Statistics for Environmental Engineers

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Newman, M. C. and P. M. Dixon (1990). “UNCENSOR: A Program to Estimate Means and Standard Deviations for Data Sets with Below Detection Limit Observations,” Anal. Chem., 26(4), 26-30.


Newman, M. C., P. M. Dixon, B. B. Looney, and J. E. Pinder (1989). “Estimating Means and Variance for Environmental Samples with Below Detection Limit Observations,” Water Resources Bull., 25(4), 905-916.


Owen, W. J. and T. A. DeRouen (1980). “Estimation of the Mean for Lognormal Data Containing Zeros and Left-Censored Values, with Applications to the Measurement of Worker Exposure to Air Contaminants,” Biometrics, 36, 707-719.


Rohlf, F. J. and R. R. Sokal (1981). Statistical Tables, 2nd ed., San Francisco, W. H. Freeman and Co.


Shumway, R. H., A. S. Azari, and P. Johnson (1989). “Estimating Mean Concentrations under Transformation for Environmental Data with Detection Limits,” Technometrics, 31(3), 347-356.


Travis, C. C. and M. L. Land (1990). “The Log-Probit Method of Analyzing Censored Data,” Envir. Sci. Tech., 24(7), 961-962.


U.S. EPA (1989). Methods for Evaluating the Attainment of Cleanup Standards, Vol. 1: Soils and Solid Media, Washington, D.C.

Exercises


15.1 Chlorophenol. The sample of n = 20 observations of chlorophenol was reported with the four values below 50 g/L, shown in brackets, reported as “not detected” (ND).


63    78    89    [32]    77    96    87    67    [28]    80


100    85    [45]    92    74    63    [42]    73    83    87


(a)    Estimate the average and variance of the sample by (i) replacing the censored values with 50, (ii) replacing the censored values with 0, (iii) replacing the censored values with half the detection limit (25) and (iv) by omitting the censored values. Comment on the bias introduced by these four replacement methods.

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