Abstract
WHEN two correlation matrices R1, and R2 have a symmetrical product R1R2 = R2 R1 they have the same latent vectors1,2, and Prof. Cyril Burt has recently proposed3 to use this as a criterion that two batteries of mental tests contain the same mental ‘factors’. I do not myself think that one can draw any safe conclusions about identity of factors in two batteries unless some tests are common to both batteries. But if one accepts Burt's criterion, I wish to point out that when R1R2 is asymmetrical, the product of the covariance matrices D1R1D1 and D2R2D2 may conceivably be symmetrical, where D 1 and D1 are diagonal matrices of standard deviations. If an experimenter therefore has psychological reasons for thinking that two batteries contain identical factors, but finds R1R2 to be asymmetric, he may be able to discover variances which would make the product D1R1D1D2R2D2, symmetric. In that case he would have considerable reason for assuming these to be the natural variances of these tests.
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References
Eckart, C., and Young, G., Psychometrica, 1, 217 (1936).
Young, G., ibid., 2, 24 (1937).
Burt, C., ibid., 3, 161 (1938).
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THOMSON, G. Natural Variances of Mental Tests, and the Symmetry Criterion. Nature 144, 516 (1939). https://doi.org/10.1038/144516a0
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DOI: https://doi.org/10.1038/144516a0
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