The essentials of mental measurement . Thomson, Mathematics and the Inductive Methods of Logic, Proc. Phil. Soc. 1912—13, v. pp. 76—99. 122 COREELATION [PT. II It is interesting to look at a correlation table in greater detail. Ifwe think of it as a plane horizontal surface, and erect over the centreof each compartment a vertical Une proportional to the number writtenin that compartment, then the tops of these Unes touch the correlationsurface. It is clear from the equation to the surface that the contours, orlines of equal z, are elUpses, given by the equation x^ 2rxy f + -fl2 . 2
The essentials of mental measurement . Thomson, Mathematics and the Inductive Methods of Logic, Proc. Phil. Soc. 1912—13, v. pp. 76—99. 122 COREELATION [PT. II It is interesting to look at a correlation table in greater detail. Ifwe think of it as a plane horizontal surface, and erect over the centreof each compartment a vertical Une proportional to the number writtenin that compartment, then the tops of these Unes touch the correlationsurface. It is clear from the equation to the surface that the contours, orlines of equal z, are elUpses, given by the equation x^ 2rxy f + -fl2 . 2 = constant .(6). In the figure the numbers 40 and over have been printed in italics sothat this contour fine can be approximately followed. It is seen to beroughly elhptical, the major axis of the elhpse lying obliquely. Themajor axes of all the contour ellipses of a surface showing correlationare inchned to the axes of coordinates; and if, as we always can, wechoose the linear units of x and y on the diagram in such a ratio that.
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