Precision for binary measurement methods and results under beta-binomial distributions
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To handle typical problems from fields dealing with biological responses, this study develops a new statistical model and method for analysing the precision of binary measurement methods and results from collaborative studies. The model is based on beta-binomial distributions. In other words, we assume that the sensitivity of each laboratory obeys a beta distribution and the binary measurement results under a given sensitivity follow a binomial distribution. We propose the key precision indicators of repeatability and reproducibility for the model and derive their unbiased estimates. We further propose a confidence interval for repeatability by applying the Jeffreys interval, which utilizes the assumption of beta distributions for sensitivity. Moreover, we propose a statistical test for determining laboratory effects, using simultaneous confidence intervals based on the confidence interval of each laboratory's sensitivity. Finally, we apply the proposed method to real-world examples in the fields of food safety and chemical risk assessment and management.
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