The origin of factor scores: Spearman, Thomson and Bartlett

The indeterminacy of factor scores has been a perennial source of debate since the time of Spearman. The main purpose of this paper is to show that, in spite of his inadequate tools and concepts, Sir Godfrey Thomson's approach of 70 years ago was on the right lines. His thinking was constrained by the primitive state of his statistical understanding but it is illuminated by his substantial exchange of the correspondence with M. S. Bartlett in the 1930s, most of which has survived in the Godfrey Thomson archive at the University of Edinburgh. In order to justify our claim and clarify the issues, we have found it necessary to fill in some of the gaps in the original derivations of Spearman, Thomson and Bartlett and to express their work in terms which are intelligible today. The opportunity is taken to relate this earlier work to contemporary debates.