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A Methodology for the Health Sciences - part 7
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Các giới hạn này rộng lớn hơn nhiều so với những người dựa trên sự so sánh mỗi t-Thống kê. Điều này là do mục đích duy nhất là thay thế của t29, 0,975 = 2,05 5F5, 29,0.95 = 3,57. Do đó, chiều rộng khoảng tin cậy được tăng lên bởi một yếu tố của 3.57/2.05 1,74 hoặc 74% =. | SIMULTANEOUS CONFIDENCE INTERVALS AND TESTS FOR LINEAR MODELS 527 or bi 3.57 sbị i 1 2 . 5 For the regression coefficient of DPMB the interval is 0.575 3.57 0.0834 resulting in 95 confidence limits of 0.277 0.873 . Computing these values the confidence intervals are as follows Variable Limits Variable Limits Lower Upper Lower Upper DPMB 0.277 0.873 Time -24.9 15.6 Trauma -50.8 32.3 Lymph A -28.5 19.4 Lymph B -44.8 27.7 These limits are much wider than those based on a per comparison t-statistic. This is due solely to the replacement of t29 0.975 2.05 by ự5F5 29 0.95 3.57. Hence the confidence interval width is increased by a factor of 3.57 2.05 1.74 or 74 . Example 12.4. In a one-way anova situation using the notation of Section 10.2.2 if we wish simultaneous confidence intervals for all I means then d I m n.-I and the standard error of the estimate of U is Thus the confidence intervals are of the form - 7T------- MSe Y 7 IF .- 1-. i 1 . . . I Suppose that we want simultaneous 99 confidence intervals for the morphine binding data of Problem 10.1. The confidence interval for the chronic group is 31.9 1 4 422 y F4 24 0.99 9.825 18 31.9 3.0 or 31.9 3.0 The four simultaneous 99 confidence intervals are Limits Limits Group Lower Upper Group Lower Upper 4 Chronic 28.9 34.9 n Dialysis 22.0 36.8 19 Acute 21.0 39.2 74 Anephric 19.2 30.8 528 MULTIPLE COMPARISONS As all four intervals overlap we cannot conclude immediately from this approach that the means differ at the 0.01 level . To compare two means we can also consider confidence intervals for I ni .As the Scheffe method allows us to look at all linear combinations we may also consider the confidence interval for I i i. The formula for the simultaneous confidence intervals is Yi. Yi-. JIF . 1 L MSA x x V ni nv i i 1 . I i i In this case the confidence intervals are Limits Limits Contrast Lower Upper Contrast Lower Upper 1 2 7.8 11.4 U 3 3 11.1 12.5 F-1 13 5.5 10.5 u 4 5.7 15.9 1 4 0.4 13.4 3 3 4 5.0 13.8 As the interval