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

TL;DR

This paper introduces a beta-binomial based statistical model and methods for analyzing the precision of binary measurement methods across laboratories, including measures of repeatability and reproducibility, with applications in food safety and chemical risk assessment.

Contribution

It presents a novel beta-binomial model for binary measurement precision analysis and proposes new statistical tests for laboratory effects, with unbiased estimates and real-world applications.

Findings

Developed a new beta-binomial model for binary measurement analysis.

Proposed unbiased estimates for repeatability and reproducibility.

Applied methods successfully to food safety and chemical risk data.

Abstract

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.