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Multivariate Statistical Inference Under Marginal Structure, II SAT

Gleser, Leon Jay; Olkin, Ingram
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
National Science Foundation (NSF), United States Air Force Office of Scientific Research, Equated Scores, Models, Research Design, Scholastic Aptitude Test (SAT), Statistical Analysis, Validity


A previous paper (Gleser and Olkin (1972) dealt with statistical inference problems in the context of an experimental design in which k randomly chosen groups of individuals from the same population of individuals are asked to take different psychological tests under identical testing conditions. The k tests (T0,T1), (T0,T2), ... , (T0,Tk) have one subtest T0 in common. It is desired to test whether (T0,T1), (T0,T2), ... , (T0,Tk) are parallel forms of the same test. The experimental design described above is a natural one for ongoing testing programs such as the Scholastic Aptitude Test (SAT), where forms must be changed from year to year (so that new items must be introduced and validated), yet experimentation with new forms and administration of old forms are done simultaneously. The design described above might be used in a given year to validate items for future years. The likelihood ratio test and relevant distribution theory is developed for a number of alternative models. (28pp.)

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