Statistics for Environmental Engineers

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Case Study: Interlaboratory Study of DO Measurements

This example is loosely based on a study by Wilcock et al. (1981). Fourteen laboratories were sent standardized solutions that were prepared to contain 1.2 mg/L dissolved oxygen (DO). They were asked to measure the DO concentration using the Winkler titration method. The concentrations, as mg/L DO, reported by the participating laboratories were:

1.2 1.4 1.4 1.3 1.2 1.35 1.4 2.0 1.95 1.1 1.75 1.05 1.05 1.4 Do the laboratories, on average, measure 1.2 mg/L, or is there some bias?

Theory: t-Test to Assess Agreement with a Standard

The known or specified value is defined as По- The true, but unknown, mean value of the tested specimens is n, which is estimated from the available data by calculating the average y .

We do not expect to observe that y = По, even if n = По- However, if y is near По, it can reasonably be concluded that n = По and that the measured value agrees with the specified value. Therefore, some statement is needed as to how close we can reasonably expect the estimate to be. If the process is on-standard or on-specification, the distance y — n0 will fall within bounds that are a multiple of the standard deviation of the measurements.

We make use of the fact that for n < 30,

t = b-n


is a random variable which has a t distribution with v = n — 1 degrees of freedom. s is the sample standard deviation- Consequently, we can assert, with probability 1 — a, that the inequality:

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