626 CHAPTER 12 Analysis of Variance 18.Bonferroni Test Shown below are weights (kg) of poplar trees obtained from trees planted in a rich and moist region. The trees were given different treatments identified in the table below. The data are from a study conducted by researchers at Pennsylvania State University and were provided by Minitab, Inc. Also shown are partial results from using the Bonferroni test with the sample data. No Treatment Fertilizer Irrigation Fertilizer and Irrigation 1.21 0.94 0.07 0.85 0.57 0.87 0.66 1.78 0.56 0.46 0.10 1.47 0.13 0.58 0.82 2.25 1.30 1.03 0.94 1.64 a. Use a 0.05 significance level to test the claim that the different treatments result in the same mean weight. b. What do the displayed Bonferroni SPSS results tell us? c. Use the Bonferroni test procedure with a 0.05 significance level to test for a significant difference between the mean amount of the irrigation treatment group and the group treated with both fertilizer and irrigation. Identify the test statistic and either the P-value or critical values. What do the results indicate? SPSS Bonferroni Results from SPSS Key Concept Section 12-1 considered data partitioned using one factor, but this section describes the method of two-way analysis of variance, which is used with data partitioned into categories according to two factors. The method of this section requires that we first test for an interaction between the two factors; then we test for an effect from the row factor, and we test for an effect from the column factor. Table 12-3 includes data of the measured force on femurs (or thighbones) in car crash tests. The data are measured in kilonewtons 1kN2. Table 12-3 has data categorized according to the two factors: 1. Femur Side: One factor is whether the femur is in the left leg or the right leg. 2. Vehicle Size Category: The second factor is the vehicle size category (small, midsize, large, SUV). 12-2 Two-Way ANOVA
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