The Factorial Analysis of Human Ability

The Factorial Analysis of Human Ability

The Factorial Analysis of Human Ability

The Factorial Analysis of Human Ability

Excerpt

The theory of factorial analysis is mathematical in nature, but this book has been written so that it can, it is hoped, be read by those who have no mathematics beyond the usual secondary school knowledge. Readers are, however, urged to repeat some at least of the arithmetical calculations for themselves.

Those who wish to understand more fully the mathematical background against which the book is written are advised to read some work on statistics, say Yule and Kendall Introduction to the Theory of Statistics (Griffin) especially Chapters 6, 7, 8, and 11; and, for more advanced knowledge, 12, 13, 14, and 18. T. L. Kelley Statistical Method (Macmillan, New York) has the advantage of using determinants freely. Since matrix algebra plays an increasing part in factorial theory, the really serious student should read Chapter I at least of Turnbull andAitken Theory of Canonical Matrices (Blackie), and if possible also the first halves of Turnbull Theory of Determinants, Matrices, and Invariants (Blackie) and Bôcher Introduction to Higher Algebra (Macmillan, New York).

Those who carry out actual factorial analyses will find it almost essential to have tabular and mechanical assistance with the arithmetic. A desk slide-rule is helpful, especially in checking, and Barlow Tables of Squares, etc., and Crelle Calculating Tables very desirable. But any psychological laboratory doing much factorial work should have a calculating machine, one on which, for example, a tetrad-difference can be calculated without the need of noting any intermediate steps.

Even professional mathematicians will, it is hoped, read not merely the appendix, but the text. An explanation directed to the non-professional layman, and couched mainly in geometrical terms, may have suggestions for the expert also, and by being more general may counteract the . . .

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