# Gini, Corrado

# Gini, Corrado

The work of Corrado Gini (1884–1965) has had a profound impact on many fields within the social sciences. The son of a manufacturer, Gini was born in Motta di Livenza, Treviso Province. He studied law at the University of Bologna, where he also took courses in mathematics. The broad scope of his scholarly contributions is reflected in the variety of subjects he taught, successively, at the universities of Cagliari, Padua, and Rome: statistics, political economy, demography, biometrics, constitutional law, and sociology.

Gini also furthered the development of social science in other than academic capacities. From 1926 to 1932 he was chairman of the Central In stitute of Statistics. He directed several scientific expeditions to study the demographic, anthropometric, and medical characteristics of particular ethnic groups in Fezzan, Palestine, Mexico, Poland and Lithuania, Calabria, and Sardinia, as well as the processes of assimilation of immigrant groups generally. He was the founder and editor of the international journal of statistics *Metron*, in 1920, and of the journal *Genus*, the organ of the Italian Committee for the Study of Population Problems.

In recognition of his achievements he was awarded honorary doctorates, one in economic science—from the Catholic University in Milan, in 1932—and another in sociology—from the Uni versity of Geneva, in 1934; and he was awarded an honorary doctor of science degree by Harvard at the 1936 tercentenary celebration of that university.

The main currents of thought in Italian culture at the time that Gini began his scientific activity were positivism and idealism. Gini’s commitment to positivism was limited. His works manifest a remarkable eclecticism, arising from his systematic study of a variety of disciplines: law, economics, statistics, mathematics, and biology. He always placed the phenomena he was studying in a more general context, bringing essential social, economic, and demographic elements to bear on the topic of his immediate concern.

Gini thoroughly understood the importance of descriptive statistics, as is shown by his particular admiration for Luigi Bodio among Italian statisticians, but at the same time he deeply felt the need to study the procedures of inferential statistics and to find suitable criteria for evaluating those procedures. To this end he studied the works of Bernoulli, Lexis, and Czuber, as well as those of the Italians Angelo Messedaglia and Rodolfo Benini.

**Contributions to statistical method** . Gini’s first scientific works deal with the statistical regularity of rare events. To the same period—1908 to 1911 —belongs his initial work on the concept and measurement of probability, with special attention and application to the human sex ratio at birth. His findings were contained in a book (1908) in which he presented analyses of extensive empirical materials on sex ratios from different countries. In the same work, he developed a theory of dispersion, that is, of the quantitative structure of the scatter or variability among measured quantities of the same kind. He later returned to the topic of dispersion (1940; 1941).

Gini made a lengthy critique of the principles of statistics in order to reinforce the logical basis of statistics and to rid it of naive empiricism. He wished to raise statistics to the level of an independent science, one of whose tasks would be the systematic investigation of the advantages and limitations of various indexes, or descriptive statistics, under differing structures of error.

In an address entitled “I pericoli della statistica” (1939; “The Dangers of Statistics“), inaugurating the first meeting of the Societa Italiana di Statistica, Gini warned statisticians about the faulty logical foundations of some statistical methods and stressed the importance of estimating meaningful parameters. He published further papers on this general subject (1943; 1947). In the latter paper, “Statistical Relations and Their Inversions,” he pointed out that poor statistical notation may lead to misunderstanding and error. For example, if one writes *y* = 3 + 7*x*, as a mathematical relationship between the real variables *x* and *y*, one may just as well write *x* =−3/7+1/7_{y} this is called invertibility. On the other hand, in a statistical context of regression, one may loosely write *y* = 3 +7*x*, meaning that the expectation (or average) of a random variable *Y* is thus linearly related to possible values of another random variable *X*. For clarity, one should use a more complete notation like the now conventional

*E* (*Y*|*X* = *x*) = 3 + 7*x*,

and, in general, *E* (*X*|*Y*=*y*) ≠ −3/7+1/7_{y}. On the other hand, taking complete averages, *EY* = 3 + 7*EX*; this situation is called one of subinvertibility.

In a paper written in collaboration with Luigi Galvani, “Di talune estensioni dei concetti di media ai caratteri qualitativi” (1929; “Extension of Mean Value Theory to Qualitative Characteristics”), Gini made an original contribution in another area. The problem here was to find a meaningful analogue of the usual arithmetic mean for a purely qualitative or nominal distribution. By defining a measure of deviation between any two classes of the qualitative classification and by a minimization argument, Gini showed how to choose one of the classes of the clas sification as a kind of mean.

The theory of generalized means was of continuing interest to Gini, and he was particularly concerned with its very general expression and with a wide variety of mean values (1938). In another article, again with Galvani, he discussed extensively the topic of location parameters for bivariate distributions, noting especially geographical problems (see Gini et al. 1933).

Next to generalized means, measures of variability are of great importance, and Gini discussed these at length, giving special attention to descriptive statistics not intrinsically tied to the normal distribution (1912). He introduced a new measure of variability, the *mean difference,* which is essentially the expected absolute value of X_{1} − X_{2}, where *X*_{1} and *X*_{2} are independent random variables with the same distribution of interest. (Gini thought primarily in terms of the sample version of the mean difference.)

Gini also worked on measures of variability for qualitative or nominal distributions and on measures of variability that are tied to the concentration curve and are considered important in the economic analysis of income and wealth (1921).

