Statistics for Environmental Engineers

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1.72 Fg/L. This agrees with the true difference of 1.8 Fg/L. This is presumptive evidence that the two laboratories are doing good work.


There is a possible weakness in this kind of a comparison. It could happen that both labs are biased. Suppose the true concentration of the master solution was 1 Fg/L. Then, although the difference is as expected, both labs are measuring about 1.5 Fg/L too high, perhaps because there is some fault in the measurement procedure they were given. Thus, “splitting and spiking” checks work only when one laboratory is known to have excellent precision and low bias. This is the reason for having certified reference laboratories.

Multiple Sources of Variation (or Reproducibility Ф Repeatability)


The measure of whether errors are becoming smaller as analysts are trained and as techniques are refined is the standard deviation of replicate measurements on identical specimens. This standard deviation must include all sources of variation that affect the measurement process.


Reproducibility and repeatability are often used as synonyms for precision. They are not the same. Suppose that identical specimens were analyzed on five different occasions using different reagents and under different laboratory conditions, and perhaps by different analysts. Measurement variation will reflect differences in analyst, laboratory, reagent, glassware, and other uncontrolled factors. This variation measures the reproducibility of the measurement process.


Compare this with the results of a single analyst who made five replicate measurements in rapid succession using the same set of reagents and glassware throughout, while temperature, humidity, and other laboratory conditions remained nearly constant. This variation measures repeatability.

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