# These results show that there were significant

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These results show that there were significant differences between 70 o and 150 o and between 70 o and 150 o . The confirms what we observed above with the Excel output.

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Case Notes 28 2. The data are analyzed using a one-way ANOVA. The independent variable is country with four classifications: Canada, Columbia, Taiwan, and the U.S. The dependent variable is the dollar cost to replace a seal. Shown below is the MINITAB output for this one-way analysis with multiple comparisons: One-way ANOVA: Cost versus Country Analysis of Variance for Cost Source DF SS MS F P Country 3 64331 21444 32.68 0.000 Error 24 15750 656 Total 27 80081 Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev -----+---------+---------+---------+- 1 7 244.29 31.01 (---*---) 2 7 323.57 30.65 (---*---) 3 7 195.00 20.82 (---*---) 4 7 222.14 17.04 (---*---) -----+---------+---------+---------+- Pooled StDev = 25.62 200 250 300 350 Tukey's pairwise comparisons Family error rate = 0.0500 Individual error rate = 0.0110 Critical value = 3.90 Intervals for (column level mean) - (row level mean) 1 2 3 2 -117.0 -41.5 3 11.5 90.8 87.0 166.3 4 -15.6 63.7 -64.9 59.9 139.2 10.6 The results show that there is a significant difference in the cost of seal replacement between countries ( F = 32.68, p -value = .000). An examination of the means shows that there is potential significant differences between countries (Canada - \$244.29, Columbia - \$323.57, Taiwan - \$195.00, and U.S. - \$222.14). The results of the Tukey multiple comparison analysis shows that there are significant pairwise differences between Canada and Columbia, between Canada and Taiwan, between Columbia and Taiwan, and between Columbia and the U.S. Clarkson might be very effective in marketing to Columbian companies because in Columbia the cost of replacing the seal is significantly higher than in other countries.
Case Notes 29 3. This is a randomized block design. The main independent variable of interest is type of valve. The blocking variable was day of the week. Below is Excel output for a two-way ANOVA without replication. ANOVA Source of Variation SS df MS F P-value F crit Day of the Week 0.7767 4 0.1942 4.98 0.00595206 2.87 Type of Valve 6.0107 5 1.2021 30.85 0.000000010 2.71 Error 0.7793 20 0.0390 Total 7.5667 29 A highly significant observed F value was obtained for type of valve ( F = 30.85 with a p -value of .000000001). The various valve types and their associated mean lead times are: Safety – 1.64 Butterfly – 2.12 Clack – 1.32 Slide – 1.66 Poppet – 2.18 Needle – 0.88 Since there is a significant difference in valve type and since the means appear to be quite different, Tukey’s multiple comparisons were used to determine which pairs of means, if any, are significantly different. The MINITAB output for this analysis is given below: Tukey's pairwise comparisons Family error rate = 0.0500 Individual error rate = 0.00501 Critical value = 4.37 Intervals for (column level mean) - (row level mean) 1 2 3 4 5 2 -0.9776 0.0176 3 -0.1776 0.3024 0.8176 1.2976 4 -0.5176 -0.0376 -0.8376 0.4776 0.9576 0.1576 5 -1.0376 -0.5576 -1.3576 -1.0176 -0.0424 0.4376 -0.3624 -0.0224 6 0.2624 0.7424 -0.0576 0.2824 0.8024 1.2576 1.7376 0.9376 1.2776 1.7976 The results of these multiple comparison tests is that lead times for the following pairs of valves are significantly different:

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Case Notes 30 Safety and Poppet, Safety and Needle, Butterfly and Clack, Butterfly and Needle, Clack and Poppet, Slide and Poppet, Slide and Needle, and Poppet and Needle.
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