A Note on Recovering the Ability Distribution from Test Scores
CARNEGIE-MELLON UNIV PITTSBURGH PA DEPT OF STATISTICS
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We propose a simple scheme for smoothly approximating the ability distribution for relatively long tests, assuming that the ICCs are known or well estimated. The scheme works for quite a general class of item characteristic curves ICCs and is guaranteed to completely recover the theta distribution as the test length. J, grows. After an initial function inversion, the scheme can be inexpensively used to recover the theta distribution in each of several different administrations of the same test or subpopulations in one test administration. Moreover, this approach could be used to recover the distribution of a dominant ability dimension when local independence fails. Finally, the scheme provides a starting place for diagnostics concerning assumptions about the shape of the theta distribution or ICCs of a particular test. Work is currently underway to further examine and refine these methods using essentially unidimensional simulation data, and to apply the estimators to real tests. Item response theory, kernel smoothing, latent trait distribution, population assessment.
- Statistics and Probability