Section Exercise 11-12 Use MegaStat, MINITAB, or another software package to per

Question

Section Exercise 11-12 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. Time in Examination Rooms (minutes) Physician 1 Physician 2 Physician 3 Physician 4 34 25 28 35 27 32 26 34 32 28 42 29 Fi (a) Calculate the mean for each group and the Tukey 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 Tealc in the appropriate boxes in the table. Round all answers to two decimal places.) Post hoc analysis: Tukey simultaneous comparison t-values (d.f. 24) Physician 3 Physician4 Physician 2 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. Physicians 1 and 4 differ Physicians 1 and 3 differ Physicians 2 and 4 differ Physicians 2 and 3 differ 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 False

Explanation / Answer

Here we have given four groups.

First we have to test,

H0 : All means are equal.

H1 : Atleast one of the mean differ.

Assume alpha = 0.05 and 0.01

Test statistic follows F-distribution.

F = 3.86

P-value = 0.0208

The p-value corresponing to the F-statistic of one-way ANOVA is lower than 0.05, suggesting that the one or more treatments are significantly different.

Tukey's test :

We first establish the critical value of the Tukey-Kramer HSD Q statistic based on the k=4 treatments and =26 degrees of freedom for the error term, for significance level = 0.01 and 0.05 (p-values) in the Studentized Range distribution. We obtain these ctitical values for Q, for of 0.01 and 0.05,

as

Qcritical=0.01,k=4,=26= 4.8653 and

Qcritical=0.05,k=4,=26 = 3.8798, respectively

Next, we establish a Tukey test statistic from our sample columns to compare with the appropriate critical value of the studentized range distribution.

Qi,j=|x¯ix¯j| / si,j

where the denominator in the above expression is:

si,j = ^/ sqrt(Hi,j) i,j=1,…,k; ij.

The quantity ^ = 4.3618 is the square root of the

Mean Square Error = 19.0255 determined in the precursor one-way ANOVA procedure

We present below color coded results of evaluating whether

Qi,j>Qcritical for all relevant pairs of treatments.

In addition, we also present the significance (p-value) of the observed Q-statistic Qi,j.

From the above resule we can see that physicians 2 and 3 are differ.

treatments
pair Tukey HSD
Q statistic Tukey HSD
p-value Tukey HSD
inferfence A vs B 3.4273 0.0974207 insignificant A vs C 0.5827 0.8999947 insignificant A vs D 2.2530 0.4010446 insignificant B vs C 4.2485 0.0279747 * p<0.05 B vs D 1.2627 0.7882740 insignificant C vs D 3.0264 0.1673253 insignificant

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