The essentials of mental measurement / by William Brown.

  • Brown, William, 1811-
Date:
1911
Catalogue details

Licence: In copyright

Credit: The essentials of mental measurement / by William Brown. Source: Wellcome Collection.

Provider: This material has been provided by King’s College London. The original may be consulted at King’s College London.

    141/172 (page 129)
    We further assume that m > n, since otherwise the m e's can be eliminated from these n equations. Then our general problem is this: supposing the independent variables, e, each follow a Gaussian distribution, what will be the frequency surface connecting the xs ? Assume that the variations of e are small relative to their mean values. In this case we may expand the functions and retain only the first powers, in other words we may make the a;'s linear functions of the e's. Let I's be deviations of x's from mean values, and Tj's „ „ „ e's „ Then = anVi + ch2V2 + ... + a^rnVm] ^2 = 0^21''71 + Cf22^2 + ... + a^inVm ,.. nm ''7m / By hypothesis, the 77's are independent and follow the Gaussian distribution. Hence the chance of a complex of variables lying between Vi, Vi + = Ci X e ^'^'dvi, the chance of a complex of variables lying between the chance of a complex of variables lying between Vm, Vm + ^V7n = C,n X 6 2«m dT}r. Whole chance = product of these. We can now eliminate one of the ?7,'s in the following manner. Let us solve the n equations (i), finding the value of Vi,V2'--Vn in terms of ^1 — (hn+iVn+i — 0,in+2Vn+2 ... — ai^Vm, ^3 — 0,m+iVn+i - a2,i+2'»7n+2 — ... - Cl2m'7?>i, ?n - a »in+i'7«H-i ~ 0.)in+2''7n+2 — ... — anmVi