Sharma Gaurav, Mathew Thomas
Department of Mathematics and Statistics, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA.
Biom J. 2011 Feb;53(1):128-36. doi: 10.1002/bimj.201000032. Epub 2010 Dec 6.
In inter-laboratory studies, a fundamental problem of interest is inference concerning the consensus mean, when the measurements are made by several laboratories which may exhibit different within-laboratory variances, apart from the between laboratory variability. A heteroscedastic one-way random model is very often used to model this scenario. Under such a model, a modified signed log-likelihood ratio procedure is developed for the interval estimation of the common mean. Furthermore, simulation results are presented to show the accuracy of the proposed confidence interval, especially for small samples. The results are illustrated using an example on the determination of selenium in non-fat milk powder by combining the results of four methods. Here, the sample size is small, and the confidence limits for the common mean obtained by different methods produce very different results. The confidence interval based on the modified signed log-likelihood ratio procedure appears to be quite satisfactory.
在实验室间研究中，一个基本的重要问题是，当测量由几个实验室进行时，除了实验室间的变异性外，这些实验室可能表现出不同的实验室内方差，此时如何推断一致性均值。异方差单向随机模型经常用于对这种情况进行建模。在这样的模型下，开发了一种修正的符号对数似然比程序用于共同均值的区间估计。此外，给出了模拟结果以显示所提出的置信区间的准确性，特别是对于小样本。通过结合四种方法的结果，以脱脂奶粉中硒的测定为例对结果进行了说明。这里，样本量较小，不同方法得到的共同均值的置信限产生了非常不同的结果。基于修正的符号对数似然比程序的置信区间似乎相当令人满意。
