Statistics Meeting Book (May 15, 2019)

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.