Three way ANOVA ExamplePopcorn!!!

Data Set

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

Popcorn Example Layout

Popcorn Layout

Popcorn 1 2 1 2 Oil 1 2

Batch

Small XX XX XX XX XX XX XX XX

Large XX XX XX XX XX XX XX XX

ANOVA TableSource DF Sum of Squares F Ratio Prob > Fpopcorn 1 34.81 17.31 0.0032*oil amt 1 4.41 2.19 0.1768batch 1 49.00 24.37 0.0011*batch *popcorn 1 37.21 18.51 0.0026*batch *oil amt 1 0.01 0.0050 0.9455popcorn*oil amt 1 4.00 1.9900 0.1960popcorn*oil amt*batch 1 4.00 1.9900 0.1960

Popcorn TypeLevelLeast Sq Mean Std Error Meangourmet 12.22 0.5012

12.2250plain 9.275000 0.5012 9.2750

Batch SizeLevelLeast Sq Mean Std Error Mean

large 9.000000 0.50124844 9.0000

small 12.500000 0.50124844 12.5000

Popcorn*Batch Interaction Plot

How to Test Interaction MeansRecode Popcorn*Batch as Trt, i.e.Trt=1 is Plain, SmallTrt=2 is Plain, LargeTrt=3 is Gourmet, SmallTrt=4 is Gourmet, Large

New ANOVA TableSource DF SS F Ratio

Prob > FTrt 3 121.0200020.0697 0.0004*

oil amt 1 4.41000 2.1940 0.1768Trt*oil amt 3 8.01000 1.3284 0.3314

Plot of Means with SD

Tukey Test of Interaction Means

Level Least Sq Mean3 A 15.5000001 B 9.5000002 B 9.0500004 B 8.950000

Levels not connected by same letter are significantly different.

Plot of Residuals

Normal Plot of Residuals

Test of NormalityGoodness-of-Fit Test Shapiro-Wilk W Test

W Prob<W0.976987 0.9352

Note: Ho = The data is from the Normal distribution. Small p-values reject Ho.

Box-Cox Plot