首页 | 本学科首页   官方微博 | 高级检索  
     检索      


Prospective evaluation of designs for analysis of variance without knowledge of effect sizes
Authors:C Patrick Doncaster  Andrew J H Davey  Philip M Dixon
Institution:1. Centre for Biological Sciences, University of Southampton, Southampton, SO17 1BJ, UK
2. WRc plc, Frankland Road, Blagrove, Swindon, SN5 8YF, UK
3. Department of Statistics, Iowa State University, Ames, IA, 50011-1210, USA
Abstract:Estimation of design power requires knowledge of treatment effect size and error variance, which are often unavailable for ecological studies. In the absence of prior information on these parameters, investigators can compare an alternative to a reference design for the same treatment(s) in terms of its precision at equal sensitivity. This measure of relative performance calculates the fractional error variance allowed of the alternative for it to just match the power of the reference. Although first suggested as a design tool in the 1950s, it has received little analysis and no uptake by environmental scientists or ecologists. We calibrate relative performance against the better known criterion of relative efficiency, in order to reveal its unique advantage in controlling sensitivity when considering the precision of estimates. The two measures differ strongly for designs with low replication. For any given design, relative performance at least doubles with each doubling of effective sample size. We show that relative performance is robustly approximated by the ratio of reference to alternative $\alpha $ quantiles of the $F$ distribution, multiplied by the ratio of alternative to reference effective sample sizes. The proxy is easy to calculate, and consistent with exact measures. Approximate or exact measurement of relative performance serves a useful purpose in enumerating trade-offs between error variance and error degrees of freedom when considering whether to block random variation or to sample from a more or less restricted domain.
Keywords:
本文献已被 SpringerLink 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号