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.

    452/474 page 438
    The simplest and best plan is to make the standard deviation everywhere equal to unity. To do this, first make the standard deviation of each single test equal to unity ; so far, there is no difficulty. Then, by known formula, the mean square deviation of the team of test will be S(w2) +2 SS(wu . wv . ruv). Replacing, now, each wu by rug/(i - rig) in accordance with (29), the preceding mean square deviation reduces with a little arith¬ metic to Z2 + S, where Z denotes S(wu). Hence, finally, denoting the team measurement by tx, we get 4 = S[mux . rj(z -1^) ]-9 (Z2 + S)4 = Gi-(Z2 + S)4. (31) 8. An example of the calculation.—For the Bonser table, we have already found r2g in iv. 2. We can similarly get rXgy r3g, r±g and r5g. Thereupon we can fill up the following scheme, which will supply all the values here required: Test. Vug Wu — y /(1 - r2 ) ug1' ug' W u • y ug Scores (imaginary) of the indi¬ vidual #. Scores x wu I 701 1*401 .984 + 1*3 + 1*822 2 •672 1*224 •823 + *9 + 11*02 3 •607 •952 •578 + 1*2 + I-I4I 4 •55o 789 *437 + i‘5 + I*l82 5 •398 •471 *l88 - *i - -047 Z =4-837 S =3*010 Gx= +5*2oo From these, rtg = 1/(1 - I/S)4 = l/(l - i/3-oio)4 = 749, ix = GxliZ2 + s)is =5-200/(4-8372 + 3-OIO)4 = i-oii. The preceding method is not theoretically inconsistent, of course, with weighting according to Yule’s well-known regression for multiple correlations. But our tetrad equation has permitted a much simpler and more illuminative method of calculation, and also one far less vitiated by the effect of sampling errors, than are the regression equations as customarily used in psychology.
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