1. Which golfer hit Brand A the furthest ? (A) Jones (B) Smith (C) Long (D) Carroll 2. Which golfer hit Brand B the furthest ? (A) Jones (B) Smith (C) Long (D) Carroll 3. Which golfer hit Brand C the furthest ? (A) Jones (B) Smith (C) Long (D) Carroll 4. Which golfer did not hit Brand C further than he did A and B ? (A) Jones (B) Smith (C) Long (D) Carroll 5. What is the average for Jones ? (A) 255.67 (B) 230.00 (C) 279.00 (D) 240.33 yards 6. What is the average for Smith ? (A) 255.67 (B) 230.00 (C) 279.00 (D) 240.33 yards IDS 371 (Sclove) Hw on ANOVA 7. What is the average for Long? (A) 255.67 (B) 230.00 (C) 279.00 (D) 240.33 yards 8. What is the average for Carroll ? (A) 255.67 (B) 230.00 (C) 279.00 (D) 240.33 yards 9. What is F(A)? (A) MS(A)/MS(E) (B) MS(A)/MS(B) (C) MS(E)/MS(A) (D) MS(B) / MS(A) ? 2 C:// DATASETS/ A 123456 1 Golfer 2 Jones 3 Smith 4 Long 5 Carroll 6 Reed ANOVA twowayWithout Reps B C D Brand A Brand B Brand C 250 255 262 225 235 230 270 282 285 235 240 246 215 220 223 Source. Advanced Statistics Demystified by Dr. Larry J. Stephens McGraw-Hill, 2004. BRAND A B C mean Jones 250 255 262 255.7 GOLFER Smith 225 235 230 230.0 Long 270 282 285 279.0 Carroll 235 240 246 240.3 Reed 215 220 223 219.3 mean 239.0 246.4 249.2 244.9 285 280 L L 275 270 L 265 260 J 255 J - yards 250 - 245 240 235 CS C 230 S 225 S 220 R R 215 RA R A B BRAND C:// DATASETS/ TABLE. Data ANOVA twowayWithoutReps length of drive (yards) BRAND A B C Jones 250 255 262 GOLFER Smith 225 235 230 Long 270 282 285 Carroll 235 240 246 Reed 215 220 223 TABLE. Output of Excel DataAnalysis Toolpak Two-Factor ANOVA ANOVA: Two-Factor Without Replication SUMMARY Count Sum Average Variance Jones 3 767 255.67 36.333 Smith 3 690 230.00 25.000 Long 3 837 279.00 63.000 Carroll 3 721 240.33 30.333 Reed 3 658 219.33 16.333 A B C 555 1195 239.00 467.500 1232 246.40 552.300 5 1246 249.20 627.700 ANOVA Source of Variation SS df MS F P-value Golfers Rows 6525.733 4 1631.433 203.083 4.487E-08 Brands Columns 277.733 2 138.867 17.286 0.001 Error 64.267 8 8.033 Total 6867.733 14 TABLE. Notation ANOVA Factor Source of Variation SS df MS A Rows SS(A) DFA = 1-1 MS(A) F F(A) B Columns SS(B) DFB = J-1 MS(B) F(B) P-value |F.DIST.RT(F(A), DFA,DFE) | F.DIST.RT(F(B),DFA,DFE) Error SSE (1-1)(J-1) MS (E) Total SST IJ-1 F(A) = MS(A)/MS(E) F(B) = MS(B)/MS(E) C:// DATASETS / ANOVA twowayWithoutReps A B D 1 Golfer Brand A Brand B Brand C 2 Jones 3 Smith 4 Long 250 255 262 225 235 230 270 282 285 5 Carroll 6 Reed 235 240 246 215 220 223 20220313 From Advanced Statistics Demystified by Dr. Larry J. Stephens TABLE. Notation Y(ij) FACTOR B B1 B2 B3 mean A1 Y(11) Y(12) Y(13) Y(1.) 285 FACTOR A A2 Y(21) Y(22) Y(23) Y(2.) 280 L L A3 Y(31) Y(32) Y(33) Y(3.) 275 A4 Y(41) Y(42) Y(43) Y(4.) 270 L A5 Y(51) Y(52) Y(53) Y(5.) 265 mean Y(.1) Y(.2) Y(.3) Y(..) 260 J 255 Model: yards 250 J Y(ab): = mu+alpha(a) + beta(b) + error(ab) fitted value of 245 C 240 |Y(ab) = y(..) + (y(a.)-y(..)) + [y(.b)-y(..) + [y(ab)-y(a.)-y(.b)+y(..)] 235 C US C S equals overrall mean + level a effect + level b effect + residual 230 S 225 S 220 R R 215 RA B C BRAND