  This study developed a new 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
sensitivity of each laboratory obeys a beta distribution, and the binary
measured values under a given sensitivity follow a binomial distribution. We
propose the key precision measures of repeatability and reproducibility for the
model, and provide their unbiased estimates. Further, through consideration of
a number of statistical test methods for homogeneity of proportions, we propose
appropriate methods for determining laboratory effects in the new model.
Finally, we apply the results to real-world examples in the fields of food
safety and chemical risk assessment and management.
