Unbalanced robust ANOVA for the estimation of measurement uncertainty at reduced cost

Location S1A1 S1A2 S2A1 S2A2 Fig. 1 Design for the estimation of the random components of uncertainty arising from both the sampling and the analytical procedures. (A) Balanced design. (B) Unbalanced design. An empirical estimation of the random components of measurement uncertainty arising from the sampling and analytical processes can be made via an experiment involving replication. Analysis of variance (ANOVA) is then used to estimate the variance components. However, the fully balanced design is unduly costly, requiring four analyses per sampling target. This cost can be reduced by 25% by using an unbalanced design. Robust ANOVA in this context is often a useful tool, as it gives a more representative estimate of the separate variances than classical ANOVA when outlying results are encountered, but software for executing unbalanced robust ANOVA has hitherto been unavailable. This Technical Brief introduces the unbalanced design and the corresponding software provided by the AMC.