Abstract
So far I have argued that differences in income, and in economic and social advantages generally, cannot form the sole or even the main cause of the observable differences in mental ability. Is it, then, reasonable to conjecture that these differences in innate mental ability may after all form the main cause, though not perhaps the only cause, of the wide differences in income or earnings? If that were so, the first and most obvious consequence would be that the distribution of individual ability would resemble the distribution of private incomes.
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References
Distribution of Educational Abilities (1917), pp. 34 f. and Fig. 6; Mental and Scholastic Tests (1921), p. 162 and Fig. 24. My conclusion in these and other crises was that the distributions were “only approximately normal”: on applying the recognised statistical test for ‘goodness of fit,’ the departure from normality proved to be significant in every instance (P always less than 01). Dearborn (Intelligence Tests, 1928) reproduces for comparison curves from various investigations in America: “In all,” he says, “the distribution is symmetrical and continuous” (and, one might add, approximately normal); “practically the same range and distribution of individual differences in intelligence which were found by Burt in the schools of London are found in the schools of Boston” (p. 85; cf. pp. 150 et seq.). In a paper on ‘The Mental Differences between Individuals’ (Brit. Ass. Ann. Rep., 1923, p. 229), Fig. 1, I later gave results for 8,599 adults. Here the conclusion was the same—approximate normality only. (I may add that data from intelligence tests now being applied in the Army seem in complete conformity with these earlier inferences.) More recently, however, Thorndike has applied the same test of significance to pooled distributions for the sixth, ninth, and twelfth grades in American schools and for freshmen at American colleges: he obtains, in every case, P=9999 or more (Measurement of Intelligence, 1927, pp. 521–56; cf. pp. 271–87). Here, however, it seems important to recall the criticisms passed by Fisher and others on such high values for P: “extremely close agreement throws as much suspicion on the hypothesis or the technique as extreme disagreement” (cf. Statistical Methods, p. 83).
These figures are based on the latest accessible returns. For earlier years, and for a discussion of the sources of information, see Colin Clark, National Income and Outlay (1937), p. 109 et seq., and refs.
Economics of Welfare, 1924, pp. 608–9. Pigou and Hugh Dalton (The Inequality of Incomes, 1920, p. 128) both insist that “the facts of bequest and inheritance of property” must tend to skew the curve of income still further. The same objection was urged against Pareto’s claim (that the ‘law’ of income-distribution is the direct result of a ‘biological fact’) by Benini (Principii di Statistica Metodologia, 1906, pp. 310 et seq.). However, it now seems generally agreed that, although the inheritance of property must unquestionably magnify the pre-existing asymmetry in the income-curve, it cannot account for that asymmetry entirely, or even to any large extent.
Capitalism the Creator (1940), chaps, xiv. and xv.
The Analysis of Economic Time Series (1941), p. 427.
Cours d’economie politique (1897), II, pp. 299–345. Both Bowley and Stamp have shown that (with certain reservations) the law is applicable to British incomes. Lord Stamp fitted Pareto’s formula to the early returns of the British super-tax; and, on the strength of the discrepancies, informed the Inland Revenue authorities that they must have missed over 1,000 payers in certain classes. He adds: “They promptly went and found them !” (Wealth and Taxable Capacity, p. 83.)
Most observers, however, seem now agreed that, instead of remaining relatively constant, it has (during the past half century at any rate) shown a discernible tendency to decline: cf. A. L. Bowley, ap. Select Committee on Income Tax, 1906; Evidence, p. 81.
For the fitting of such a type, see Elderton, Frequency Curves, p. 110. Elderton, curiousty enough, remarks that he has “not come across a distribution really represented by Type XI.”
J. Soc. Psych., V (1934), pp. 141 et seq. What about those who do not conform, or who fail in the examination, or have incomes below the mode ? These have to be treated as rare except jns beyond the pale of the J-law: in the same way the initial rise of pressure in experiment on Boyle’s law, and the extreme cases in experiments on Weber’s law, used to be treated as exceptions to the theoretical curve, not as part of it. It would seem better, however, to meet the difficulty by regarding the Pareto equation as a first approximation to a Type V or VI formula: an instructive modification of this kind has indeed been proposed by one of his Italian followers (Amoroso, ‘Ricerche intorno alla curva dei redditi,’ Ann. di Matern. II, 1925, pp. 123–60). The psychologist would probably think first of rescaling the base line by taking a logarithmic function of income, and then using the ordinary formula for the normal distribution; and, in point of fact, except for the highest incomes of all, this device has been claimed to give a very plausible fit (Gibrat, Les inégalitiés économiques, 1931): but the fit is a poor one for British incomes.
Other parallels are the law relating rate of working and resistance in an electrical conductor circuit, and the laws of friction in mechanical processes. At the Ministry oi Munitions, during the last war, I found that the ‘output’ of the heavier howitzers (number of rounds fired during its life) and the ‘output’ of accidents among munition workers both gave frequency-distributions conforming approximately to the formula just cited.
Miss Harwood has recently analysed the marks of many groups of candidates sitting for two or three typical university academic examinations over a period of years; and finds that, even when no instructions are given the examiners about the allotment of such marks, they nevertheless show an approximately normal distribution, i.e., the prior attempt to admit only suitable candidates on entrance has not skewed the distribution so much as might be supposed.
I may add that Miss Stevenson has recently analysed a number of output-curves in this way; and further confirmed this result.
This would seem to be Pareto’s own explanation. In his later work he writes: “au-dessus de la moyenne il n’y a pas de limite de hauteur; il y a une limite au-dessous”; and he claims that this is so both for income and for ability, as measured, for example, at ordinary scholastic examinations (Manuel, 1927, p. 385).
Principles of Economics, p. 213. Cf. Pigou, loc. cit., p. 707: “Stupidly organised investments in children’s capacities, like other stupidly organised investments, will yield little return: well-organised investments, especially investments adjusted to the natural abilities of the children affected, hold out large promise.”
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© 1973 H. J. Eysenck
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Burt, C. (1973). Ability and Income. In: The Measurement of Intelligence. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-6129-9_26
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