Relative Standard Deviation and Other Precision Estimators

RELATIVE STANDARD DEVIATION AND OTHER PRECISION ESTIMATORS 

Precision (as discussed previously) is the ability of the assay to give the same result when repeated multiple times either within the same run, or from day to day (i.e., between runs). Precision data are usually collected early in the evaluation at a new method, since the quality of the method depends on the level of precision. If precision is poor, more elaborate validation experiments must be postponed until the sources of imprecision are identified and controlled. 

Relative standard deviation and coefficient of variation (CV), are used to estimate precision, and are defined by the following equations  

Other parameters frequently used are the mean absolute deviation (MAD), as an estimator of the dispersion of groups of single observations, and the standard error of the mean (SEM), which is used to calculate the confidence limits of a mean value. Their formulae are presented in Eqs. 16.6 and 16.7. 

Precision varies with concentration because of this, precision should be evaluated at the low, middle, and high concentration regions of the standard curve, and should be evaluated in the different matrices that will be encountered in real assays. The precision profile (Section 16.4.3) is used to establish the working range of the assay. 

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RELATIVE STANDARD DEVIATION AND OTHER PRECISION ESTIMATORS 325... 

Thus we have 16 determinations (without the difference values) from which to calculate the mean in samples 1 and 2, and four in sample 3. Sample 3 (NBS SRM 124c) has a known value of 84.22%, with which we can compare our value (from four laboratories) of 82.6%. Our mean is somewhat low. The median, higher in each case, may be a better estimate of what the copper content actually is in each sample. The standard deviation and relative standard deviation are shown (see footnote b, Table IV). The relative standard deviation decreases from sample 1 to sample 2 and from sample 2 to sample 3. This may reflect greater inhomogeneity in sample 1 than sample 2 and in sample 2 than sample 3 it may also simply reflect the fact that we have fewer laboratories reporting on sample 3. Since the relative standard deviation on copper is so low, some of it may indeed arise from the materials themselves. On the other hand, the relative standard deviations for other elements (Table IV) do not show this pattern. In fact, they seem to be more closely related to the amount present, implying that the determinations become less precise as the amount of the element decreases (viz., Sn 1 + 2 Zn 1, 2, + 3 Ag 2 + 3 Si 1 + 2). 

The estimates of the standard deviation and relative standard deviation were not comparable. In particular, the estimates obtained from the duplicate results were significantly different from the other estimates (F-tests, 95% confidence). There were no obvious patterns in the data so no particular matrix and/or concentration could be identified as being the cause of the variability. There was therefore no justification for removing any data and restricting the coverage of the uncertainty estimate, as in the case of Cl solvent yellow 124 (see below). The results of the precision studies indicate that... 

When standard and test sample spots of several concentrations are applied to the plate, the amount of mycotoxin in the test sample can be estimated with a moderate degree of accuracy (80% recovery) and precision (30% relative standard deviation among laboratories), either visually or with a densitometer. Development solvents for the TLC plates are chosen to separate the mycotoxin from other components of the test extract, including other mycotoxins. 

In order to evaluate the influence of other parameters on the measuring precision, an expression of the relative standard deviation was derived from eqs. (2) and (3). If we assume r = 1 and infinite measuring accuracy, i.e., no errors affecting the estimate of k, we have... 

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