3 22 EXAMPLE ANOVA JMP output Problem 3

3. 22 EXAMPLE ANOVA JMP output

Problem 3. 22 Data Circuit Design Noise 1 19 1 20 1 19 1 30 1 8 2 80 2 61 2 73 2 56 2 80 3 47 3 26 3 25 3 35 3 50 4 95 4 46 4 83 4 78 4 97

Trt. Means with s. e.

Problem 3. 22 ANOVA � � Oneway Anova Summary of Fit � � � Rsquare 0. 803293 Adj Rsquare 0. 76641 Root Mean Square Error 13. 57571 Mean of Response 51. 4 Observations (or Sum Wgts) 20 Analysis of Variance Source DF Sum of Squares Mean Square Circuit Design Error C. Total 12042. 000 4014. 00 2948. 800 184. 30 14990. 800 21. 7797 Mean 6. 0712 Lower 95% Upper 95% 32. 070 82. 870 49. 470 92. 670 3 16 19 � Means for Oneway Anova Level Number 1 5 19. 2000 2 5 70. 0000 3 5 36. 6000 4 5 79. 8000 � Std Error uses a pooled estimate of error variance � � � Std Error 6. 330 57. 130 23. 730 66. 930 <. 0001* F Ratio Prob > F

T-test range test � Level Mean 4 A 79. 800000 � 2 A 70. 000000 � 3 B 36. 600000 � 1 B 19. 200000 � Levels not connected by same letter are significantly different. �

T-test Comparisons � � � Comparisons for each pair using Student's t t Alpha 2. 11991 0. 05 4 -8. 402 -18. 202 15. 198 32. 598 2 24. 998 15. 198 -18. 202 -0. 802 3 42. 398 32. 598 -0. 802 -18. 202 � Abs(Dif)-LSD 4 -18. 202 2 -8. 402 3 24. 998 1 42. 398 � Positive values show pairs of means that are significantly different. � � Level 4 A 2 A 3 1 � Levels not connected by same letter are significantly different. � Level 4 2 3 4 � � � � - Level 1 1 3 3 1 2 1 Mean 79. 800000 70. 000000 36. 600000 19. 200000 B B Difference 60. 60000 50. 80000 43. 20000 33. 40000 17. 40000 9. 80000 Std Err Dif 8. 586035 Lower CL 42. 3984 32. 5984 24. 9984 15. 1984 -0. 8016 -8. 4016 Upper CL 78. 80158 69. 00158 61. 40158 51. 60158 35. 60158 28. 00158 p-Value <. 0001* 0. 0013* 0. 0597 0. 2705 Difference

Tukey-Kraemer range test � Level Mean 4 A 79. 800000 � 2 A 70. 000000 � 3 B 36. 600000 � 1 B 19. 200000 � Levels not connected by same letter are significantly different. �

Tukey-Kramer HSD Comparison � � � Comparisons for all pairs using Tukey-Kramer HSD q* Alpha 2. 86102 0. 05 4 -14. 765 -24. 565 8. 835 26. 235 2 18. 635 8. 835 -24. 565 -7. 165 3 36. 035 26. 235 -7. 165 -24. 565 � Abs(Dif)-HSD 4 -24. 565 2 -14. 765 3 18. 635 1 36. 035 � Positive values show pairs of means that are significantly different. � � Level 4 A 2 A 3 1 � Levels not connected by same letter are significantly different. � Level 4 2 3 4 � � � � - Level 1 1 3 3 1 2 1 Mean 79. 800000 70. 000000 36. 600000 19. 200000 B B Difference 60. 60000 50. 80000 43. 20000 33. 40000 17. 40000 9. 80000 Std Err Dif 8. 586035 Lower CL 36. 0352 26. 2352 18. 6352 8. 8352 -7. 1648 -14. 7648 Upper CL 85. 16482 75. 36482 67. 76482 57. 96482 41. 96482 34. 36482 p-Value <. 0001* 0. 0006* 0. 0064* 0. 2195 0. 6703 Difference

Box Plot of Residuals

Normal Plot of Residuals

Parameter Estimates and Goodness of Fit � Parameter Estimates Type Parameter Estimate Lower 95% Upper 95% Location μ 5. 329 e-16 -5. 8304903 Dispersion σ 12. 457929 9. 4741355 18. 195698 � -2 log(Likelihood) = 156. 651833483169 � Goodness-of-Fit Test Shapiro-Wilk W Test � � � � W 0. 926866 Prob<W 0. 1344 Note: Ho = The data is from the Normal distribution. Small p-values reject Ho.

Plot of Residual vs. Predicted Values

Tests for Equality of Variances � Level Count Std Dev Mean. Abs. Dif to Median 10 3 51. 9615 40. 00000 30. 00000 15 3 77. 6745 57. 77778 63. 33333 20 3 107. 8579 82. 22222 76. 66667 � 25 3 � Test F Ratio O'Brien[. 5] 0. 9839 Brown-Forsythe Levene 4. 2528 Bartlett 1. 9797 � � � � 10. 0000 6. 66667 10. 00000 DFNum 3 1. 0266 3 3 DFDen 8 3 8. Prob > F 0. 4475 8 0. 4308 0. 0451* 0. 1146