Testing Deviation for a Set of Serial Dilution Most Probable Numbers from a Poisson-Binomial Model

Abstract

Abstract A serial dilution experiment estimates the microbial concentration in a broth by inoculating several sets of tubes with various amounts of the broth. The estimation uses the Poisson distribution and the number of tubes in each of these sets that show growth. Several factors, such as interfering microbes, toxins, or disaggregation of adhering microbes, may distort the results of a serial dilution experiment. A mild enough distortion may not raise suspicion with a single outcome. The test introduced here judges whether the entire set of serial dilution outcomes appears unusual. This test forms lists of the possible outcomes. The set of outcomes is declared unusual if any occurrence of an observed outcome is on the first list, or more than one is on the first or second list, etc. A similar test can apply when there are only a finite number of possible outcomes, and each outcome has a calculable probability, and few outcomes have tied probabilities.