Interpreting and Extending the Maximum Ratio Test of Unacceptability

Tsao and Wright (1983) proposes the use of a statistic called the "maximum ratio" to assess the reliability of K estimates θ₁, . . . , θ_Kof an unknown population parameter θ. This statistic can be used to test whether one of these estimates is outside of an "acceptable" region, whose radius is a multiple α of the unknown true parameter θ. Because θis unknown, it is difficult to know whether a large α value reflects a large error in the underlying metric, or just a large proportion of a small θ. This paper generalizes the maximum ratio test to multiple dimensions, considers some broad approaches for selecting an α value for this test in the absence of knowledge of θ, applies the test to five estimates of the population proportions for eight demographic subgroups within the United States, and visualizes the results. We then repeat the process after intentionally introducing errors into one of the estimates.