### Abstract

Language | English |
---|---|

Pages | 37-39 |

Number of pages | 3 |

Volume | 15 |

Specialist publication | Microbiologist |

Publication status | Published - Jun 2014 |

### Fingerprint

### Keywords

- data analysis methods
- negative binomial distribution
- clustering analysis
- freshwater environments

### Cite this

*Microbiologist*,

*15*, 37-39.

}

*Microbiologist*, vol. 15, pp. 37-39.

**Statnote 37 : the negative binomial distribution.** / Hilton, Anthony; Armstrong, Richard.

Research output: Contribution to specialist publication › Article

TY - GEN

T1 - Statnote 37 : the negative binomial distribution

AU - Hilton, Anthony

AU - Armstrong, Richard

PY - 2014/6

Y1 - 2014/6

N2 - An organism living in water, and present at low density, may be distributed at random and therefore, samples taken from the water are likely to be distributed according to the Poisson distribution. The distribution of many organisms, however, is not random, individuals being either aggregated into clusters or more uniformly distributed. By fitting a Poisson distribution to data, it is only possible to test the hypothesis that an observed set of frequencies does not deviate significantly from an expected random pattern. Significant deviations from random, either as a result of increasing uniformity or aggregation, may be recognized by either rejection of the random hypothesis or by examining the variance/mean (V/M) ratio of the data. Hence, a V/M ratio not significantly different from unity indicates a random distribution, greater than unity a clustered distribution, and less then unity a regular or uniform distribution . If individual cells are clustered, however, the negative binomial distribution should provide a better description of the data. In addition, a parameter of this distribution, viz., the binomial exponent (k), may be used as a measure of the ‘intensity’ of aggregation present. Hence, this Statnote describes how to fit the negative binomial distribution to counts of a microorganism in samples taken from a freshwater environment.

AB - An organism living in water, and present at low density, may be distributed at random and therefore, samples taken from the water are likely to be distributed according to the Poisson distribution. The distribution of many organisms, however, is not random, individuals being either aggregated into clusters or more uniformly distributed. By fitting a Poisson distribution to data, it is only possible to test the hypothesis that an observed set of frequencies does not deviate significantly from an expected random pattern. Significant deviations from random, either as a result of increasing uniformity or aggregation, may be recognized by either rejection of the random hypothesis or by examining the variance/mean (V/M) ratio of the data. Hence, a V/M ratio not significantly different from unity indicates a random distribution, greater than unity a clustered distribution, and less then unity a regular or uniform distribution . If individual cells are clustered, however, the negative binomial distribution should provide a better description of the data. In addition, a parameter of this distribution, viz., the binomial exponent (k), may be used as a measure of the ‘intensity’ of aggregation present. Hence, this Statnote describes how to fit the negative binomial distribution to counts of a microorganism in samples taken from a freshwater environment.

KW - data analysis methods

KW - negative binomial distribution

KW - clustering analysis

KW - freshwater environments

UR - http://issuu.com/societyforappliedmicrobiology/docs/2014_06_microbiologist

M3 - Article

VL - 15

SP - 37

EP - 39

JO - Microbiologist

T2 - Microbiologist

JF - Microbiologist

SN - 1479-2699

ER -