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.
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.
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