This paper argues that: test data are ordinal; latent trait scores are only determined ordinally; and test data are used largely for ordinal purposes. A set of ordinal assumptions is presented, including an ordinal version of local independence. It is concluded that a purely ordinal test theory is possible. (TJH)

In almost all applications of measurement there is some sort of response by a human subject. Almost always, the response scale is ordinal, but almost always it is treated as if it were an interval measure. Methods for treating data ordinally are currently being developed in three areas: ordinal analysis for questionnaire responses, ordinal…

This paper traces the course of the consequences of viewing test responses as simply providing dichotomous data concerning ordinal relations. It begins by proposing that the score matrix is best considered to be items-plus-persons by items-plus-persons, and recording the wrongs as well as the rights. (Author/CTM)

A test theory using only ordinal assumptions is presented, based on the idea that the test items are a sample from a universe of items. The sum across items of the ordinal relations for a pair of persons on the universe items is analogous to a true score. (SLD)

The validity of the assumptions under which the ordinal true score test theory was derived was examined using (1) simulation based on classical test theory; (2) a long empirical test with data from 321 sixth graders; and (3) an extensive simulation with 480 datasets based on the 3-parameter model. (SLD)