The abilities of man : their nature and measurement / by C. Spearman.

  • Charles Spearman
Date:
1927
Catalogue details

Licence: In copyright

Credit: The abilities of man : their nature and measurement / by C. Spearman. Source: Wellcome Collection.

    443/474 page 429
    where r denotes the mean of the correlations taken into account. The values given in this way, however, turned out to be often appreciably too small. We then proposed the following approxi¬ mation. p.e. =^40[r>(r-r)2 + s:!]* (I5) N2 where s2 is the mean squared deviation of all the r’s from their mean.* But this was usually found to err somewhat in the opposite direction, that of giving too large values.! A much closer approximation than either is given by the following : p.e. = I/2(i “ ri2 ~ rz\ + y2) + i1 ~ zr2)s2]K (16) There is possible, however, quite a different procedure ; it is one which—although on some theoretical points still awaiting further elucidation—in practice at any rate appears to be far more convenient, and even more reliable, than (14), (15), or (16). Here, one single frequency distribution is made up of all the tetrad differences that arise from any number of variables. Its squared p.e. can easily be shown to equal the mean of the squared p.e.’s for all the tetrad differences taken separately ; and this mean has been proved to have approximately the follow¬ ing value, which has been used in the preceding volume.! where p.e. = ^349 _ ry + (Z-R)s2]h, N* n -4 n -2 2 r- n — 6 n - 2 ’ (i6a) It should be noted that in this equation (as in all the previous ones), the p.e. is obtained by the usual convention that it = *67450-. Sometimes, this will be appreciably inaccurate. Usually, however, it will be near enough for the present purpose of estimating the range of sampling errors, especially where (as here) the frequency distribution proves to be fairly “ normal.” See the distributions on pages 146 and 149, as also the lower one on page 154. * Ibidem, 1925, xvi. p. 86. | In arriving at (15), we had treated as negligibly small the terms of the form dxydxz. But Prof. Truman Kelley has kindly suggested that they may be worth taking into account. This, accordingly, we have now done. ! The proof will be published shortly.
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