630 CHAPTER 12 Analysis of Variance Given the Table 12-3 measurements of crash forces on the left and right femurs in car crash tests, use two-way analysis of variance to test for an interaction effect, an effect from the row factor of femur side (left, right), and an effect from the column factor of vehicle size category (small, midsize, large, SUV). Use a 0.05 significance level. CP EXAMPLE 1 Femur Impact in Car Crash Tests SOLUTION REQUIREMENT CHECK (1) Except for the right>small and right>SUV cells, the sample values appear to be from populations with distributions that are approximately normal, as indicated by normal quantile plots. The right>small and right>SUV cells appear to be normal using a 0.01 significance level, so they don’t deviate from normal distributions by substantial amounts. (2) The variances of the cells (0.40, 0.07, 0.35, 0.03, 1.21, 0.11, 0.39, 1.36) differ considerably, but the test is robust against departures from equal variances. (3) The samples are simple random samples of vehicles. (4) The samples are independent of each other; the vehicles are not matched in any way. (5) The sample values are categorized in two ways (femur side and vehicle size category). (6) All of the cells have the same number (five) of sample values. The requirements are satisfied. The calculations are quite involved, so we use technology. The StatCrunch twoway analysis of variance display for the data in Table 12-3 is shown here. StatCrunch Step 1: Interaction Effect: We begin by testing the null hypothesis that there is no interaction between the two factors. Using StatCrunch for the data in Table 12-3, we get the results shown in the preceding StatCrunch display, and we can see that the test statistic for the interaction is F = 0.3872. This test statistic can be calculated as follows: F = MS1interaction2 MS1error2 = 0.18966667 0.489875 = 0.3872 Interpretation: The corresponding P-value is shown in the StatCrunch display as 0.763, so we fail to reject the null hypothesis of no interaction between the two factors. It does not appear that femur crash force measurements are affected by an interaction between the femur side (left, right) and vehicle size category. There does not appear to be an interaction effect.
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