12-2 Two-Way ANOVA 631 Step 2: Row, Column Effects: Because there does not appear to be an interaction effect, we proceed to test for effects from the row and column factors. The two hypothesis tests use these null hypotheses: H0: There are no effects from the row factor 1that is, the row values are from populations with equal means2. H0: There are no effects from the column factor 1that is, the column values are from populations with equal means2. Row Factor: For the row factor (femur side), we refer to the preceding StatCrunch display of results to see that the test statistic for the row factor is F = 0.9002 (rounded). This test statistic can be calculated as follows: F = MS1leg side2 MS1error2 = 0.441 0.489875 = 0.9002 Conclusion: The corresponding P-value is shown in the StatCrunch display as 0.3498. Because that P-value is greater than the significance level of 0.05, we fail to reject the null hypothesis of no effects from femur side. That is, the car crash force measurements do not appear to be affected by whether the femur is in the left leg or right leg. Column Factor: For the column factor (vehicle size category), we refer to the preceding StatCrunch display of results to see that the test statistic for the column factor is F = 0.4280 (rounded). This test statistic can be calculated as follows: F = MS1size2 MS1error2 = 0.2096667 0.489875 = 0.4280 Conclusion: The corresponding P-value is shown in the StatCrunch display as 0.7343. Because that P-value is not less than the significance level of 0.05, we fail to reject the null hypothesis of no effects from vehicle size category. The femur crash force measurements do not appear to be affected by the size of the vehicle. INTERPRETATION On the basis of the sample data in Table 12-3, we conclude that the crash force measurements on the femur are not affected by an interaction between the femur side (left, right) and the vehicle size category, they are not affected by the femur side (left, right), and they are not affected by the vehicle size category. YOUR TURN. Do Exercise 5 “Car Crash Test Measurements.” CAUTION Two-way analysis of variance is not one-way analysis of variance done twice. When conducting a two-way analysis of variance, be sure to test for an interaction between the two factors.
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