Proficiency test programs require laboratories to periodically determine (at successive times or rounds) the amount of a particular compound in test samples. Often, determinations by the same lab are correlated. When trends in the coefficient of variation (CV, for determinations at time t), also known as relative standard deviation, of analysis determinations are estimated, the correlation between estimated CV,s should be estimated. Taylor series are used to derive an approximation for this correlation in terms of the correlation between individual lab determinations. The approximation suggests that the correlation between estimated CV,s is smaller than that between lab determinations. To assess the approximation's accuracy, results of a simulation study are given. Next a model is presented for correlations of lab determinations over multiple rounds of the Proficiency Analytical Testing Program (PAT). By using the Taylor series approximation with estimates of average correlations of PAT lab determinations, this model provides estimated average correlations of PAT CV, estimates. The form of the correlation is also developed for predicted CV,s modeled as functions of the mean. A decision can then be made whether to adjust for correlations in modeling PAT CV, data. The formulas for correlations are applied to PAT asbestos and silica data, previously analyzed elsewhere (1.2). Conclusions from these papers still hold, in general, even after adjustment for correlation, though the confidence intervals for comparisons of interest are wider after adjustment for correlation.
Stanley Shulman, NIOSH, 4676 Columbia Parkway, MS-R3, Cincinnati, OH 45226