ES&T
LETTERS Trace analyses for wastewaters Dear Sir: The recent feature article by Glaser et al. {1 ) in the December 1981 issue presents an operational approach to defining detection limit as "the minimum concentration of a substance that can be identified, measured, and reported with 99% confidence that the analyte concentration is greater than zero and is determined from replicate analyses of a sample." A theory is presented to justify the approach used in defining the detection limit. This theory deviates from most others that have been proposed in that the variability of blank measurements is not the basis of establishing the detection limit (2-6). An error distribution is presented for the measured analyte concentration when the true value of the analyte is equal to MDL. While no mention is made of blanks, presumably the distribution corresponds to the final analytical results, which may or may not have included blank correction. Both cases are included in the application of theory to the organic priority pollutant methods (i.e., the single-step procedure gives the option of including blank measurements, which was done, for example, in the analysis of heptachlor epoxide by Method 608). If blank correction is included in the recommended procedure, then the theory should also include treatment of blanks. Assuming that the measured analyte concentration includes any blank correction that may be necessary, the measured analyte concentration or analytical result is equal to the difference between sample response and blank response. However, if blank responses are considered, there is the possibility of obtaining a blank-corrected result for a sample not containing the analyte which is greater than the MDL. This is due to the random nature of both blank and sample responses. This type of error is termed error of the first kind (i.e., the error of accepting an apparent effect arising by chance as a real effect) and is not accounted for in the theory presented, which only considers 430A
Environ. Sci. Technol., Vol. 16, No. 8, 1982
error of the second kind (i.e., the error of failing to recognize a real effect). Also, the statement that sample standard deviation at zero concentration is "a concept which necessitates the possibility of negative analytical responses at zero concentration of analyte" is not correct. As has already been mentioned, an analytical result is equal to the difference between sample response and blank response, and it is the difference that may be negative, not the analytical responses themselves. Indeed, the error distribution presented by Glaser et al. indicates that there is a 1% chance for analyte concentration to be negative when the true value is equal to the defined method detection limit (MDL). It is not clear how MDL would be used in practice. O'Haver has stated that "a concentration at the detection limit can only be detected, as the term 'detection limit' implies, and not measured quantitatively." (7) Yet Glaser et al. state that " . . . the MDL for a given analyte in a given matrix does not preclude quantitation below the MDL." Besides the theoretical deficiencies mentioned, the procedures presented for determining MDL are somewhat arbitrary. This is indicated by the failure of the single-step procedure to give reasonable detection limit values, and such statements as "the closeness of the initial estimate to the final calculated MDL is a critical concern in using this procedure," and "the MDL procedure can give meaningless values when the analyte or analyte plus interference is present at levels much larger than 10 times the MDL value in reagent water." The statement is also made that "experience has shown that when the relative standard deviation is at or near 10% the calculated MDL values can be below instrumental detection limits." It is difficult to understand how a detection limit based on a "complete analytical procedure" can be less than a detection limit of one component in the procedure. I share with Glaser et al. their concern over the limitations in the application of definitions of detection limit based on the variability of blank mea-
surements. These limitations have been summarized by Cheeseman and Wilson (#). The definitions assume that the standard deviations of both the blank and samples containing low concentrations of the analyte are the same. The definitions are also not necessarily valid when the analytical response is zero for finite concentrations of the analyte. Finally, if the sample and blank are biased with respect to each other (for example, by the presence of interfering substances in the sample and/or the blank), the definitions are not valid. Unfortunately, the approach suggested by Glaser et al. in response to these limitations suffers from a lack of both a complete theoretical justification and a logically consistent procedure for determining the MDL, and I believe that application of the suggested procedures is not to be recommended. Cliff J. Kirchmer, Ph.D. Quality Assurance Manager Envirodyne Engineers 12161 Lackland Rd. St. Louis, Mo. 63141
References (1) Glaser, J. A. et al. Environ. Sci. Technol. 1981, 75,1426-1435. (2) Kaiser, H. "Two Papers on the Limit of Detection of a Complete Analytical Procedure"; Adam Hilger: London, 1968. (3) Currie, L. A. Anal. Chem. 1968, 40, 586-593. (4) Roos, J. B. Analyst 1962,87, 832-833. (5) Wilson, A. L. Talanta 1973, 20, 725732. (6) Morrison, G. H.; Skogerboe, R. K. In "Trace Analysis: Physical Methods"; Morrison, G. H., Ed.; Interscience Publishers: New York, 1965; Chap. 1. (7) O'Haver, T. C. In "Analytical Considerations in Trace Analysis: Spectroscopic Methods for Elements;" Winefordner, J. D., Ed.; John Wiley & Sons: New York, 1976; Chap. 2. (8) Cheeseman, R. V.; Wilson, A. L. "Manual on Analytical Quality Control for the Water Industry," Technical Report 66; Water Research Centre: England, January 1978.
Author's response The major premise in our practical approach to estimating the method detection limit (MDL) is that the MDL must reflect method perfor-
