## Electronic Theses and Dissertations

#### Title

Analysis of one-way layout of count data.

1989

Dissertation

Ph.D.

#### Department

Mathematics and Statistics

Paul, S. R.,

Statistics.

CC BY-NC-ND 4.0

#### Abstract

Inadequacy of the Poisson assumption, due to the presence of overdispersion, in analysing count data has been reported by several authors (see McCaughran and Arnold (1976), Bliss and Owen (1958) etc.). Negative binomial distribution has been widely used to incorporate overdispersion in analysing the count data. Several test statistics for detecting negative binomial variation have been presented-C($\alpha$) tests, range-justified tests (appealing to the nonnegativity of the dispersion parameter) are compared with the static presented by Collings and Margolin (1985). One-way layout of data in the form of counts is often reported as a result of laboratory experiment or field work. Assuming the underlying distribution for the groups to be negative binomial with common dispersion parameter, two C($\alpha$) tests are developed for comparing the means of the groups. Their performance is compared in terms of level and power with the likelihood ratio test and test based on variance establishing transformation (Anscombe (1948)). A test for checking the validity of assumption of common dispersion is also developed. In several situations the assumption of a common dispersion parameter might not be tenable. A C($\alpha$) test is derived for comparing the means of negative binomial distributions with unequal dispersion parameters. For two groups, this test is compared with the Welch's approximate degree of freedom formula and Banerji's procedure (1960) for empirical level and power. Methods for testing the presence of an outlier in data coming from a population following Poisson distribution have also been derived. In deriving the C($\alpha$) test statistics for the above problems, the method presented by Neyman (1959) has been presented under a more general setting, which covers many situations concerning inferences on several parameters in presence of nuisance parameters.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1990 .B276. Source: Dissertation Abstracts International, Volume: 52-11, Section: B, page: 5913. Supervisor: S. R. Paul. Thesis (Ph.D.)--University of Windsor (Canada), 1989.

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