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Approximations to Item Parameters of Mental Test Models and Their Uses1

University of Washington

Equations were derived to enable the graphic approximation of the item parameters of the stochastic mental test models, i.e., the generalized normal ogive and logistic models. The item parameters for the models are discriminatory power (a_i), difficulty (b_i), and lower asymptote of the item characteristic curve (c_i) where the item characteristic curve (ICC) is the regression of the binary item on latent ability. In brief, c _i can be approximated through visual inspection of the left-hand (lower) asymptote of the proportion passing the item plotted against the total test score minus the particular item. Thereafter, a graph appropriate to the approximate c_i can be consulted to convert an ordinary item-total test point-biserial correlation and proportion passing the item into approximations of item discriminatory power (a_i) and item difficulty (b_i). Suggested uses for the approximations were to provide a basis for screening items for tailored testing, to enable a determination as to the appropriateness of a set of items for tailored testing, and to provide starting values for parameter estimation in maximum likelihood procedures. The conditions and assumptions necessary for an effective application of the method were delineated. Recent empirical results which bear on the properties of the approximations were examined. An investigation was suggested to evaluate a further possible use of the approximations that of their direct applicability in tailored testing procedures. The generated graphs may also be helpful pedagogically in appreciating the relationships between conventional and mental test model parameters.

Educational and Psychological Measurement, Vol. 34, No. 2, 253-269 (1974)
DOI: 10.1177/001316447403400206


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