# Statistics for Environmental Engineers

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The simplest method is the Youden pairs test (Youden, 1972; Kateman and Buydens, 1993). Youden proposed having different laboratories each analyze two similar test specimens, one having a low concentration and one having a high concentration. The two measurements from each laboratory are a Youden pair.

The data in Table 9.1 are eight Youden pairs from eight laboratories and the differences between the pairs for each lab. Figure 9.1 is the Youden plot of these eight pairs. Each point represents one laboratory. Vertical and horizontal lines are drawn through sample averages of the laboratories, which are 2.11 [ig/L for the low concentration and 6.66 [ig/L for the high concentration. If the measurement errors are unbiased and random, the plotted pairs will scatter randomly about the intersection of the two lines, with about the same number of points in each quadrant.

TABLE 9.1

Youden Pairs from Eight Laboratories

 Lab Low Hig di (2.0 lg/L) (6.2 ig/L) i 2.0 6.3 4.3 2 3.6 6.6 3.0 3 1.8 6.8 5.0 4 1.1 6.8 5.7 5 2.5 7.4 4.9 6 2.4 6.9 4.5 7 1.8 6.1 4.4 8 1.7 6.3 4.6

Measured on the 2.0-mg/L Specimen

FIGURE 9.1 Plot of Youden pairs to evaluate the performance of eight laboratories.

The center of the circle is located by the average sample concentrations of the laboratories. The radius, which is proportional to the interlaboratory precision, is quantified by the standard deviation:

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