Popcorn Production: An In-depth Analysis

 
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
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
 
Popcorn Example Layout
 
 
ANOVA Table
 
Source    
 
DF   Sum of Squares   F Ratio        Prob > F
popcorn
 
1
 
34.81                   17.31           0.0032*
oil amt
 
1
 
4.41
 
                2.19
 
         0.1768
batch  
 
1
 
49.00
 
              24.37
 
         0.0011*
batch *popcorn
            
 
1
 
37.21
 
              18.51
 
         0.0026*
batch *oil amt
                         1
 
0.01
 
                0.0050        0.9455
popcorn*oil amt
             
 
1
 
4.00
 
               1.9900
 
         0.1960
popcorn*oil amt*batch
            
 
1
 
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
large
 
9.000000
  
0.50124844
 
9.0000
small
 
12.500000
  
0.50124844
 
12.5000
 
Popcorn*Batch Interaction Plot
 
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
 
  1
 
4.41000
 
2.1940
 
0.1768
Trt*oil amt  3
 
8.01000
 
1.3284
 
0.3314
 
Plot of Means with SD
 
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.
 
Plot of Residuals
 
Normal Plot of Residuals
 
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.
 
Box-Cox Plot
Slide Note
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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.

  • Popcorn Production
  • Data Analysis
  • ANOVA Tables
  • Interaction Plots
  • Tukey Test

Uploaded on Aug 02, 2024 | 0 Views


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  1. Popcorn!!!

  2. 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

  3. 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

  4. 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

  5. Popcorn Type Level Least Sq Mean Std Error Mean gourmet 12.22 0.5012 12.2250 plain 9.275000 0.5012 9.2750

  6. Batch Size Level Least Sq Mean Std Error Mean large9.000000 small 0.50124844 9.0000 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 Trt*oil amt 3 1 4.41000 8.01000 2.19400.1768 1.32840.3314

  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 0.976987 Prob<W 0.9352 Note: Ho = The data is from the Normal distribution. Small p-values reject Ho.

  15. Box-Cox Plot

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