Two technical papers recognized as significant early contributions in the discussion of the limitations of analytical accuracy and uncertainty include those by Horwitz of the U.S. FDA (1,2). For this next series of articles, we will be discussing both the topic and the approaches to this topic taken by the classic papers just referenced. The determination and understanding of analytical error is often approached using interlaboratory collaborative studies. We have previously delved into that subject in "Chemometrics in Spectroscopy" with a multipart column series (3–8).
Jerome Workman, Jr.
Horwitz points out in his Analytical Chemistry A-pages paper (1), inserting the statement made by John Mandel, "the basic objective of conducting interlaboratory tests is not to detect the known statistically significant differences among laboratories: 'The real aim is to achieve the practical interchangeability of test results.' Interlaboratory tests are conducted to determine how much allowance must be made for variability among laboratories in order to make the values interchangeable."
Horwitz also points out the universal recognition of irreproducible differences in supposedly identical method results between laboratories. It has even been determined that when the same analyst is moved between laboratories, the variability of results obtained by that analyst increases. One government laboratory study concluded that variability in results could be minimized only if one was to "conduct all analyses in a single laboratory . . . by the same analyst." So if we must always have interlaboratory variability, how much allowance in results should be regarded as valid — or legally permissible — as indicating "identical" results? What are the practical limits of acceptable variability between methods of analysis, especially for regulatory purposes?
We will address aspects of reproducibility, which has been defined previously as "the precision between laboratories." It also has been defined as "total between-laboratory precision." This is a measure of the ability of different laboratories to evaluate each other. Reproducibility includes all the measurement errors or variances, including the within-laboratory error. Other terms include precision, defined as "the closeness of agreement between independent test results obtained under stipulated conditions" (9); and repeatability, or "the precision for the same analyst within the same laboratory, or within-laboratory precision." Note that for none of these definitions do we require the "true value for an analytical sample." In practice, we do not know the true analyte value unless we have created the sample, and then it is only known to a given certainty (that is, within a determined uncertainty).
Systematic error is also known as bias. The bias is the constant value difference between a measured value (or set of values) and a consensus value (or true value if known). Specificity is the analytical property of a method or technique to be insensitive to interferences and to yield a signal relative to the analyte of interest only. Limit of reliable measurement predates the use of minimum detection limit (MDL). The MDL is the minimum amount of analyte present that can be detected with known certainty. Standard error of the laboratory (SEL) represents the precision of a laboratory method. A statistical definition is given in the following paragraph. The SEL can be determined by using one or more samples properly aliquoted and analyzed in replicate by one or more laboratories. The average analytical value for the replicates on a single sample is determined as
SEL is given by