University of Notre Dame, Indiana 46556, USA.
Br J Math Stat Psychol. 2012 May;65(2):350-70. doi: 10.1111/j.2044-8317.2011.02029.x. Epub 2011 Oct 17.
Contrasts of means are often of interest because they describe the effect size among multiple treatments. High-quality inference of population effect sizes can be achieved through narrow confidence intervals (CIs). Given the close relation between CI width and sample size, we propose two methods to plan the sample size for an ANCOVA or ANOVA study, so that a sufficiently narrow CI for the population (standardized or unstandardized) contrast of interest will be obtained. The standard method plans the sample size so that the expected CI width is sufficiently small. Since CI width is a random variable, the expected width being sufficiently small does not guarantee that the width obtained in a particular study will be sufficiently small. An extended procedure ensures with some specified, high degree of assurance (e.g., 90% of the time) that the CI observed in a particular study will be sufficiently narrow. We also discuss the rationale and usefulness of two different ways to standardize an ANCOVA contrast, and compare three types of standardized contrast in the ANCOVA/ANOVA context. All of the methods we propose have been implemented in the freely available MBESS package in R so that they can be easily applied by researchers.
均值对比通常很有研究价值，因为它们可以描述多种处理方式的效果大小。通过狭窄的置信区间 (CI) 可以实现对总体效应大小的高质量推断。鉴于 CI 宽度和样本量之间的密切关系，我们提出了两种方法来为协方差分析或方差分析研究规划样本量，以便为感兴趣的总体（标准化或非标准化）对比获得足够窄的 CI。标准方法规划样本量，以使预期的 CI 宽度足够小。由于 CI 宽度是一个随机变量，因此预期宽度足够小并不能保证在特定研究中获得的宽度足够小。扩展程序以特定的、高保证程度（例如，90%的时间）确保在特定研究中观察到的 CI 足够窄。我们还讨论了两种标准化协方差分析对比的不同方法的基本原理和有用性，并在协方差分析/方差分析的上下文中比较了三种标准化对比类型。我们提出的所有方法都已在 R 语言中免费提供的 MBESS 包中实现，以便研究人员可以轻松应用。
