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© 2012 AOAC INTERNATIONAL
AOAC O
FFICIAL
M
ETHODS
OF
A
NALYSIS
(2012)
M
ICROBIOLOGY
G
UIDELINES
Appendix J, p. 21
ANNEX H
Logarithmic Transformation of Data from
Quantitative Method Single Laboratory and
Collaborative Data
Quantitative microbiological count data from experiments
spanning multiple dilutions often do not show a Poisson nor a
Gaussian statistical distribution. When the underlying physical
mechanism allows for “clustering,” typically a logarithmic
transformation will normalize the data.
Perform a logarithmic transformation on the reported CFU/unit
(including any zero results) as follows:
Y = log
10
[CFU/unit + (0.1)f]
where f is the reported CFU/unit corresponding to the smallest
reportable result, and “unit” is the reported unit of measure (e.g.,
g, mL, 25 g).
Examples
(
1
) For the control concentration, the CFU/g is reported as
“<0.003.” So CFU/unit = 0.0, and Y =
log
10
[0.0 + (0.1)(0.003)]
= –3.52.
(
2
) For the low concentration, the CFU/g is 0.042. So Y = log
10
[0.042 + (0.1)(0.003)] = –1.37.
(
3
) For the high concentration, the CFU/g is 0.231. So Y = log
10
[0.231 + (0.1)(0.003)] = –0.64.