Example of a 2-factor Factorial Experiment

Data were collected on the yield (in cups of popped corn) from a 1/4 cup
of unpopped kernels based on two factors. The factors of interest are:
Type of popcorn maker (oil based or air based) and brand 
(gourmet, national or generic). The data are below:

                           Brand

Popper |    Gourmet   |   National   |   Generic 
-------|--------------|--------------|------------
Oil    |  5.5 5.5 6.0 |  4.5 4.5 4.0 | 3.5 4.0 3.0 
-------|--------------|--------------|------------
Air    |  6.5 7.0 7.0 |  5.0 5.5 5.0 | 4.0 5.0 4.5 


 Questions to consider:

 1. Do the type of popper and brand of popcorn interact in their effect
on yield?

 2. Does the popper used affect the yield (independent of the brand)?

 3. Does the brand used affect the yield (independent of the popper)?

 Procedure: 
 
 1. The test for Interaction is ALWAYS done first.  







 If we conclude that the factors interact, then we can't separate the
effects of the factors on the response variable. So it would be
inappropriate to try and assess the main factor effects. 

 If the interaction test shows little evidence against the null
hypothesis of no interaction, we can conduct the main factor effects for
each factor. 

 2. Test for main effect of Factor A:

 




 3. Test for main effect of Factor B:
 





The Minitab output for this problem is below. 

 Although not necessary, the first thing constructed below is a table of
the data in Minitab. This can be done using the

  Stat -> Tables -> Cross Tabulation

option, selecting Popper and Brand as the classification variables,
and under Summaries, selecting Yield as the Associated Variable, and
choosing the Display Data option.



  ROWS: Popper   COLUMNS: Brand
  
       Gourmet  National  Generic
   
  Oil   5.5000    4.5000   3.5000
        5.5000    4.5000   4.0000
        6.0000    4.0000   3.0000
   
  Air   6.5000    5.0000   4.0000
        7.0000    5.5000   5.0000
        7.0000    5.0000   4.5000
  
   CELL CONTENTS --
             Yield: DATA

------------------------------------------------------

 We use the ANOVA -> Two-way ANOVA pull down menu in Minitab to analyze
 this data:


 Two-way ANOVA: Yield versus Popper, Brand   
 
 SOURCE        DF        SS        MS       F       p
 Popper         1     4.500     4.500   32.40   0.000
 Brand          2    15.750     7.875   56.70   0.000
 Interaction    2     0.083     0.042    0.30   0.746
 Error         12     1.667     0.139
 Total         17    22.000