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Analysis of two-way layout of count data with negative binomial variation

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Abstract

A number of methods has been proposed for dealing with single-factor or factorial experiments when the requirements for performing the normal theory analysis of variance procedure are not satisfied. This paper suggests the use of the likelihood ratio statistic for testing the main effects and the interaction between the factors in two-way layout of count data following negative binomial distributions with a common dispersion parameter. The likelihood ratio statistic for testing the equality of the dispersion parameters of several groups of count data is also derived. The methods is illustrated by an example concerning the study of spatial and temporal variation of bacterial counts.

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References

  • AnscombeF. J.: 1948, ‘The Transformation of Poisson, Binomial and Negative Binomial Data’, Biometrikla 38, 246–254.

    Google Scholar 

  • AnscombeF. J.: 1949, ‘The Analysis of Insect Counts Based on the Negative Binomial Distribution’, Biometrics 5, 165–173.

    Google Scholar 

  • BarnwallR. K. and PaulS. R.: 1988, ‘Analysis of One-Way Layout of Count Data with Negative Binomial variation’, Biometrika 75, 215–222.

    Google Scholar 

  • BlissC. I. and FisherR. A.: 1953, ‘Fitting the Negative Binomial Distribution to Biological Data’, Biometrics 9, 176–200.

    Google Scholar 

  • El-ShaarawiA. H., EsterbyS. R., and DutkaB. J.: 1981, ‘Bacterial Density in Water Determined by Poisson or Negative Binomial Distributions’, Appl. Environ. Microbiol. 41, 107–116.

    Google Scholar 

  • LawlessJ. F.: 1987, ‘Negative Binomial and Mixed Poisson Regression’, Can. J. Statist. 15, 205–225.

    Google Scholar 

  • MaulA. and BlockJ. C.: 1983, ‘Microplate Fecal Coliform Method to Monitor Strea Water Pollution’, Appl. Environ. Microbiol. 46, 1032–1037.

    Google Scholar 

  • MaulA., El-ShaarwaiA. H., and BlockJ. C.: 1985, ‘Heterotrophic Bacteria in Water Distribution Systems, I. Spatial and Temporal Variation, II. Sampling Design for Monitoring’, Sci. Total Environ. 44, 201–224.

    Google Scholar 

  • Maul. A., El-Shaarawi, A. H., and Ferard, J. F.: 1989, ‘Application of Negative Binomial Regression Models to the Analysis of Quantal Bioassays Data’, Environmetrics (to appear).

  • SchefféH.: 1959, The Analysis of Variance, John Wiley, New York.

    Google Scholar 

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Authors and Affiliations

  1. Département Informatique, Université de Nancy II, 2bd Charlemagne, 54000, Nancy, France

    A. Maul & A. H. El-Shaarawi

  2. Rivers Research Branche, National Water Research Institute, Canada Centre for Inland Waters, L7R 4A6, Burlington, Ontario, Canada

    A. Maul & A. H. El-Shaarawi

Authors
  1. A. Maul
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  2. A. H. El-Shaarawi
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Maul, A., El-Shaarawi, A.H. Analysis of two-way layout of count data with negative binomial variation. Environ Monit Assess 17, 315–322 (1991). https://doi.org/10.1007/BF00399311

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