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

Charles Spearman

Date:: 1927

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

437/474 page 423

$it would have if % and x took all values quite independently of each other. And this is zero. Again owing to the largeness of m, rax> and rhx> approximate respectively to rax and rbx. ¥ ' Y ' Accordingly, rab approximates to ‘ - bz, which by (9) ^ x'x — rayfbyj, so that rSasb = o and condition 4 is fulfilled as re¬ quired. (n) This not only corroborates the result obtained in the above- mentioned paper of Garnett, but dispenses with his particular assumption of “ normal ” frequency distributions, so that it extends the theorem to one of perfect generality, except that m must be very large. In order to fulfil condition 4 freed even from this limitation, the constitution of must be more complicated. Let us choose for it the value expressed in the following determinant PV(S/Mii) pfxaa p^hb -1 Ma2 -1 0 -1 o /V*-! PPzZ o o -1 o o where /xa = i/y^A^r^), ^ having a meaning as in (6), so that juLa retains the same value whatever variable may be taken as q, i == any new variable uncorrelated with all the others (<r = l),t Mi = the complementary minor of the first element J in the first row, 5 = the sum of such minors for all elements in the first row, and p is such a value as will make a\, = 1. This gives us, expanding the determinant according to the elements of the first row,§ ra = a T zVaz V+... +Vz2Mz2 +MiS +2Sa,S1/[njiyMxMvrxy\)' f This is here assumed to be possible, at any rate if the present theorem is only applied to a finite number of variables. The case of an infinite number has already been demonstrated by (n). + Of course, “ element ” is here no longer used with the same meaning as previously in this paper. § Spearman, Brit. J. Psych, vol. v. p. 419.$

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

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