The abilities of man : their nature and measurement / [Charles Edward Spearman].

  • Charles Spearman
Date:
1927
Catalogue details

Licence: In copyright

Credit: The abilities of man : their nature and measurement / [Charles Edward Spearman]. Source: Wellcome Collection.

    442/472 (page 428)
    In order to exemplify these formulas for the p.e., let us take the following table of Bonser : * 1 2 3 4 5 1. Mathematical judgment - — •485 •400 •397 •295 2. Controlled association •485 — •397 •397 •247 3. Literary interpretation - •400 •397 — •335 •275 4. Selective judgment •397 •397 •335 — •195 5. Spelling - •295 •247 •275 •195 — Now, a tetrad consists of any four correlations which in such a table form a rectangle. The following are three examples : 12 25 3 4 3. -400 -397 1. -485 -295 2. -397 -397 4- -397 '397 3- ‘397 *275 5- '275 ^95 Each such tetrad supplies a tetrad difference, that is, the differ- ence between the product of the top left value with the bottom right value and the product of the top right with bottom left value. In the above cases they are respectively : •400 x -379 ~ -397 x -397 = -ooi, •485 x -275 ~ -295 x -397 = -028 and -397 x -195 ~ -397 x -275 = -032. The total number of different tetrad differences for n different variables is 3MC4 ; and this for our table, comes to 15, since n, the number of variables, =5. Let us first consider the case of a single tetrad difference taken alone, so that we employ the formula (16). This, with the left of the three examples given above, yields the following values : y = (-400 + -397 + -397 + -397)/4 = ’398, S2 = (-0222 + -ooi2 + -ooi2 + -OOI2)/4, which is negligibly small, N=757- Putting these values into (16), there ensues, p.e. = -012. Next we will take an example of calculating the p.e. collec- tively for a whole table of correlations, and therefore using the formula (i6a). In the table given above, the mean (i.e. r) is •342 ; the mean squared deviation (i.e. s2) is -007 ; whilst n is 5. Hence R — 3 x -342 x ^ - 2 x *3422 x — = -264, so that p.e. =——v f-3422 x -6582 + (1 - -227) x -007]^ 757' = -oir, or much the same as before.