Understanding Popcorn Production: An In-depth Analysis
Explore the intricacies of popcorn production through detailed data sets, ANOVA tables, types, batch sizes, interaction plots, and Tukey tests. Learn about testing interaction means and delving into new ANOVA tables to uncover insights into popcorn variants. Dive into the world of popcorn research with this comprehensive analysis.
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Data Set Popcorn Oil amt. Batch Yield plain little gourmet little plain lots gourmet lots plain little gourmet little plain lots gourmet lots plain little gourmet little plain lots gourmet lots plain little gourmet little plain lots gourmet lots large large large large small 9.9 small small 10.6 small large large 8.2 large large 9.8 small small small 7.4 small 8.2 8.6 10.4 9.2 12.1 18.0 8.8 8.8 10.1 15.9 16.0
Popcorn Example Layout Popcorn Layout Popcorn 1 Oil 1 Small XX 2 1 2 XX XX 2 Batch XX XX XX XX XX Large XX XX XX XX XX XX XX XX
ANOVA Table Source popcorn oil amt 1 batch 1 batch *popcorn DF Sum of Squares F Ratio Prob > F 1 34.81 17.31 0.0032* 4.41 2.19 49.00 24.37 0.1768 0.0011* 1 37.21 18.51 0.0026* batch *oil amt 1 0.01 0.0050 0.9455 popcorn*oil amt 1 popcorn*oil amt*batch 1 4.00 1.9900 0.1960 4.00 1.9900 0.1960
Popcorn Type Level Least Sq Mean Std Error Mean gourmet 12.22 0.5012 12.2250 plain 9.275000 0.5012 9.2750
Batch Size Level Least Sq Mean Std Error Mean large9.000000 small 0.50124844 9.0000 12.500000 0.50124844 12.5000
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
New ANOVA Table Source DF SS F Ratio Prob > F Trt 3 121.02000 20.0697 0.0004* oil amt Trt*oil amt 3 1 4.41000 8.01000 2.19400.1768 1.32840.3314
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.
Test of Normality Goodness-of-Fit Test Shapiro-Wilk W Test W 0.976987 Prob<W 0.9352 Note: Ho = The data is from the Normal distribution. Small p-values reject Ho.
