Article: Test of the validity of the Poisson assumption for analysis of most-probable-number results

A test of the validity of the Poisson assumption for sample replicates in dilution series of finite length is proposed and its properties are examined by using Monte Carlo simulation. The test is based on an examination of the number of intervals between complete sterility and complete infection in a series. The test is applied to a data set of routine influent coliform samples at the Chicago water supply intake. By this test, the data set is rejected as being drawn from a Poisson replication. Tables for direct application to a 3-dilution, 5-tube decimal series are presented, and their application is illustrated.

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References

1.

Cochran W . Estimation of bacterial densities by means of the "most probable number". Biometrics. 1950; 6(2):105-16. View

2.

Chang S, Berg G, Busch K, Stevenson R, Clarke N, KABLER P . Application of the most probable number method for estimating concentrations of animal viruses by the tissue culture technique. Virology. 1958; 6(1):27-42. DOI: 10.1016/0042-6822(58)90057-6. View

3.

Cowell N, Morisetti M . Microbiological techniques--some statistical aspects. J Sci Food Agric. 1969; 20(10):573-9. DOI: 10.1002/jsfa.2740201001. View

4.

Savage G, HALVORSON H . The Effect of Culture Environment on Results Obtained with the Dilution Method of Determining Bacterial Population. J Bacteriol. 1941; 41(3):355-62. PMC: 374701. DOI: 10.1128/jb.41.3.355-362.1941. View

5.

Moran P . The dilution assay of viruses. J Hyg (Lond). 1954; 52(2):189-93. PMC: 2217753. DOI: 10.1017/s002217240002739x. View

6.

Loyer M, Hamilton M . Interval estimation of the density of organisms using a serial-dilution experiment. Biometrics. 1984; 40(4):907-16. View

7.

El-Shaarawi A, Esterby S, Dutka B . Bacterial density in water determined by poisson or negative binomial distributions. Appl Environ Microbiol. 1981; 41(1):107-16. PMC: 243648. DOI: 10.1128/aem.41.1.107-116.1981. View

8.

EISENHART C, Wilson P . STATISTICAL METHODS AND CONTROL IN BACTERIOLOGY. Bacteriol Rev. 1943; 7(2):57-137. PMC: 440868. DOI: 10.1128/br.7.2.57-137.1943. View

9.

WADLEY F . Limitations of the zero method of population counts. Science. 1954; 119(3098):689-90. DOI: 10.1126/science.119.3098.689. View

10.

Armitage P, Spicer C . The detection of variation in host susceptibility in dilution counting experiments. J Hyg (Lond). 1956; 54(3):401-14. PMC: 2217850. DOI: 10.1017/s0022172400044661. View

11.

Margolin B, Kaplan N, Zeiger E . Statistical analysis of the Ames Salmonella/microsome test. Proc Natl Acad Sci U S A. 1981; 78(6):3779-83. PMC: 319656. DOI: 10.1073/pnas.78.6.3779. View

Test of the Validity of the Poisson Assumption for Analysis of Most-probable-number Results