A model and method for analyzing the precision of binary measurement methods based on beta-binomial distributions, and related statistical tests

This study developed a statistical model and method for analyzing the precision of binary measurement methods from collaborative studies. The model is based on beta-binomial distributions. In other words, it assumes that the probability of detection (POD) of each laboratory obeys a beta distribution, and the binary measured values under a given POD follow a binomial distribution. We propose the key precision measures of repeatability and reproducibility for the model, and provide their unbiased estimators. Then, our precision measures and estimators are theoretically compared to three existing binary methods. Further, through consideration of a number of statistical tests for homogeneity of proportions, we propose appropriate methods for determining laboratory effects in the new model. Finally, we apply the results to a real-world example in the field of food safety.