The Validity of the Poisson Distribution to Analyze Microbial Colony Counts on Agar Plates for Food Samples

Microbial colony counts of food samples in microbiological examinations are one of the most important items. The probability distributions for the colony counts per agar plate at the dilution of counting had not been intensively studied so far. Recently we analyzed the colony counts of food samples with several probability distributions using the Pearson’s chi-square value by the “traditional” statistics as the index of fit [Fujikawa and Tsubaki, Food Hyg.Saf.Sc., 60, 88–95 (2019)]. As a result, the selected probability distributions depended on the samples. In this study we newly selected a probability distribution, namely a statistical model, suitable for the above data with the method of maximum likelihood from the probabilistic point of view. The Akaike’s Information Criterion (AIC) was used as the index of fit. Consequently, the Poisson model were better than the negative binomial model for all of four food samples. The Poisson model was also better than the binomial for three of four microbial culture samples. With Baysian Information Criterion (BIC), the Poisson model was also better than these two models for all the samples. These results suggested that the Poisson distribution would be the best model to estimate the colony counts of food samples. The present study would be the first report on the statistical model selection for the colony counts of food samples with AIC and BIC.