Question

In a study of Marfan syndrome, Pyeritz et al.(A-34) reported the following severity scores of
patients
with no, mild, and marked dural ectasia. May we conclude, on the basis of these data, that mean
severity
scores differ among the three populations represented in the study? Let a ¼ :05 and find the p
value. Use Tukey’s procedure to test for significant differences among individual pairs of sample
means.
No dural ectasia: 18, 18, 20, 21, 23, 23, 24, 26, 26, 27, 28, 29, 29, 29, 30, 30, 30,
30, 32, 34, 34, 38
Mild dural ectasia: 10, 16, 22, 22, 23, 26, 28, 28, 28, 29, 29, 30, 31, 32, 32, 33, 33,
38, 39, 40, 47
Marked dural ectasia: 17, 24, 26, 27, 29, 30, 30, 33, 34, 35, 35, 36, 39
Source: DSPSS printouts should be included ata provided courtesy of Reed E. Pyeritz, M.D., Ph.D.

Answer 1

Tests of Between-Subjects Effects
Dependent Variable: Severity Score
Source	Type III Sum of Squares	df	Mean Square	F	Sig.
Corrected Model	92.893a	2	46.446	1.044	.359
Intercept	44468.351	1	44468.351	999.667	.000
Dural	92.893	2	46.446	1.044	.359
Error	2357.607	53	44.483
Total	48738.000	56
Corrected Total	2450.500	55

Comment: The p-value for Dural Ectasia is 0.359. Hence, the factor dural ectasia does not have a significant effect on the severity score at the 0.05 significance level. So, the post-hoc test is not required in general.

Tukey’s procedure to test for significant differences among individual pairs of sample means is

Multiple Comparisons
Severity Score Tukey HSD
(I) Dural Ectasia	(J) Dural Ectasia	Mean Difference (I-J)	Std. Error	Sig.	95% Confidence Interval
					Lower Bound	Upper Bound
No	Mid	-2.1061	2.03475	.558	-7.0124	2.8003
	Marked	-3.1573	2.33318	.373	-8.7833	2.4686
Mid	No	2.1061	2.03475	.558	-2.8003	7.0124
	Marked	-1.0513	2.35373	.896	-6.7267	4.6242
Marked	No	3.1573	2.33318	.373	-2.4686	8.7833
	Mid	1.0513	2.35373	.896	-4.6242	6.7267

Comment: All the p-values are more than 0.05 significance level. Hence, there is no significant difference between the pairs of means.