Applied Statistics and Probability for Engineers

516 CHAPTER 14 DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS

application method affect adhesion force. Furthermore, since 1.5 f0.05,2,12, there is no

indication of interaction between these factors. The last column of Table 14-6 shows the

P-value for each F-ratio. Notice that the P-values for the two test statistics for the main effects

are considerably less than 0.05, while the P-value for the test statistic for the interaction is

greater than 0.05.

A graph of the cell adhesion force averages versus levels of primer type for each ap-

plication method is shown in Fig. 14-8. The no-interaction conclusion is obvious in this graph,

because the two lines are nearly parallel. Furthermore, since a large response indicates greater

adhesion force, we conclude that spraying is the best application method and that primer

type 2 is most effective.

Tests on Individual Means

When both factors are fixed, comparisons between the individual means of either factor may

be made using any multiple comparison technique such as Fisher’s LSD method (described in

Chapter 13). When there is no interaction, these comparisons may be made using either the

row averages or the column averages. However, when interaction is significant, com-

parisons between the means of one factor (say, A) may be obscured by the ABinteraction. In

this case, we could apply a procedure such as Fisher’s LSD method to the means of factor A,

with factor Bset at a particular level.

Minitab Output

Table 14-7 shows some of the output from the Minitab analysis of variance procedure for the

aircraft primer paint experiment in Example 14-1. The upper portion of the table gives factor

name and level information, and the lower portion of the table presents the analysis of vari-

ance for the adhesion force response. The results are identical to the manual calculations dis-

played in Table 14-6 apart from rounding.

yi.. y.j.

5 yij. 6

Table 14-6 ANOVA for Example 14-1

Source of Sum of Degrees of Mean

Variation Squares Freedom Square f 0 P-Value

Primer types 4.58 2 2.29 28.63 2.7 E-5

Application methods 4.91 1 4.91 61.38 5.0 E-7

Interaction 0.24 2 0.12 1.50 0.2621

Error 0.99 12 0.08

Total 10.72 17

1

3.0

4.0

5.0

6.0

7.0

23

Spraying

Dipping

Primer type

yij•

Figure 14-8 Graph of

average adhesion force

versus primer types for

both application

methods.

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