Methods for optimal sample size determination are developed using four popular multiple comparison procedures (Scheffe's, Bonferroni's, Tukey's and Dunnett's procedures), where random samples of the sa...
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Methods for optimal sample size determination are developed using four popular multiple comparison procedures (Scheffe's, Bonferroni's, Tukey's and Dunnett's procedures), where random samples of the same size n are to be selected from k(greater than or equal to 2) normal populations with common variance sigma(2), and where primary interest concerns inferences about a family of L linear contrasts among the k population means. For a simultaneous coverage probability of (1 - alpha), the optimal sample size is defined to be the smallest integer value n(m)* such that, simultaneously for all L confidence intervals, the width of the lth confidence interval will be no greater than tolerance 2 delta(t) (l = 1, 2, ..., L) with tolerance probability at least (1 - gamma), treating the pooled sample variance S-p(2) as a random variable. Using Scheffe's procedure as an illustration, comparisons are made to usual sample size methods that incorrectly ignore the stochastic nature of S-p(2). The latter approach can lead to serious underestimation of required sample sizes and hence to unacceptably low values of the actually tolerance probability (1 - gamma'). Our approach guarantees a lower bound of [1 - (alpha + gamma)] for the probability that the L confidence intervals will both cover the parametric functions of interest and also be sufficiently narrow. Recommendations are provided regarding the choices among the four multiple comparison procedures for sample size determination and inference-making. Copyright (C) 1999 John Wiley & Sons, Ltd.
Efforts to evaluate the plethora of recent programs adopted by public and private payers to promote hospital price competition critically depend on the availability of measures of local market structure. To gauge the ...
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Efforts to evaluate the plethora of recent programs adopted by public and private payers to promote hospital price competition critically depend on the availability of measures of local market structure. To gauge the effects of these policies, researchers must be able to delineate hospital market areas and measure the intensity of competition within these markets. This article reviews alternative methods that have been used to define hospital market areas and measure market structure. We propose an empirical patient origin-based method for measuring hospital market structure. The results of sensitivity analyses using data on California hospitals demonstrate the robustness of our measures over a broad range of parameter values.
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