12-1 One-Way ANOVA 621 We now evaluate the test statistic using the unrounded sample means: t = x1 - x2 B MS1error2 # a 1 n1 + 1 n2b = 290.0 - 180.75 B 5026.337121# a 1 12 + 1 12b = 3.775 The number of degrees of freedom is df = N - k = 48 - 4 = 44. (N = 48 because there are 48 different sample values in all four samples combined, and k = 4 because there are four different samples.) With a test statistic of t = 3.775 and with df = 44, the two-tailed P-value is 0.000476, but we adjust this P-value by multiplying it by 6 (the number of different possible pairs of samples) to get a final adjusted P-value of 0.002856 or 0.003 when rounded. Because this P-value is small (less than 0.05), we reject the null hypothesis. It appears that Samples 1 and 2 do have significantly different means. Instead of continuing with separate hypothesis tests for the other five pairings, see the SPSS display showing all of the Bonferroni test results. In these results, the vehicle size categories are represented as follows: 1 = small, 2 = midsize, 3 = large, 4 = SUV. The first row of results corresponds to the results found here; see the P-value of 0.003 that was previously calculated and see the same significance (“Sig”) value of 0.003 shown in the display. Consequently, there is a significance difference between small cars and medium cars. In addition, the SPSS display shows that the pairing of small>large yields a P-value of 0.001, so there is a significant difference between small cars and large cars. Also, the pairing of small>SUV yields a P-value of 0.002, so there is a significant difference between small cars and SUVs. YOUR TURN. Do Exercise 18 “Bonferroni Test.” SPSS Bonferroni Results INTERPRETATION Although the analysis of variance test tells us that at least one of the means is significantly different from the others, the Bonferroni test results do show that the first sample (small cars) has HIC values with a mean that is significantly different from the three other means. Examining all of the P-values (“Sig”) in the last column of the SPSS display, we see that the only significant differences in means occur when one of the means is from the small cars. None of the other three samples yields a mean that is significantly different. In this case, the Bonferroni test results did identify which mean appears to be significantly different from the others. Go Figure Since the beginning of humankind, about 100 billion humans have been born. There are roughly 7 billion humans alive now, so about 7% of all humans are still alive.
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