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Higher order inference for the consensus mean in inter‐laboratory studies
Author(s) -
Sharma Gaurav,
Mathew Thomas
Publication year - 2011
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201000032
Subject(s) - confidence interval , statistics , heteroscedasticity , inference , mathematics , sample size determination , coverage probability , interval (graph theory) , prediction interval , computer science , artificial intelligence , combinatorics
Abstract 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.