A Factor Analysis of the Mathematical Sections of the Scholastic Aptitude Test1

Abstract

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 ‐ S2 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 ‐ S2 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.

The Effects of Special Instruction for Three Kinds of Mathematics Aptitude Items1

“…Students assigned to the control group were assured that instruction would be available to them after the posttest. In a factor analytic study of SAT-M content, Pruzek and Coffman (1966) found that most of the items that presented a geometric figure loaded heavily on the first factor, "Geometric Interpretation." Because of this finding, and the fact that about one-fourth to one-third of the items in each format present geometric figures, coaching effects were examined separately for geometry and nongeometry items within each item format.…”

“…The complexity of the DS format becomes apparent when one reads the directions. In their factor analysis of the SAT-M, Pruzek and Coffman (1966) commented that the Data Sufficiency factor " ••• appears to reflect the ability to read, interpret, and remember a rather extensive set of (1) alone is sufficient to answer the question~the correct choice must be A or D, so B, C, and E can be eliminated. On the other hand~i f (1) alone is not sufficient, B~C~or E must be correct~and A and D can be eliminated.…”