title: Reconsideration of the derivation of Most Probable Numbers, their standard deviations, confidence bounds and rarity values.
abstract: OBJECTIVE
  The purpose of this work was to derive a simple Excel spreadsheet and a set of standard tables of most probable number (MPN) values that can be applied by users of International Standard Methods to obtain the same output values for MPN, SD of the MPN, 95% confidence limits and test validity. With respect to the latter, it is considered that the Blodgett concept of 'rarity' is more valuable than the frequently used approach of improbability (vide de Man).
  
  
  RESULTS
  The paper describes the statistical procedures used in the work and the reasons for introducing a new set of conceptual and practical approaches to the determination of MPNs and their parameters. Examples of MPNs derived using these procedures are provided. The Excel spreadsheet can be downloaded from http://www.wiwiss.fu-berlin.de/institute/iso/mitarbeiter/wilrich/index.html.
  
  
  CONCLUSIONS
  The application of the revised approach to the determination of MPN parameters permits those who wish to use tabulated values, and those who require access to a simple spreadsheet to determine values for nonstandard test protocols, to obtain the same output values for any specific set of multiple test results. The concept of 'rarity' is a more easily understood parameter to describe test result combinations that are not statistically valid. Provision of the SD of the log MPN value permits derivation of uncertainty parameters that have not previously been possible.
  
  
  CONCLUSIONS
  A consistent approach for the derivation of MPNs and their parameters is essential for coherence between International Standard Methods. It is intended that future microbiology standard methods will be based on the procedures described in this paper.
authors.affiliation: Ross Biosciences Ltd., Upton Bishop, Ross-on-Wye, UK. basil.jarvis@btconnect.com
authors.forename: B
authors.initials: B
authors.lastname: Jarvis
authors.forename: C
authors.initials: C
authors.lastname: Wilrich
authors.forename: P-T
authors.initials: PT
authors.lastname: Wilrich
mesh_terms: D015169:Colony Count, Microbial / Q000379:methods*; D003627:Data Interpretation, Statistical; D006801:Humans; D008297:Male; D011336:Probability; D012984:Software / Q000592:standards