A Basic Test Theory Generalizable to Tailored Testing.
UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES DEPT OF PSYCHOLOGY
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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 tailored testing. The measures are based on consideration of the item-plus-persons by items-plus-persons matrix as an adjacency matrix in which a 1 means that the row element dominated the column element regardless of whether it is item or person which dominates. 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. The indices of consistency are shown to relate to test variance, the Kuder-Richardson formulas, and Loevingers homogeneity indices. Indices of completeness are also proposed. Author