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The estimation of bacterial densities from dilution series

Published online by Cambridge University Press:  15 May 2009

D. J. Finney
D. J. Finney
Affiliation:
Lecturer in the Design and Analysis of Scientific Experiment, University of Oxford
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A transformation devised by Mather is applied to give a new scheme for computing the maximum likelihood estimate of a bacterial density from the evidence of a dilution series. Tables are provided to expedite the application of the method; with their aid, the calculations take a from similar to, but much simpler than, those for probit analysis of quantal responses.

Maximum likelihood estimation is compared with the method proposed by Fisher. The latter has the advantage of extreme simplicity, at least for series to which existing tables can be applied, and the loss of information involved in its use may often be compensated by the saving of time in calculation. An experimenter who has fairly reliable prior indications of an approximate value for the density, however, ought to concentrate his attention on dilutions that he believes will contain between 4 and 1/4 organisms per sample; he must not apply Fisher's method to his results, but the maximum likehood estimate will be so much more precise than any estimate from an experimental design using more extreme dilutions as to repay the small additional labour in computation.

Type
Research Article
Information
Journal of Hygiene , Volume 49 , Issue 1 , March 1951 , pp. 26 - 35
Copyright
Copyright © Cambridge University Press 1951

References

REFERENCES

Barkworth, H. & Irwin, J. O. (1938). Distribution of coliform organisms in milk and the accuracy of the presumptive coliform test. J. Hugg. Camb., 38, 446–57.Google ScholarPubMed
Cochran, W. G. (1950). Estimation of bacterial densities by means of the ‘most probable number’. Biometrics, 6, 105–16.CrossRefGoogle ScholarPubMed
Esisenhart, C. & Wilson, P. W. (1943). Statistical method and control in bacteriology. Bact. Rev. 7, 57–137.CrossRefGoogle Scholar
Finney, D. J. (1947). The principles of biological assay.J.R.statist. Soc. (Suppl.s). 9, 46–91.Google Scholar
Finney, D. J. (1949). The estimation of the parameters of tolerance distributions. Biometrika, 36, 239–56.CrossRefGoogle ScholarPubMed
Finney, D. J. (1951). Probit Analysis: A Statistical Treatment of the Sigmoid Response Curve, 2nd ed.London: Cambridge University Press.Google Scholar
Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics. Philos Trans A, 222, 309–68.Google Scholar
Fisher, R. A. & Yates, F. (1948). Statistical Tables for Biological, Agriculture and Medical Research, 3rd ed.Edinburgh: Oliver and Boyd.Google Scholar
Halvorson, H. O. & Ziegler, N. R. (1933). Application of statistics to problems in bacteriology. I. A means of determining bacterial population by the dilution method. J. Bact. 25, 101–21.CrossRefGoogle Scholar
Mather, K. (1949). The analysis of extinction time data in bioassay. Biometrics, 5, 127–43.CrossRefGoogle ScholarPubMed
New York Works Project Administration (1939). Tables of the Exponential Function. New York: Federal Works Agency.Google Scholar