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Three way ANOVA Example

Three way ANOVA Example. Popcorn!!!. Data Set. Popcorn Oil amt. Batch Yield plain little large 8.2 gourmet little large 8.6 plain lots large 10.4 gourmet lots large 9.2 plain little small 9.9

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Three way ANOVA Example

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  1. Three way ANOVA Example Popcorn!!!

  2. Data Set Popcorn Oil amt. Batch Yield plain little large 8.2 gourmet little large 8.6 plain lots large 10.4 gourmet lots large 9.2 plain little small 9.9 gourmet little small 12.1 plain lots small 10.6 gourmet lots small 18.0 plain little large 8.8 gourmet little large 8.2 plain lots large 8.8 gourmet lots large 9.8 plain little small 10.1 gourmet little small 15.9 plain lots small 7.4 gourmet lots small 16.0

  3. Popcorn Example Layout

  4. ANOVA Table Source DF Sum of Squares F Ratio Prob> F popcorn 134.81 17.31 0.0032* oil amt 14.41 2.19 0.1768 batch 149.00 24.37 0.0011* batch *popcorn 137.21 18.51 0.0026* batch *oil amt 10.01 0.0050 0.9455 popcorn*oil amt 14.00 1.9900 0.1960 popcorn*oil amt*batch 14.00 1.9900 0.1960

  5. Popcorn Type • Level Least Sq Mean Std Error Mean • gourmet 12.22 0.5012 12.2250 • plain 9.2750000.5012 9.2750

  6. Batch Size • Level Least Sq Mean Std Error Mean • large 9.000000 0.50124844 9.0000 • small 12.500000 0.50124844 12.5000

  7. Popcorn*Batch Interaction Plot

  8. How to Test Interaction Means Recode Popcorn*Batch as Trt, i.e. Trt=1 is Plain, Small Trt=2 is Plain, Large Trt=3 is Gourmet, Small Trt=4 is Gourmet, Large

  9. New ANOVA Table Source DF SS F Ratio Prob > F Trt 3 121.02000 20.0697 0.0004* oil amt 1 4.41000 2.1940 0.1768 Trt*oil amt 3 8.01000 1.3284 0.3314

  10. Plot of Means with SD

  11. Tukey Test of Interaction Means • Level Least Sq Mean • 3 A 15.500000 • 1 B 9.500000 • 2 B 9.050000 • 4 B 8.950000 • Levels not connected by same letter are significantly different.

  12. Plot of Residuals

  13. Normal Plot of Residuals

  14. Test of Normality • Goodness-of-Fit Test • Shapiro-Wilk W Test • W Prob<W • 0.976987 0.9352 • Note: Ho = The data is from the Normal distribution. Small p-values reject Ho.

  15. Box-Cox Plot

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