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Estimating Scores for an Optional Test Section Using Information From a Common Section

Allen, Nancy L.; Holland, Paul W.; Thayer, Dorothy T.
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Estimation (Mathematics), Missing Data, Nonresponse, Optional Items, Scaling, Score Distribution


(39pp.) Some tests include a section of optional questions in addition to mandatory parts of the test. The purpose of this paper is to provide a general method based on missing-data methods for nonignorable nonresponse (Little & Rubin, 1987) to estimate distributions of scores on an optional part of the test taking into account information from a mandatory part of the test. The scores for the optional section can then be placed on comparable scales using "equating" or moderation methods. This paper is the third in a series of three papers. In the first, "Approaches to Nonignorable Nonresponse with Application to Selection Bias" (Allen, Holland, & Thayer, in press, a), we apply missing-data methods from settings external to education to this setting. A method from the econometric literature (Heckman, 1976) is contrasted to methods proposed by Little and Rubin (1987) and Tukey (Holland, 1986). In the second paper, "A Missing Data Approach to Estimating Distributions of Scores for Optional Test Sections" (Allen, Holland, & Thayer, in press, b), the perspective of measurement specialists who proposed methods to transform scores for optional questions to comparable scales is contrasted with the approach based on the work of Little and Rubin. In this paper, the methods of Rubin and Tukey are extended to include common scores for the mandatory part of the test. Data from an example are actually transformed to comparable scales.

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