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A Factor Analysis of the Mathematical Sections of the Scholastic Aptitude Test SAT

Coffman, William E.; Pruzek, Robert M.
Publication Year:
Report Number:
RB-66-12, RDR-65-66, No. 10
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
College Board, College Entrance Examinations, Factor Structure, Mathematics Tests, Scholastic Aptitude Test (SAT)


The purpose of the research reported here was to explore ways of generating a factor pattern from interrelationships among items. The basic data consisted of tetrachoric correlations among the 60 items in the mathematical sections of one form of the Scholastic Aptitude Test. Two methods of factoring and four methods of analytical rotation were compared. The factoring methods were: (1) a factoring of the tetrachoric correlation matrix with squared multiple correlations as communality estimates, the R - (S squared) matrix, and (2) a principal axis factoring of the tetrachoric covariance matrix using communality estimates obtained by an iterative procedure. The rotations were the varimax, the equamax, the promax, and an oblique rotation recently described by Harris and Kaiser. All methods produced compatible results; however, the clearest simple structure resulted when the first 11 factors extracted from the R -(S squared) matrix were rotated to oblique simple structure by the oblique rotation described by Harris and Kaiser. Six factors were interpreted: geometric interpretation, computation, speed, arithmetic reasoning, data sufficiency, and rules.

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