LATIN SQUARE for testing Cloth Wear 5 See Table 4.12 in text (Box-Hunter-Hunter) p163 MEANS FOR EACH LEVEL OF EACH FACTOR 11:38 Thursday, January 24, 2008 (In order of how they appear on p163 in text) Note that Greek letters are listed alphabetically and NOT in their natural order (alpha,beta,gamma,delta,....) The MEANS Procedure Analysis Variable : Yy N Emory Obs Mean Std Dev ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ al 4 276.0 39.2 be 4 264.5 23.6 de 4 278.5 34.3 ep 4 256.0 26.5 ga 4 249.5 34.1 ka 4 295.3 17.1 th 4 286.8 30.1 xi 4 265.3 15.7 ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ A REPLICATED HYPER-GRAECO-LATIN SQUARE for testing Cloth Wear 6 See Table 4.12 in text (Box-Hunter-Hunter) p163 MEANS FOR EACH LEVEL OF EACH FACTOR 11:38 Thursday, January 24, 2008 (In order of how they appear on p163 in text) ' The MEANS Procedure Analysis Variable : Yy N Cycle Obs Mean Std Dev ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ C1 4 307.3 11.1 C2 4 248.3 18.0 C3 4 245.0 19.4 C4 4 268.0 32.1 C5 4 301.8 23.8 C6 4 268.0 25.2 C7 4 253.8 18.3 C8 4 279.8 17.5 ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ A REPLICATED HYPER-GRAECO-LATIN SQUARE for testing Cloth Wear 7 See Table 4.12 in text (Box-Hunter-Hunter) p163 MEANS FOR EACH LEVEL OF EACH FACTOR 11:38 Thursday, January 24, 2008 (In order of how they appear on p163 in text) There is typo in the text for the value of Rep1 For a balanced design, the average of the two Rep values should be the overall mean (271.5), but it is not The MEANS Procedure Analysis Variable : Yy N Replicate Obs Mean Std Dev ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Rep1 16 267.1 32.0 Rep2 16 275.8 26.4 ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ A REPLICATED HYPER-GRAECO-LATIN SQUARE for testing Cloth Wear 8 See Table 4.12 in text (Box-Hunter-Hunter) p163 ANOVA MODEL for Replicated Hyper-Graeco-Latin Squares 11:38 Thursday, January 24, 2008 The GLM Procedure Class Level Information Class Levels Values Treat 4 A B C D Replicate 2 Rep1 Rep2 Cycle 8 C1 C2 C3 C4 C5 C6 C7 C8 Position 4 P1 P2 P3 P4 Emory 8 al be de ep ga ka th xi Holder 4 1 2 3 4 Number of Observations Read 32 Number of Observations Used 32 A REPLICATED HYPER-GRAECO-LATIN SQUARE for testing Cloth Wear 9 See Table 4.12 in text (Box-Hunter-Hunter) p163 ANOVA MODEL for Replicated Hyper-Graeco-Latin Squares 11:38 Thursday, January 24, 2008 The GLM Procedure Dependent Variable: Yy Sum of Source DF Squares Mean Square F Value Pr > F Model 22 25514.93750 1159.76989 11.00 0.0004 Error 9 949.03125 105.44792 Corrected Total 31 26463.96875 R-Square Coeff Var Root MSE Yy Mean 0.964139 3.782676 10.26878 271.4688 Source DF Type I SS Mean Square F Value Pr > F Treat 3 1705.34375 568.44792 5.39 0.0212 Replicate 1 603.78125 603.78125 5.73 0.0404 Cycle(Replicate) 6 14770.43750 2461.73958 23.35 <.0001 Position 3 2217.34375 739.11458 7.01 0.0099 Emory(Replicate) 6 6108.93750 1018.15625 9.66 0.0017 Holder 3 109.09375 36.36458 0.34 0.7938 Source DF Type III SS Mean Square F Value Pr > F Treat 3 1705.34375 568.44792 5.39 0.0212 Replicate 1 603.78125 603.78125 5.73 0.0404 Cycle(Replicate) 6 14770.43750 2461.73958 23.35 <.0001 Position 3 2217.34375 739.11458 7.01 0.0099 Emory(Replicate) 6 6108.93750 1018.15625 9.66 0.0017 Holder 3 109.09375 36.36458 0.34 0.7938 A REPLICATED HYPER-GRAECO-LATIN SQUARE for testing Cloth Wear 10 See Table 4.12 in text (Box-Hunter-Hunter) p163 ANOVA MODEL for Replicated Hyper-Graeco-Latin Squares RESIDUALxPREDICTED VALUE PLOT 11:38 Thursday, January 24, 2008 No apparent extreme outliers nor apparent dependence between residuals and fitted values Plot of Residuals*Predicted. Symbol used is '*'. 20 ˆ ‚ ‚ ‚ ‚ ‚ * 10 ˆ ‚ * ‚ * * * Residuals ‚ * * * ‚ ** * ‚ * * * 0 ˆ * * * * ‚ * * * ‚ * * * ‚ * * * ‚ * * * ‚ * -10 ˆ ‚ * ‚ ‚ ‚ ‚ -20 ˆ Šƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒ 220 240 260 280 300 320 340 Predicted