Question

To test for any significant difference in the mean number of hours between breakdowns for four machines, the following data were obtained.

Machine 1	Machine 2		Machine 3		Machine 4
6.4	8.7		11.1		9.9
7.8	7.4		10.3		12.8
5.3	9.4		9.7		12.1
7.4	10.1		10.3		10.8
8.4	9.2		9.2		11.3
7.3	9.8		8.8		11.5

The mean times between breakdowns are 7.1, 9.1, 9.9 and 11.4 hours respectively. In the analysis of variance, MSTR = 19.26 and MSE = .97. Use the Bonferroni adjustment to test for a significant difference between all pairs of means. Assume that a maximum overall experiment error rate of .05 is desired.

There are six pairwise comparisons among the 4 machines. What error rate should be used for each pairwise comparison (to 4 decimals)?

Using t = 2.845 for the above error rate, calculate the Bonferroni LSD value (to 2 decimals).
  

Complete the table below to determine whether there are any significant differences between population means.

Difference	Absolute Value	Conclusion
1 -  2		SelectSignificant differenceNo significant differenceItem 4
1 -  3		SelectSignificant differenceNo significant differenceItem 6
1 -  4		SelectSignificant differenceNo significant differenceItem 8
2 -  3		SelectSignificant differenceNo significant differenceItem 10
2 -  4		SelectSignificant differenceNo significant differenceItem 12
3 -  4		SelectSignificant differenceNo significant differenceItem 14

Answer 1

SPSS output: ANOVA Values Sum of Squares 57.765 19.260 77.025 Mean Square 19.255 .963 F 19.995 Between Groups Within Groups Total Sig. .000 The value of the test statistic is F=19.995. p-value = 0. Conclusion: Since p-value (= 0) <0.05, then reject the null hypothesis. Therefore, there is significant difference in the mean number of hours between breakdowns for four machines.

Multiple Comparisons Dependent Variable: Values Bonferroni Mean Difference (I- (O Group (J) Group Std. Error .567 .567 -1.14 567 Sig. .013 .000 .000 .013 1.000 -2.000 -2.800 - 4.300 2.000 - 800 -2.300 2.800 .800 - 1.500 -34 .567 -567 95% Confidence Interval Lower Bound Upper Bound -3.66 -34 -4.46 -5.96 -2.64 3.66 -2.46 -3.96 - 64 1.14 4.46 -.86 2.46 -3.16 ..16 2.64 5.96 .64 3.96 - 16 3.16 .86 .567 .004 .567 .567 .567 -567 .000 1.000 .093 .000 .004 .093 4.300 2.300 -567 1.500 .567 *The mean difference is significant at the 0.05 level.

Difference Absolute Value Conclusion 1 - 2 2 Significant difference (1-3 12.8 Significant difference 11 - 4 Significant difference No significant difference 2 - 4 Significant difference 3 - 4 No significant difference 43 lo 8