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A Maximum Likelihood Approach to Test Scores

Lord, Frederic M.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Constructed Responses, Guessing (Tests), Maximum Likelihood Statistics, Scores


It is proposed here to use a more accurate metric than the usual mental test score for measuring the ability underlying test scores and to investigate what may be learned from a maximum likelihood approach to the problem of estimating the examinee's ability, as defined by this metric. If certain relations can be suitably specified mathematically, Fisher's method of maximum likelihood can be applied to estimate parameters describing the test items and parameters describing the ability of each examinee individually. The likelihood approach may also be used for the purpose of making tests of significance. This metric, an "ability score", is considered here for cases of free-response items, equivalent free-response items and multiple-choice items. (JGL)

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