Unless the individuals concerned are very elaborately tested on several days, the correlations obtained are "attenuated" toward 0 by the "accidental" errors in the original measurements. This effect was not known until 1904; consequently the correlations in the earlier studies of arithmetic are all too low.
In general, the correlation between ability in any one important feature of computation and ability in any other important feature of computation is high. If we make enough tests to measure each individual exactly in:—
(A) Subtraction with integers and decimals,
(B) Multiplication with integers and decimals,
(C) Division with integers and decimals,
(D) Multiplication and division with common fractions, and
(E) Computing with percents,
we shall probably find the intercorrelations for a thousand 14-year-olds to be near .90. Addition of integers (F) will, however, correlate less closely with any of the above, being apparently dependent on simpler and more isolated abilities.
The correlation between problem-solving (G) and computation will be very much less, probably not over .60.
It should be noted that even when the correlation is as high as .90, there will be some individuals very high in one ability and very low in the other. Such disparities are to some extent, as Courtis ['13, pp. 67-75] and Cobb ['17] have argued, due to inborn characteristics of the individual in question which predispose him to very special sorts of strength and weakness. They are often due, however, to defects in his learning whereby he has acquired more ability than he needs in one line of work or has failed to acquire some needed ability which was well within his capacity.