Letter | Published:

The Orthogonal Matrix transforming Spearman's Two-Factor Equations into Thomson's Sampling Equations in the Theory of Ability

Naturevolume 134page700 (1934) | Download Citation

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Abstract

IF is a column vector of t elements representing scores in t tests, and s a column vector of t + 1 elements of which the first, s0, represents Spearman's g and the rest his specific factors, then = Ls represents t Spearman equations giving the com-position of the ‘s, which will in that case be perfectly hierarchical. Here L is an oblong matrix of t rows and t + 1 columns. Its first column is {l1 l2 It} where lt is the correlation of i with g. The principal diagonal of the remainder of L is (m1 m2 mt) where m2i = 1 — l2i. The remaining elements in L are zero.

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  1. University, Edinburgh

    • GODFREY H. THOMSON

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https://doi.org/10.1038/134700c0

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