Cost effective, robust estimation of measurement uncertainty from sampling using unbalanced ANOVA
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There is an increasing appreciation that the uncertainty in environmental measurements is vitally important for their reliable interpretation. However, the adoption of methods to estimate this uncertainty has been limited by the extra cost of implementation. One method that can be used to estimate the random components of uncertainty in the sampling and analytical processes requires the collection of duplicate samples at 10% of the primary sampling locations and duplicating the analyses of these samples. A new program has been written and applied to a modified experimental design to enable a 33% reduction in the cost of analysing this 10% subset, whilst accommodating outlying values. This unbalanced robust analysis of variance (U-RANOVA) uses an unbalanced rather than the balanced experimental design usually employed. Simulation techniques have been used to validate the results of the program, by comparison of the results between the proposed unbalanced and the established balanced designs. Comparisons are also made against the seed parameters (mean and standard deviation) used to simulate the parent population, prior to the addition of a proportion (up to 10%) of outlying values. Application to a large number of different simulated populations shows that U-RANOVA produces results that are effectively indistinguishable from the results produced by the accepted balanced approach and are equally close to the true (seed) parameters of the parent normal population.
KeywordsUncertainty Unbalanced design Duplicate sample Robust ANOVA Accommodating outliers Optimized uncertainty
The authors would like to thank Prof. Tom Fearn of University College London, for his helpful advice on certain aspects of the robust calculations.