Analysis of variance of paired data without repetition of measurement

Author： Martin Klaus  

Publisher： Springer Publishing Company

ISSN： 0002-6018

Source： Allgemeines Statistisches Archiv, Vol.90, Iss.3, 2006-09, pp. : 365-384

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Abstract

The objective of this analysis of variance of paired data is to estimate positive random error variances for each ofN=2 measurement methods. The two methods measure the same item only once without measurement repetition. The well-known unbiased Grubbs' estimators are not suitable for practical purpose because they can become negative. With the help of Chebyshev's inequality the probability was determined that Grubbs' estimators become negative. Based on the Grubbs' estimators new estimators were derived. The new estimators are indeed always positive, but they are biased. It is shown that the biases are small. In case the Grubbs' estimators are positive a bias correction of the new estimators may be envisaged.

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