Abstract
Formulas are derived by which, given the factor loadings and the internal reliability of a test of unit length, the following estimates can be made: (1) the common-factor loadings for a similar (homogeneous) test of lengthn; (2) the number of times (n) that a test needs to be lengthened homogeneously to achieve a factor loading of a desired magnitude; and (3) the correlation between two tests, either or both of which have been altered in length, as a function of (a) the new factor loadings in the altered tests or (b) the original loadings in the unit-length tests. The appropriate use of the derived formulas depends upon the fulfillment of four assumptions enumerated.
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References
Kelley, Truman L. Fundamentals of statistics. Cambridge: Harvard Univ. Press, 1947.
Thurstone, L. L. Multiple-factor analysis. Chicago: Univ. Chicago Press, 1947.
Tucker, Ledyard. The role of correlated factors in factor analysis.Psychometrika, 1940, 5, 141–152.
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This article is based on a paper read by the authors at the annual meeting of the Western Psychological Association in Eugene, Oregon, June 25, 1949.
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Guilford, J.P., Michael, W.B. Changes in common-factor loadings as tests are altered homogeneously in length. Psychometrika 15, 237–249 (1950). https://doi.org/10.1007/BF02289040
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DOI: https://doi.org/10.1007/BF02289040