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

MSE=			0.970
df(error)=			20
number of treatments =			4
pooled standard deviation=Sp =√MSE=			0.985

error rate =0.05/6 = 0.0083

critical value level & N-k=0.0083 df=			2.845
Bonferroni LSD = (tB|D)*(sp*√(1/ni+1/nj)=			1.618

Difference	Absolute Value	Conclusion
x1-x2	2.00	significant difference
x1-x3	2.80	significant difference
x1-x4	4.30	significant difference
x2-x3	0.80	not significant difference
x2-x4	2.30	significant difference
x3-x4	1.50	not significant difference