Question

Consider the data set below of the 14” pizzas at Little Italy. There are two pizza chefs (Anna and Lorenzo, Factor A), two work shifts (day and evening, Factor B), and two dough companies (Sysco and PFG Holdings, Factor C). For each combination, there are four pizzas made (n = 4). The diameter of each pizza is measured.

                                                                        Measurements                                                

Pizza                                       Anna                                                   Lorenzo

Dough                Shift             1          2        3        4                    1            2        3        4

Sysco                   Day             14.1     14.1     14.2     14.1                 14.2     14.1     14.1     13.9

Sysco                   Evening       14.1     14.2     14.3     14.2                 14.3     14.2     14.3     14.1

PFG Holdings     Day             13.9     14.0     14.0     14.1                 13.9     13.9     13.8     13.9

PFG Holdings     Evening       13.8     13.7     13.9     14.0                 14.3     14.2     14.2     14.1

Using the main effects and the interactions effects and the contrasts you calculated in part 1:

1. Calculate the SS of each factor, the factor interactions, the error, and the total.
2. Construct the ANOVA table showing the MS of each factor, interaction and error, along with the F values.
3. Which main effects and interactions are significant at 95% confidence?

Answer 1

The ANOVA table is:

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Pizza	1	0.02000	0.020000	1.21	0.281
Work Shift	1	0.08000	0.080000	4.83	0.036
Dough Company	1	0.24500	0.245000	14.79	0.001
Error	28	0.46375	0.016562
Lack-of-Fit	4	0.26375	0.065937	7.91	0.000
Pure Error	24	0.20000	0.008333
Total	31	0.80875

There is a main effect of Work Shift.

There is a main effect of Dough Company.

There is an interaction effect.

Pizza	Work Shift	Dough Company	Data
Anna	Day	Sysco	14.1
Anna	Evening	Sysco	14.1
Anna	Day	PFG Holdings	13.9
Anna	Evening	PFG Holdings	13.8
Anna	Day	Sysco	14.1
Anna	Evening	Sysco	14.2
Anna	Day	PFG Holdings	14
Anna	Evening	PFG Holdings	13.7
Anna	Day	Sysco	14.2
Anna	Evening	Sysco	14.3
Anna	Day	PFG Holdings	14
Anna	Evening	PFG Holdings	13.9
Anna	Day	Sysco	14.1
Anna	Evening	Sysco	14.2
Anna	Day	PFG Holdings	14.1
Anna	Evening	PFG Holdings	14
Lorenzo	Day	Sysco	14.2
Lorenzo	Evening	Sysco	14.3
Lorenzo	Day	PFG Holdings	13.9
Lorenzo	Evening	PFG Holdings	14.3
Lorenzo	Day	Sysco	14.1
Lorenzo	Evening	Sysco	14.2
Lorenzo	Day	PFG Holdings	13.9
Lorenzo	Evening	PFG Holdings	14.2
Lorenzo	Day	Sysco	14.1
Lorenzo	Evening	Sysco	14.3
Lorenzo	Day	PFG Holdings	13.8
Lorenzo	Evening	PFG Holdings	14.2
Lorenzo	Day	Sysco	13.9
Lorenzo	Evening	Sysco	14.1
Lorenzo	Day	PFG Holdings	13.9
Lorenzo	Evening	PFG Holdings	14.1