Two-Sample Collaborative Testing

The design of a collaborative test must provide the additional information needed to separate the effect of random error from that due to systematic errors introduced by the analysts. One simple approach, which is accepted by the Association of Official Analytical Chemists, is to have each analyst analyze two samples, X and Y, that are similar in both matrix and concentration of analyte. The results obtained by each analyst are plotted as a single point on a two-sample chart, using the result for one sample as the x-coordinate and the value for the other sample as the -coordinate.  

A two-sample chart is divided into four quadrants, identified as (-P, -p), (-, -p), (-, -), and (-P, -), depending on whether the points in the quadrant have values for the two samples that are larger or smaller than the mean values for samples X and Y. Thus, the quadrant (-P, -) contains all points for which the result for sample X is larger than the mean for sample X, and for which the result for sample Y is less than the mean for sample Y. If the variation in results is dominated by random errors. 

Typical two-sample plot when (a) random errors are larger than systematic errors due to the analysts and (b) systematic errors due to the analysts are larger than the random errors. 

The data used to construct a two-sample chart can also be used to separate the total variation of the data, Otot into contributions from random error. Grand) and systematic errors due to the analysts, Osys. Since an analyst s systematic errors should be present at the same level in the analysis of samples X and Y, the difference, D, between the results for the two samples 

Relationship between point In a two-sample plot and the random error and systematic error due to the analyst. 

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In the two-sample collaborative test, each analyst performs a single determination on two separate samples. The resulting data are reduced to a set of differences, D, and a set of totals, T, each characterized by a mean value and a standard deviation. Extracting values for random errors affecting precision and systematic differences between analysts is relatively straightforward for this experimental design. 

Collaborative testing provides a means for estimating the variability (or reproducibility) among analysts in different labs. If the variability is significant, we can determine that portion due to random errors traceable to the method (Orand) and that due to systematic differences between the analysts (Osys). In the previous two sections we saw how a two-sample collaborative test, or an analysis of variance can be used to estimate Grand and Osys (or oJand and Osys). We have not considered, however, what is a reasonable value for a method s reproducibility. 

The sample matrix problem has stimulated the development of two pragmatic solutions matrix reference materials and interlaboratory comparisons. The matrix-matched, certified reference material (CRM) is a unique type of chemical standard commonly used to validate complete measurement methods and sometimes for instrumental cafibration (e.g., in XRF). Such standards must be available for each required analyte/matrix combination. Similarly, interlaboratory comparisons are vmdertaken for each relevant analyte/matrix combination in order to establish comparability of data between laboratories. These comparisons range from rovmd robin studies, which collaboratively test a new method, to formal PT schemes that assess agreement between laboratories on an ongoing basis. 

Accuracy The closeness of agreement between a test result and the accepted reference value. Interlaboratory comparison (ILC) The organization, performance, and evaluation of tests on the same sample by two or more laboratories in accordance with predetermined conditions to determine testing performance. According to purpose, they can be classified as collaborative studies or proficiency studies. 

Foster and Gonzales [10] reported a collaborative study by 11 laboratories of Soxtec and Soxhlet methods for the determination of total fat in meat and meat products. Each lab analyzed six samples canned ham, ground beef, frankfurters, fresh pork sausage, hard salami, and beef patties with added soy. In general, results for the Soxtec system showed improved performance. The method was first adopted by AOAC International for the extraction of fat from meat. Membrado et al. [11] tested Soxtec against Soxhlet extraction for the extraction of coal and coal-derived products. Optimization of Soxtec operating conditions reduced the total extraction time to 10% of what was needed by Soxhlet extraction. The recovery and precision by the two methods were comparable. 

At the beginning of the Triad field investigation, only the uppermost two 1 -ft intervals at each location were analyzed in the field. Ultraviolet fluorescence test kits, which require 5 min per sample for collection and analysis, were used for field detection of PAH and TPH at all sampling locations. A percentage of the PAH and TPH samples were sent to an off-site laboratory for independent collaboration of the field results. 

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