Technical Abstract: A theory is developed for predicting the variance resulting from comminuting (by grinding) a sample taken from a lot of contaminated particles, such as tree nuts contaminated with aflatoxin. The predicted variance is a function of the weight distribution of comminuted particles, the sample size and the probability that a nut in the lot is contaminated. This prediction is tested experimentally by grinding 10kg samples dry or by wet slurrying, which results in significantly differing weight distributions. Agreement within 30% is obtained between experimental and calculated coefficients of variation without the use of any adjustable parameters. Optimum comminuting conditions for both dry and wet methods are explored, as both are in use in N. America and Europe.