Acceptance-region design for finer classification partitions

Determine how to construct acceptance-region boundaries for classification tests with finer partitions, including more than three compact classes, when the error rate alone does not uniquely determine the test design.

Background

The paper develops optimal acceptance regions for sign, magnitude, and sign-and-magnitude classification tests, focusing on partitions with two or three substantively meaningful classes. It notes that researchers can design tests with finer partitions, but that the benefits relative to reporting raw estimates diminish as the partition becomes more detailed.

For partitions with more than three compact classes, the error rate at class boundaries is insufficient to determine a unique test. Additional criteria—such as maximizing expected power under a prior distribution for the estimand—may therefore be required to select among possible designs. The paper leaves the resulting questions about acceptance-region boundaries unresolved.