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The Effective Sample Size and an Alternative Small-Sample Degrees-of-Freedom Method

机译：有效样本量和替代的小样本自由度方法

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摘要

Correlated data frequently arise in contexts such as, for example, repeated measures and meta-analysis. The amount of information in such data depends not only on the sample size, but also on the structure and strength of the correlations among observations from the same independent block. A general concept is discussed, the effective sample size, as a way of quantifying the amount of information in such data. It is defined as the sample size one would need in an independent sample to equal the amount of information in the actual correlated sample. This concept is widely applicable, for Gaussian data and beyond, and provides important insight. For example, it helps explain why fixed-effects and random-effects inferences of meta-analytic data can be so radically divergent. Further, we show that in some cases the amount of information is bounded, even when the number of measures per independent block approaches infinity. We use the method to devise a new denominator degrees-of-freedom method for fixed-effects testing. It is compared to the classical Satterthwaite and Kenward-Roger methods for performance and, more importantly, to enhance insight. A key feature of the proposed degrees-of-freedom method is that it, unlike the others, can be used for non-Gaussian data, too.
机译：相关数据经常出现在诸如重复测量和荟萃分析之类的环境中。此类数据中的信息量不仅取决于样本量，还取决于来自同一独立块的观测值之间相关性的结构和强度。讨论了一个通用概念，即有效样本大小，作为量化此类数据中信息量的一种方式。它被定义为一个独立样本中需要的样本量，以等于实际相关样本中的信息量。此概念可广泛应用于高斯数据及其他数据，并提供重要的见解。例如，它有助于解释为什么元分析数据的固定效应和随机效应推论如此根本地不同。此外，我们表明，在某些情况下，即使每个独立块的度量数量接近无穷大，信息量也会受到限制。我们使用该方法设计一种新的分母自由度方法进行固定效果测试。将其与经典的Satterthwaite和Kenward-Roger方法进行比较，以提高性能，更重要的是，可以增强洞察力。所提出的自由度方法的关键特征在于，与其他方法不同，它也可以用于非高斯数据。

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  • 来源
    《The American statistician》 |2009年第4期|389-399|共11页
  • 作者

    Christel Faes; Geert Molenberghs; Marc Aerts; Geert Verbeke; Michael G. Kenward;

  • 作者单位

    Interuniver- sity Institute for Biostatistics and statistical Bioinformatics, Hasselt University, Diepenbeek, Belgium;

    Interuniver- sity Institute for Biostatistics and statistical Bioinformatics, Hasselt University, Diepenbeek, Belgium;

    Interuniver- sity Institute for Biostatistics and statistical Bioinformatics, Hasselt University, Diepenbeek, Belgium;

    Interuniver-sity Institute for Biostatistics and Statistical Bioinformatics, Katholieke Universiteit Leuven, Belgium;

    Medical Statistics Unit, London School of Hygiene and Tropical Medicine, U.K. All authors gratefully acknowledge the financial support from the IAP research Network P6/03 of the Belgian Government (Belgian Science Policy);

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  • 正文语种 eng
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  • 关键词

    amount of information; correlated data; information limit; mixed models; small-sample inference;

    机译：信息量;相关数据;信息限制;混合模型小样本推论;

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