Statistics for Environmental Engineers

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695


575


1300


854


780


580


1380


1056


688


495


Bioreactor


1327


982


550


325


1320


865


674


310


1253


803


666


465

Source: Dobbins, D. C. (1994). J. Air & Waste Mgmt. Assoc., 44, 1226-1229.

21

Tolerance Intervals and Prediction Intervals


KEY WORDS confidence interval, coverage, groundwater monitoring, interval estimate, lognormal distribution, mean, normal distribution, point estimate, precision, prediction interval, random sampling, random variation, spare parts inventory, standard deviation, tolerance coefficient, tolerance interval, transformation, variance, water quality monitoring.


Often we are interested more in an interval estimate of a parameter than in a point estimate. When told that the average efficiency of a sample of eight pumps was 88.3%, an engineer might say, “The point estimate of 88.3% is a concise summary of the results, but it provides no information about their precision.” The estimate based on the sample of 8 pumps may be quite different from the results if a different sample of 8 pumps were tested, or if 50 pumps were tested. Is the estimate 88.3 ± 1%, or 88.3 ± 5%? How good is 88.3% as an estimate of the efficiency of the next pump that will be delivered? Can we be reasonably confident that it will be within 1% or 10% of 88.3%?


Understanding this uncertainty is as important as making the point estimate. The main goal of statistical analysis is to quantify these kinds of uncertainties, which are expressed as intervals.

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