Estimating the mean and standard deviation of concentration distributions using censored samples

Environmental data sets of pollutant concentrations in air, water, and soil frequently include unquantified sample values reported only as being below the analytical method detection limit. These values, referred to as censored values, should be considered in the estimation of distribution parameters as each represents some value of pollutant concentration between zero and the detection limit. Most of the currently accepted methods for estimating the population parameters of environmental data sets containing censored values rely upon the assumption of an underlying normal (or transformed normal) distribution. This assumption can result in unacceptable levels of error in parameter estimation due to the unbounded left tail of the normal distribution. With the beta distribution, which is bounded by the same range of a distribution of concentrations, $\rm\lbrack0\le x\le1\rbrack,$ parameter estimation errors resulting from improper distribution bounds are avoided. This work developed a method that uses the beta distribution to estimate population parameters from censored environmental data sets and evaluated its performance in comparison to currently accepted methods that rely upon an underlying normal (or transformed normal) distribution. Data sets were generated assuming typical values encountered in environmental pollutant evaluation for mean, standard deviation, and number of variates. For each set of model values, data sets were generated assuming that the data was distributed either normally, lognormally, or according to a beta distribution. For varying levels of censoring, two established methods of parameter estimation, regression on normal ordered statistics, and regression on lognormal ordered statistics, were used to estimate the known mean and standard deviation of each data set. The method developed for this study, employing a beta distribution assumption, was also used to estimate parameters and the relative accuracy of all three methods were compared. For data sets of all three distribution types, and for censoring levels up to 50%, the performance of the new method equaled, if not exceeded, the performance of the two established methods. Because of its robustness in parameter estimation regardless of distribution type or censoring level, the method employing the beta distribution should be considered for full development in estimating parameters for censored environmental data sets. ^

AN INVESTIGATION OF THE EFFECT OF FORMALDEHYDE SPECIES ON ENVIRONMENTAL MEASUREMENT METHODS UNDER AMBIENT CONDITIONS

Species variations in formaldehyde solutions and gases were investigated by means of infrared spectral analysis. Double beam infrared spectrometry in conjunction with sodium chloride wafer technique and solvent compensation technique were employed. Formaldehyde species in various solutions were investigated. Formalin 37% was stable for many months. Refrigeration had no effects on its stability. Spectral changes were detected in 1000 ppm formaldehyde solutions. The absorbances of very diluted solutions up to 100 ppm were lower than the detection limit of the instruments. Solvent compensation improved resolution, but was associated with an observed lack of repeatability. Formaldehyde species in animal chambers containing animals and in mobile home air were analyzed with the infrared spectrophotometer equipped with a 10 cm gas cell. Spectra were not different from the spectrum of clean air. A portable single beam infrared spectrometer with a 20 meter pathlength was used for reinvestigation. Indoor formaldehyde could not be detected in the spectral; conversely, an absorption peak at 3.58 microns was found in the spectra of 3 and 15 ppm formaldehyde gas in animal chambers. This peak did not appear in the spectrum of the control chamber. Because of concerns over measurement bias among various analytical methods for formaldehyde, side-by-side comparisons were conducted in both laboratory and field measurements. The chromotropic acid method with water and 1% sodium bisulfite as collection media, the pararosaniline method, and a single beam infrared spectrometer were compared. Measurement bias was elucidated and the extent of the effects of temperature and humidity was also determined. The problems associated with related methods were discussed. ^