Distribution of aflatoxin in whole peanut kernels, sampling plans for small samples

It is well known that the distribution of aflatoxin in a lot of whole peanut kernels is extremely heterogeneous. Several different statistical distribution models have been proposed, fitting the experimental data reasonably well as long as the samples are very large, but differing considerably when applied to small samples. Therefore, it is important to know the real distribution between single kernels for the evaluation of the effectiveness of sampling plans for small samples. It is shown by the analysis of 368 samples of 1-10,000 kernels from the same lot of peanuts that the negative binomial distribution represents a good statistical model. The variance can be estimated from the mean concentration of the analysed samples, as confirmed by the comparison of data from several independent investigations. Decisions based on small samples are especially unfavourable to the consumer, as even a lot with a high mean concentration will tend to give negative results. A reasonably small risk of a false decision, both to the consumer and to the producer, can be reached only if very large samples are analysed.