The formation of a table of correlations on paper ruled in squares, is
easily explained on the blackboard (Fig. 9). The pairs of correlated
values _A_ and _B_ have to be expressed in units of their respective
variabilities. They are then sorted into the squares of the
paper,—vertically according to the magnitudes of _A_, horizontally
according to those of _B_—, and the Mean of each partial array of _B_
values, corresponding to each grade of _A_, has to be determined. It is
found theoretically that where variability is normal, the Means of _B_
lie practically in a straight line on the face of the Table, and
observation shows they do so in most other cases. It follows that the
average deviation of a _B_ value bears a constant ratio to the deviation
of the corresponding _A_ value. This ratio is called the ‘Index of
Correlation,’ and is expressed by a single figure. For example: if the
thigh-bone of many persons deviate ‘very much’ from the usual length of
the thigh-bones of their race, the average of the lengths of the
corresponding arm-bones will differ ‘much,’ but not ‘very much,’ from
the usual length of arm-bones, and the ratio between this ‘very much’
and ‘much’ is constant and in the same direction, whatever be the
numerical value attached to the word ‘very much.’ Lastly, the
trustworthiness of the Index of Correlation, when applied to individual
cases, is readily calculable. When the closeness of correlation is
absolute, it is expressed by the number 1·0; and by 0·0, when the
correlation is nil.
(New words and ideas—Correlation and Index of Correlation.)
This concludes what I have to say on these suggested Object lessons. It
will have been tedious to follow in its necessarily much compressed
form,—but will serve, I trust, to convey its main purpose of showing
that a very brief course of lessons, copiously illustrated by diagrams
and objects to handle, would give an acceptable introduction to the
newer methods employed in Biometry and in Eugenics. Further, that when
read leisurely by experts in its printed form, it would give them
sufficient guidance for elaborating details.
INFLUENCE OF COLLECTIVE TRUTHS UPON INDIVIDUAL CONDUCT.
Public-domain text, read in full here on John Shaqi.
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