Interpreting and Extending the Maximum Ratio Test of Unacceptability

Scientists might have access to multiple estimates of an unknown quantity without knowing whether all of them are good. In response to this concern, Tsao and Wright (1983) proposed a method called the “maximum ratio test” that flags groups of estimates when one is “too far” from the truth. An estimate is “too far” when it is farther than some percentage of the (unknown) true value away from the truth. This can make the test difficult to interpret: a collection of estimates could be flagged because one of the estimates is far from the truth, or because the true value is small enough that negligible estimation errors look large by comparison. This paper addresses this problem by proposing two generalizations of the maximum ratio test that can be used when a parameter and its estimates are vectors. It applies these new tests to estimates of the population proportions for eight demographic subgroups within the United States, and visualizes the results. It then repeats this analysis after intentionally introducing errors into one of the estimates. The results suggest the multidimensional tests are less likely to confuse large estimation errors with small parameter values than the one-dimensional version.