Predictive food microbiology Gedanken experiment: why do microbial growth data require a transformation?

Most microbial growth rate data are heteroscedastic, or non-normally distributed. If data heteroscedasticity is not taken into account prior to regression analysis, the analysis will be flawed. The resulting model will imply lower accuracy than the data warrant at low growth rates, and greater accuracy than the data warrant at high growth rates. A simplified, artificial but realistic microbial growth curve was constructed for use in 'gedanken' or thought experiments. Two time intervals representing early and late exponential phase were chosen for making supposed plate counts. It was assumed that this same general microbial population density change occurred at all of the postulated growth rates. For each pair of growth curves at each condition, a mean growth rate estimate, and growth rate variance was determined. These data have a gamma distribution, because the ratio between the variance and the square of the mean is a constant. We would propose, on the basis of these findings that the predictive food microbiologist considers microbial growth data to be log-normally distributed. Where actual data show greater variability (than can be stabilized by a logarithmic transformation) this may be explained by the operation of a physiological or biochemical based mechanism. Should the data actually support a less extreme transformation (implying greater variability than expected at the extremes), we hypothesize that in those cases either a physiological or biochemical based mechanism may be operating. (C) 1998 Academic Press Limited.