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### Calculation of the relative random error (RRE) of laboratory standard deviation s_{L}

The goal of any interlaboratory study is the estimation of precision parameters, such as the laboratory-to-laboratory standard deviation or repeatability standard deviation. These precision parameters allow the desired assessment (e.g. of an analytical method). An important aspect is the fact, that precision parameters are subject to uncertainties, and that the experimental design itself has to be composed with respect to the desired margin of uncertainty in e.g. the laboratory-to-laboratory standard deviation s_{L}. In 2009 McClure & Lee published an article giving estimates for the minimal number of laboratories, which give too optimistic results due to some unregarded aspects of s

_{L}. Here you find our own calculation for the minimal required number of laboratories at a desired level of certainty in s

_{L}.

The minimal design of an interlaboratory study used by AOAC INTERNATIONAL includes 8 laboratories and 2 replicas (Θr = ½ , probability level=95 % ) and yields a margin of relative error in s

_{L}of 0.617 (61.7 %) according to McClure & Lee. This level of certainty was termed “appreciable” but we want to point out that an unbiased calculation of the minimal number of laboratories in order to reach a relative random error in s

_{L}of 0.617 results in 10 laboratories and not in 8. The application above shows the distribution of the relative random error and the minimal number of laboratories required in order to reach the desired certainty in s

_{L}at a selected probability level.