**ERIC Number:**ED348399

**Record Type:**RIE

**Publication Date:**1992-May

**Pages:**36

**Abstractor:**N/A

**Reference Count:**N/A

**ISBN:**N/A

**ISSN:**N/A

A Note on Recovering the Ability Distribution from Test Scores.

Junker, Brian W.

A simple scheme is proposed for smoothly approximating the ability distribution for relatively long tests, assuming that the item characteristic curves (ICCs) are known or well estimated. The scheme works for a general class of ICCs and is guaranteed to completely recover the theta distribution as the test length increases. The proposed method of estimating the ability distribution is robust to some violations of local independence. 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 several subpopulations in one test administration. Moreover, this approach could be used to recover the distribution of a dominant ability dimension when local independence fails. 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 under way to further examine and refine these methods using essentially unidimensional simulation data and to apply the estimator to real tests. Kernel smoothing is also considered. A 16-item list of references, 10 tables, 8 graphs, and 2 appendixes that provide details of the simulation and proofs are included. (RLC)

**Publication Type:**Reports - Evaluative

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**Office of Naval Research, Arlington, VA. Cognitive and Neural Sciences Div.

**Authoring Institution:**Carnegie Mellon Univ., Pittsburgh, PA. Dept. of Statistics.

**Identifiers:**Ability Estimates; Local Independence (Tests); Population Parameters; Smoothing Methods; Theta Estimates