Statistics for Environmental Engineers

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Testing proportions is straightforward if the sample size and proportions are large enough for the normal approximation to be used. However, when the proportions approach one or zero, a transformation is needed (Mowery et al., 1985). When the sample size is small, the normal approximation becomes invalid; consult Fleiss (1981) or Rosner (1990).


Fleiss, J. L. (1981). Statistical Methods for Rates and Proportions, New York, John Wiley.

Mowery, P. D., J. A. Fava, and L. W. Clatlin (1985). “A Statistical Test Procedure for Effluent Toxicity Screening,” Aquatic Toxicol. Haz. Assess., 7th Symp., ASTM STP 854.

Rosner, B. (1990). Fundamentals of Biostatistics, 3rd ed., Boston, PWS-Kent Publishing Co.


19.1 Well Monitoring. Twenty monitoring wells that are down-gradient from a hazardous waste landfill are monitoring groundwater quality every three months. The standard is that 19 of the 20 wells must have a concentration less than 10 Rg/L or special studies must be undertaken. To allow for sampling error, the monitoring agency is allowed to judge compliance based on a 5% probability

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that a well truly in compliance may register above the 10 pg/L limit. Assuming that all wells are truly in compliance: (a) What is the probability that 2 of 20 wells will be observed above the limit? (b) What is the probability that 3 of 20 are above? (c) That none are above?

19.2    Control Group. Two groups, A and B, consist of 100 healthy organisms each. Group A, a control group, is put into a pond that is fed by a clean stream. Group B is put into a pond that receives a portion of wastewater effluent in the same stream water. After some time it is found that in groups A and B, 25 and 35 organisms, respectively, have an unusual condition. At significance levels of (a) 0.01, (b) 0.05, and (c) 0.10, test the hypothesis that something in the wastewater is harming the organisms.

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