Question

Four factors influence the taste of pizza: crust (A), toppings (B), temperature (C), and sauce (D). Each can be run at two levels, producing a 2⁴ design. At each run in the design, samples of pizza are given to a test panel consisting of 20 people. Each tester assigns a point score from 1 to 10 to the pizza. Total score is the response variable, and the objective is to find a formulation that maximizes the total score. Two replicates of the design are run, and the results are shown in the Table. Analyze this data and draw conclusions.

Replicate Treatment Combination 188 195 172 179 185 175 183 190 175 200 170 189 183 201 181 180 187 178 180 178 180 168 193 178 181 188 188 173 ac bd abd acd 189 182 178 182 abcd

Answer 1

Performing analysis in SPSS

Crust	Toppings	Temperature	Sauce	Replication	Observations
0	0	0	0	1	188.00
1	0	0	0	1	172.00
0	1	0	0	1	179.00
1	1	0	0	1	185.00
0	0	1	0	1	175.00
1	0	1	0	1	183.00
0	1	1	0	1	190.00
1	1	1	0	1	175.00
0	0	0	1	1	200.00
1	0	0	1	1	170.00
0	1	0	1	1	189.00
1	1	0	1	1	183.00
0	0	1	1	1	201.00
1	0	1	1	1	181.00
0	1	1	1	1	189.00
1	1	1	1	1	178.00
0	0	0	0	2	195.00
1	0	0	0	2	180.00
0	1	0	0	2	187.00
1	1	0	0	2	178.00
0	0	1	0	2	180.00
1	0	1	0	2	178.00
0	1	1	0	2	180.00
1	1	1	0	2	168.00
0	0	0	1	2	193.00
1	0	0	1	2	178.00
0	1	0	1	2	181.00
1	1	0	1	2	188.00
0	0	1	1	2	188.00
1	0	1	1	2	173.00
0	1	1	1	2	182.00
1	1	1	1	2	182.00

ANOVA TABLE

Tests of Between-Subjects Effects
Dependent Variable: Observations
Source	Type III Sum of Squares	df	Mean Square	F	Sig.
Corrected Model	1504.969a	15	100.331	3.471	.009
Intercept	1069087.531	1	1069087.531	36984.650	.000
Crust	657.031	1	657.031	22.730	.000
Toppings	13.781	1	13.781	.477	.500
Temperature	57.781	1	57.781	1.999	.177
Sauce	124.031	1	124.031	4.291	.055
Crust * Sauce	38.281	1	38.281	1.324	.267
Crust * Temperature	3.781	1	3.781	.131	.722
Crust * Toppings	132.031	1	132.031	4.568	.048
Temperature * Sauce	22.781	1	22.781	.788	.388
Toppings * Sauce	.281	1	.281	.010	.923
Toppings * Temperature	2.531	1	2.531	.088	.771
Crust * Temperature * Sauce	7.031	1	7.031	.243	.629
Crust * Toppings * Sauce	175.781	1	175.781	6.081	.025
Crust * Toppings * Temperature	215.281	1	215.281	7.448	.015
Toppings * Temperature * Sauce	7.031	1	7.031	.243	.629
Crust * Toppings * Temperature * Sauce	47.531	1	47.531	1.644	.218
Error	462.500	16	28.906
Total	1071055.000	32
Corrected Total	1967.469	31
a. R Squared = .765 (Adjusted R Squared = .545)

From ANOVA TABLE

One factor effect of crust is significantly different from other

In two factor interaction, crust*topping( p value 0.048) is significantly different from other two factor interaction effects.

In three factor interaction, (Crust * Toppings * Sauce) (p value 0.025) and (Crust * Toppings * Temperature) (p value 0.015) are significantly different from other three factor interaction effects.

Four factor interaction effects do not have significant effect.

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