Applied Statistics and Probability for Engineers

14-4 TWO-FACTOR FACTORIAL EXPERIMENTS 515

A factorial experiment was performed to investigate the effect of paint primer type and ap-

plication method on paint adhesion. For each combination of primer type and application

method, three specimens were painted, then a finish paint was applied, and the adhesion

force was measured. The data from the experiment are shown in Table 14-5. The circled

numbers in the cells are the cell totals yij.. The sums of squares required to perform the

ANOVA are computed as follows:

and

SSESSTSStypesSSmethodsSSinteraction

10.72 4.58 4.91 0.24 0.99

The ANOVA is summarized in Table 14-6. The experimenter has decided to use 0.05.

Since f0.05,2,123.89 and f0.05,1,124.75, we conclude that the main effects of primer type and



1 89.8 22

18

4.584.910.24



1 12.8 22  1 15.9 22  1 11.5 22  1 15.9 22  1 18.2 22  1 15.5 22

3

SSinteraction a

a

i 1

a

b

j 1

y^2 ij#.

n 

y^2 ...

abn

SStypesSSmethods



1 40.2 22  1 49.6 22

9



1 89.8 22

18

4.91

SSmethods a

b

j 1

y^2 .j.

an

y...^2

abn



1 28.7 22  1 34.1 22  1 27.0 22

6



1 89.8 22

18

4.58

SStypes a

a

i 1

y^2 i..

bn



y...^2

abn

 1 4.0 22  1 4.5 22 p 1 5.0 22 

1 89.8 22

18

10.72

SST a

a

i 1

a

b

j 1

a

n

k 1

y

2

ijk

y...^2

abn

Table 14-5 Adhesion Force Data for Example 14-1

Primer Type Dipping Spraying yi..

1 4.0, 4.5, 4.3 12.8 5.4, 4.9, 5.6 15.9 28.7

2 5.6, 4.9, 5.4 15.9 5.8, 6.1, 6.3 18.2 34.1

3 3.8, 3.7, 4.0 11.5 5.5, 5.0, 5.0 15.5 27.0

y.j. 40.2 49.6 89.8 y...

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