12-2 Two-Way ANOVA 627 TABLE 12-3 Crash Test Force on Femur with Two Factors: Femur Side and Vehicle Size Category Small Midsize Large SUV Left Femur 1.6 1.4 0.5 0.2 0.4 0.4 0.7 1.1 0.7 0.5 0.6 1.8 0.3 1.3 1.1 0.4 0.4 0.6 0.2 0.2 Right Femur 2.8 1.0 0.3 0.3 0.2 0.6 0.8 1.3 0.5 1.1 1.5 1.7 0.2 0.6 0.9 0.7 0.7 3.0 0.2 0.2 The subcategories in Table 12-3 are called cells, so Table 12-3 has eight cells containing five values each. In analyzing the sample data in Table 12-3, we have already discussed one-way analysis of variance for a single factor (Section 12-1), so it might seem reasonable to simply proceed with one-way ANOVA for the factor of femur side and another oneway ANOVA for the factor of vehicle size category. However, that approach wastes information and totally ignores a very important feature: the possible effect of an interaction between the two factors. DEFINITION There is an interaction between two factors if the effect of one of the factors changes for different categories of the other factor. As an example of an interaction between two factors, consider food pairings. Peanut butter and jelly interact well, but ketchup and ice cream interact in a way that results in a bad taste, so we rarely see someone eating ice cream topped with ketchup. In general, consider an interaction to be an effect due to the combination of the two factors. Explore Data with Means and an Interaction Graph Let’s explore the data in Table 12-3 by calculating the mean for each cell and by constructing a graph. The individual cell means are shown in Table 12-4. Those means vary from a low of 0.68 to a high of 1.02, so they vary considerably. Figure 12-3 is an interaction graph, which shows graphs of those means. We can interpret an interaction graph as follows: ■ Interaction Effect: An interaction effect is suggested when line segments are far from being parallel. ■ No Interaction Effect: If the line segments are approximately parallel, as in Figure 12-3, it appears that the different categories of a variable have the same effect for the different categories of the other variable, so there does not appear to be an interaction effect. FIGURE 12-3 Interaction Graph of Femur Side and Vehicle Size Category from Table 12-4 TABLE 12-4 Means of Cells from Table 12-3 Small Midsize Large SUV Left Femur 0.82 0.68 1.02 0.36 Right Femur 0.92 0.86 0.98 0.96
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