A Theory of Consistency of Ordering Generalizable to Tailored Testing

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Abstract
Measures of consistency and completeness of order relations derived from test-type data are proposed. The measures are generalized to apply to incomplete data such as from tailored testing. The measures are based on consideration of the items-plus-persons by items-plus-persons matrix as an adjacency matrix in which a 1 means that the row element, whether item or person, dominated the column element. From this the number of item-item and person-person dominance relations can be derived. Indices of consistency are developed which compare the number of dominance relations in a matrix to the number that would occur if it were perfectly consistent and to the number in a random matrix; relations to other indices are noted.

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