Sample size determination for multiple comparison studies treating confidence interval width as random
✍ Scribed by Zhiying Pan; Lawrence L. Kupper
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 156 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0277-6715
No coin nor oath required. For personal study only.
✦ Synopsis
Methods for optimal sample size determination are developed using four popular multiple comparison procedures (Sche!e's, Bonferroni's, Tukey's and Dunnett's procedures), where random samples of the same size n are to be selected from k (*2) normal populations with common variance , and where primary interest concerns inferences about a family of ¸linear contrasts among the k population means. For a simultaneous coverage probability of (1! ), the optimal sample size is de"ned to be the smallest integer value n* such that, simultaneously for all ¸con"dence intervals, the width of the lth con"dence interval will be no greater than tolerance 2 J (l"1, 2, 2 , ¸) with tolerance probability at least (1! ), treating the pooled sample variance S as a random variable. Using Sche!e's procedure as an illustration, comparisons are made to usual sample size methods that incorrectly ignore the stochastic nature of S . The latter approach can lead to serious underestimation of required sample sizes and hence to unacceptably low values of the actually tolerance probability (1! ). Our approach guarantees a lower bound of [1!( # )] for the probability that the ¸con"dence intervals will both cover the parametric functions of interest and also be su$ciently narrow. Recommendations are provided regarding the choices among the four multiple comparison procedures for sample size determination and inference-making.