# Statistics for Environmental Engineers

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The precision of the two laboratories is the same; there is no significant difference between standard deviations of 0.32 and 0.50 Fg/L. Roughly speaking, the ratios of the variances would have to exceed a value of 3 before we would reject the hypothesis that they are the same. The ratio in this example is 0.52/0.322 = 2.5 . The test statistic (the “roughly three”) is the F-statistic and this test is called the F-test on the variances. It will be explained more in Chapter 24 when we discuss analysis of variance.

Having a “blind” analyst make measurements on specimens with known concentrations is the only way to identify bias. Any certified laboratory must invest a portion of its effort in doing such checks on measurement accuracy. Preparing test specimens with precisely known concentrations is not easy. Such standard solutions can be obtained from certified laboratories (U.S. EPA labs, for example).

Another quality check is to split a well-mixed sample and add a known quantity of analyte to one or more of the resulting portions. Example 9.3 suggests how splitting and spiking would work.

Example 9.3

Consider that the measured values in Example 9.2 were obtained in the following way. A large portion of a test solution with unknown concentration was divided into 28 portions. To 14 of the portions a quantity of analyte was added to increase the concentration by exactly 1.8 Fg/L. The true concentration is not known for the spiked or the unspiked specimens, but the measured values should differ by 1.8 Fg/L. The observed difference between labs A and B is 4.38 — 2.66 =

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