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A New Interpretation of Augmented Subscores and Their Added Value in Terms of Parallel Forms
Author(s) -
Sinharay Sandip
Publication year - 2018
Publication title -
journal of educational measurement
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.917
H-Index - 47
eISSN - 1745-3984
pISSN - 0022-0655
DOI - 10.1111/jedm.12171
Subject(s) - mathematics , value (mathematics) , interpretation (philosophy) , statistics , mean squared error , correlation coefficient , computer science , programming language
Abstract The value‐added method of Haberman is arguably one of the most popular methods to evaluate the quality of subscores. The method is based on the classical test theory and deems a subscore to be of added value if the subscore predicts the corresponding true subscore better than does the total score. Sinharay provided an interpretation of the added value of subscores in terms of scores and subscores on parallel forms. This article extends the results of Sinharay and considers the prediction of a subscore on a parallel form from both the subscore and the total raw score on the original form. The resulting predictor essentially becomes the augmented subscore suggested by Haberman. The proportional reduction in mean squared error of the resulting predictor is interpreted as a squared multiple correlation coefficient. The practical usefulness of the derived results is demonstrated using an operational data set.