Question

Award: 10.00 points 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 moming. the length of time spent in the examination rooms is recorded for each patient seen by each physician at a orthopedic clinic. Time in Examination Rooms (minutes) Physician 3 18 Physician 2 33 38 33 28 Physician 1 32 Physician 4 26 34 24 29 31 27 38 20 32 32 25 31 29 33 44 32 29 26 31 28 40 27 Click here for the Excel Data File (a) Calculate the mean for each group and the Tukey test statistic Teale for each pair. Provide the critical values for both a- 05 and 01 (Input the mean values within the input boxes of the first row and input boxes of the first column. Input Teale in the appropriate boxes in the table. Round all answers to two decimal places.) Post hoc analysis: Tukey simultaneous comparison -values (d.f., 24) Physician 3 Physician 1 Physician 2 Physician 4 Physician 3 Physician 1 Physician 4 Physician 2 Critical values for experimentwise error rate: 0.05 0.01 (b) Use Tukey simultaneous comparison t-values and choose the correct answer. OPhysicians 1 and 4 differ Physicians 1 and 3 differ OPhysicians 2 and 4 differ ONo means differ (c) The Tukey test is used for simultaneously comparing means because it offers good power and maintains the desired overall probability of Type I error True OFalse heducation.com/hm.tpx?todo-C15PrintView&wid-13252710709731844&role student&pid 27 3361761360 1_107260468

Answer 1

One-way ANOVA: Time versus Physician

Source DF SS MS F P
Physician 3 232.8 77.6 3.03 0.049
Error 24 615.6 25.7
Total 27 848.4

$T_{calc}(i,j)=\frac{\bar{x}_i-\bar{x}_j}{\sqrt{\frac{MSE}{2}\left(\frac{1}{n_i}+\frac{1}{n_j} \right )}}\\ where,~\bar{x}_i=mean~time~for~Physician~i,~n_i=sample~size~of~Physician~i\\ MSE=mean~sum~of~square~due~to~error= 25.7\\ Here,~n_1=7,~n_2=6,~n_3=8,~n_4=7,~\bar{x}_1= 28.71,~\bar{x}_2=34.67,\\ ~\bar{x}_3=27.13,~\bar{x}_4=32.00\\ T_{calc}(1,3)=0.85,~T_{calc}(4,3)=2.62,~T_{calc}(2,3)=3.89,~T_{calc}(4,1)=1.72,\\ T_{Calc}(2,1)=2.99,~T_{Calc}(2,4)=1.34\\$

		Physician 3	Physician 1	Physician 4	Physician 2
		27.125	28.714	32.000	34.667
Physician 3	27.125
Physician 1	28.714	0.85
Physician 4	32.000	2.62	1.72
Physician 2	34.667	3.89	2.99	1.34

$Critical~values~for~experiment wise~error~rate:\\ At~0.05,~~~Critical~value=3.90\\ At~0.01,~~~Critical~value=4.91\\ (b)~No~means~differ.\\ (c)~True.$