CI-90A User’s Manual
Page 32
Appendix — Feller Correction
There is a statistical analysis that corrects the observation to a
probable statistical
total
. This compensates for the fact that the probability of a
colony forming unit (CFU)
passing through a given perforation increases with the actual concentration of microbes
per cubic meter. What this means is that as the total number of CFUs passing through the
perforated plate increases, the likelihood of a CFU passing through a hole that has
already passed a CFU during the sample increases. The result is an undercount.
William Feller provides the correction in
An Introduction to Probability Theory and its
Applications.
Vol 1. 3
rd
ed. New York: John Wiley and Sons, 1968. pp. 224-225.
The governing equation for this correction is:
Pr = N * [1/N + 1/(N-1) + 1/(N-2) + … + 1/(N-r+1)]
Pr := Probable statistical total
N :=
Number of holes in perforated lid (Climet has 333 holes)
r :=
Number of CFUs observed on the incubated Petri dish
It is relatively easy to add a
Feller
function to an
Excel
spreadsheet. Simply execute the
following steps:
On the
Tools
menu, point to
Macro
, and then select
Visual Basic Editor
On the
Insert
menu in the
Microsoft Visual Basic
window, select
Module
In the
Module
window, type the code below
Function Feller(r)
If r = 1 Then
Feller = 1
Else
Feller = Feller(r - 1) + 333 / (334 - r)
End If
End Function
On the
File
menu, select
Close and Return to Microsoft Excel
On the worksheet, insert the formula
=Feller(A2)
in the cell where you want the Probable
Statistical Total to appear (assuming you have placed the observed value in cell A2).
The Feller Table below shows the corrected totals for every value one might observe with the
Climet samplers. For example, if you obtain a sample on which you observe 105 colonies, you
simply find 105 in column A in the table, and obtain 125.9 from the adjacent column B to the
right.
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