Question

Use MegaStat, MINITAB, or another software package to perform Tukey's test for significant pairwise differences. Perform the test using both the 5 percent and 1 percent levels of significance.

One particular morning, the length of time spent in the examination rooms is recorded for each patient seen by each physician at an orthopedic clinic.

Chart:

Time in Examination Rooms (minutes)

Physician 1 Physician 2 Physician 3 Physician 4

34   33 17 28

25   35 30 33

27   31 30 31

31 31 26 27

26 42 32 32

34 33 28 33

21 26 40

29

(a) Calculate the mean for each group and the Turkey test statistic Tcalc for each pair. Provide the critical values for both a = .05 and a = .01. (Input the mean values within the input boxes of the first row and input boxes of the first column. Input Tcalc in the appropriate boxes in the table. Round all answers to 2 decimal places.)

Chart:

Turkey Simultaneous Comparison t-values (d.f. = 24)

Physician 3 Physician 1 Physician 4 Physician 2

_________ __________ _________ __________

Physician 3 _________

Physician 1 _________ __________

Physician 4 _________ __________ _________

Physician 2. _________ __________ _________ _________

Critical values for experimentwise error rates:

0.05 _________

0.01 _________

( "______" is where an answer is needed)

Answer 1

count, ni =	8	7	7	6
mean , x̅ i =	28.375	33.00	29.00	30.67
std. dev., si =	4.5	4.9	6.9	2.6
sample variances, si^2 =	20.554	23.667	47.667	6.667
total sum	227	231	203	184			845	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =	30.18

	SS	df	MS	F	p-value
Between:	92.9	3	31.0	1.2	0.321
Within:	605.2	24	25.2
Total:	698.1	27

Critical value for alpha = 0.05

Level of significance   0.05
no. of treatments,k   4
DF error =N-k=   24
MSE =    25.2170
q-critical value(0.05,4,24)=   3.9013

	mean difference	absolute mean difference	std error	critical value	lower limit	upper limit	test stat	p value	result
µ1-µ2	-4.63	4.63	1.838	7.17	-11.79	2.54	2.52	0.0189	means are not different
µ1-µ3	-0.63	0.63	1.838	7.17	-7.79	6.54	0.34	0.7367	means are not different
µ1-µ4	-2.29	2.29	1.918	7.48	-9.77	5.19	1.20	0.2438	means are not different
µ2-µ3	4.00	4.00	1.898	7.40	-3.40	11.40	2.11	0.0457	means are not different
µ2-µ4	2.33	2.33	1.976	7.71	-5.37	10.04	1.18	0.2491	means are not different
µ3-µ4	-1.67	1.67	1.976	7.71	-9.37	6.04	0.84	0.4072	means are not different

-------------------------

Level of significance   0.01
no. of treatments,k   4
DF error =N-k=   24
MSE =    25.2170
q-critical value(0.01,4,24)=   4.9063

	mean difference	absolute mean difference	std error	critical value	lower limit	upper limit	test stat	p value	result
µ1-µ2	-4.63	4.63	1.838	9.02	-13.64	4.39	2.52	0.0189	means are not different
µ1-µ3	-0.63	0.63	1.838	9.02	-9.64	8.39	0.34	0.7367	means are not different
µ1-µ4	-2.29	2.29	1.918	9.41	-11.70	7.12	1.20	0.2438	means are not different
µ2-µ3	4.00	4.00	1.898	9.31	-5.31	13.31	2.11	0.0457	means are not different
µ2-µ4	2.33	2.33	1.976	9.69	-7.36	12.03	1.18	0.2491	means are not different
µ3-µ4	-1.67	1.67	1.976	9.69	-11.36	8.03	0.84	0.4072	means are not different

Please let me know in case of any doubt.

Thanks in advance!

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