Influence of mild selection on a and r—Rigorous selection and partial correlation— Three correlated variables represented by dice throws—Multiple correlation— Spurious correlation—Variate difference correlation method.

THE INFLUENCE OF MILD SELECTION

THE essential point about the whole theory of correlation is that it tells us how a group of individuals selected from the general population according to some characteristic (say as being within certain limits of height, or possessing some mental ability or manual dexterity in a high degree) will also differ from the general population in other characteristics.

The ordinary correlation coefficient already tells us much in this respect. For example, if the correlation between two abilities, say (1) the ability, whatever it may be, which is measured by Dr McDougall's Dotting Machine and (2) the ability to memorise Nonsense Syllables according to certain experimental regulations, be known to be •4 for the whole population, this means that if a group be selected with “Dotting” ability equal to x (measured from the general mean in a units) then this group will most probably have an average “Nonsense Syllable” ability equal to 4 x; (measured in a similar way).

Clearly in practice we do not usually know the means and the correlation for the whole population but only for samples. We take large samples and endeavour to ensure that they are random and not selected samples from the population we wish to investigate.

The selection contemplated in the above example is very rigorous: all the individuals are presumed alike in regard to “Dotting” ability. In practice such a rigorous selection never takes place. The boys in a school form, for instance, are more alike in say ability in Latin than the general population, yet not absolutely alike. The “scatter” of this variate (Latin) has been reduced, yet not to zero.

Just as selecting a group of individuals for one variate will alter the average value of other variates, so it will alter the scatter of these other variates, and their intercorrelations. It is this phenomenon which in an extreme form gives us what we already know as “partial correlation” (see p. 105).

In fact, selecting a group of individuals within certain limits of a quality A implies an indirect and less rigorous but frequently very important selection of the other qualities B, C,… of these individuals and of their intercorrelations.