EXAMPLE 15 Two-way ANOVA when interaction is present

computerrating

Consumer Reports also provides ratings for computers. A random sample of laptop computers and desktop computers from three leading manufacturers, together with the Consumer Reports rating, is shown in Table 11. Table 12 organizes this information into a 2 × 3 contingency table, with three levels of Factor A (company) and two levels of Factor B (type), along with the ratings for each company/type combination, and the cell mean ratings. If appropriate, perform a two-way ANOVA for this data, using level of significance . Assume that the requirements are met.

Table 12.45: Table 11 Consumer Reports ratings of six laptops and six desktops
Computer Company Type Rating
MacBook MC372 Apple Laptop 78
MacBook MC024 Apple Laptop 80
Studio 15 Dell Laptop 72
Inspiron 1545 Dell Laptop 62
Pavilion DV6 HP Laptop 64
G60 HP Laptop 58
iMac MC510 Apple Desktop 73
iMac MC024 Apple Desktop 67
XPS 8100 Dell Desktop 84
XPS 7100 Dell Desktop 80
Pavilion HPE HP Desktop 89
Pavilion Elite HP Desktop 83

706

Table 12.46: Table 12 Contingency table organization of Consumer Reports computer ratings
Factor A: Company
Apple Dell HP
Factor B: Type Laptop
Desktop

What Result Might We Expect?

The interaction plot in Figure 41 indicates the presence of substantial interaction. We would therefore expect that the test for interaction will find that interaction is present.

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Figure 12.41: FIGURE 41 Interaction plot shows evidence of interaction.

  • Step 1 Test for interaction. The hypotheses are:

Reject if the . The results of the two-way ANOVA are provided in Figure 42.

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Figure 12.42: FIGURE 42 Two-way ANOVA results for the computer ratings data.

The presence of interaction between the effects makes it problematical to draw conclusions about the factors company and type.

The -value in the Interaction row in Figure 42 is 0.004, which is ≤0.01; therefore, reject . As expected, there is evidence of interaction between company and type at level of significance . Therefore, we may not proceed with the tests for the main effects.