**Nontypicality of typical census areas** . Gini set himself the task of selecting a sample of typical census areas in Italy. To this end, he showed that it is not adequate simply to select the sample in such a way that the averages of various characteristics calculated for the sample are equal to those calculated for the entire territory of Italy. Even when the examination is confined to only the characteristics used in selecting the sample, the sample proves to be unrepresentative with respect to the variability and concentration of those characteristics and to the relations existing between them. Accordingly, Gini included in the criteria of representativeness these last two aspects of the distributions of characteristics, and he examined the conditions to which each of the proposed criteria subjects the other criteria.

**Theory of price indexes** . To the theory of price indexes, which is of great importance in economic statistics, Gini contributed a classic paper, “Quelques considérations au sujet des nombres indices des prix et des questions analogues” (1924), in which he solved some logical and technical problems connected with elimination methods.

Distinguishing between simple and complex indices, Gini showed how, in general, the methods for obtaining complex indexes can be considered as particular cases of the method of elimination (which consists in separating the different circumstances affecting a phenomenon in order to make comparisons *ceteris paribus* with similar phenom ena at different times or places). The problem was to keep the phenomenon of “price variation” distinct from the phenomenon of “quantity variation.”

Operating with the general method of the “typical population” organized into four special methods, Gini obtained various formulas for index numbers, at the same time providing criteria for choosing that one of the formulas best suited to the aims of particular problems. (Another of his papers on the same topic is “Methods of Eliminating the Influence of Several Groups of Factors,” 1937).

**Theory of distributions** . Gini made substantial contributions to the study of relationships between two probability distributions and between two random variables with a joint distribution. Particularly important are the following:

(*a*) *Transvariation*. Suppose that one considers two probability distributions, represented for convenience by (independent) random variables *X*, *Y*. Suppose further that *EX <* EY; it may still be quite probable that *X >Y*, that is, the difference between the observations *X* and *Y* may show a different sign than the corresponding difference between expected values. Gini proposed a specific measure for this phenomenon, which he called transvariation (1953; 1959a; see also Kruskal 1957).

(*b*)*Distance between two distributions.* Gini was one of the first to consider the problem of measuring meaningfully how much two probability distributions differ in gross (1914a). He proposed a measure of distance, based on the two cumulative distribution functions, that was in fact a metric in the technical mathematical sense (see Fréchet 1947).

(*c*)*Association between two random variables with a joint distribution.* Gini made the basic distinction between *connection* (any kind of statistical dependence) and *concordance* (dependence in which it makes sense to speak of one variable tending to increase—or decrease—along with the other). The correlation ratio, for example, is a measure of connection, while the coefficient of correlation is a measure of concordance. Gini analyzed previously suggested measures of association and proposed new ones both for the case of numerical variates and for that of qualitative variates (see Goodman & Kruskal 1959, which contains relevant references to Gini, Weida, and Pietra).

**Demography and biometrics** . Gini pioneered in studies that relate demographic phenomena to social and biological phenomena. Thus, he studied the sources of differential fertility (1949), and he related the phenomenon of migration to broader social and demographic considerations (1946*b*).

Gini also proposed a unified research program for analyzing the eugenic and dysgenic effects of war, with special emphasis on the measurement of the effects of war on mortality (1915–1920). Also related to demographic phenomena are Gini’s studies of various populations in phases of expansion, regression, and extinction (1934).

**Economic and sociological research** . From the earliest years of his career, Gini tackled the difficult problem of estimating national wealth. He made a constructive criticism of the method of the interval of devolution and the first calculation by a direct method of the private wealth of Italy (1914*b*). He followed a methodological organization of the data with a comparative study of the qualitative composition of wealth, clarifying the conditions that make nations wealthy (1959*b*).

Gini originated the idea of including the value of human capital in the calculation of wealth [*see*Capital, human]. This makes it possible to indicate the preponderant cause for the incommensu rability in time and territory of the wealth and economic well-being of various collectivities (1956*a*). The value-as-property of the man who labors becomes a factor in estimating wealth, just as the share derived from human labor is included in income (1914*a*). This conception clearly links economic considerations with sociological and demographic ones.

Related to Gini’s conception of human capital is his cyclical theory of population. Observing the differential rates of reproduction of social classes, Gini formulated a theory of social metabolism that is based on an analogy to organic metabolism: the upper classes, having low rates of reproduction, will tend to extinction unless they get new members from the lower classes, which have higher rates of reproduction (1927). Gini intended this theory to replace Pareto’s concept of the circulation of elites.

Gini also developed a theory of phases of population growth, these being related to social and economic phenomena (1923). According to his theory, a particular population grows rapidly in the first phase of its development, then has a diminishing rate of growth until it is approximately stationary, and finally begins a decline that may even lead to total extinction. In the first phase, capital is very scarce and there is little differentiation between social classes; later, as capital is accumulated, classes become increasingly differentiated, and there is a concomitant differentiation of reproductive behavior. As birth control spreads, a deterioration in the quality of the population can be avoided only by the influence of external factors, such as the immigration of young people from populations in the phase of demographic expansion.

Gini’s neo-organicist approach makes it possible to distinguish normal economic processes from pathological ones—those in which the state of a society is unbalanced—and to initiate economic processes of restoration. In general, he believed that states of imbalance could be remedied by the regulatory activities of political agencies and of economic organizations.

In Gini’s view, an important aspect of the development of society is the transition from forced to free labor and then to spontaneous labor (1956b). This last represents the final stage in a psychological process that raises labor from a primordial means of obtaining a living to a free and autonomous activity that enriches the human person ality.

Gini’s pre-eminent place in the development of Italian statistics is based on a dual contribution: his work in scientific statistics, which included important teaching and editorial activities; and his efforts toward the development of official statistics, notably, the consolidation in a single institute of all the various agencies for the collection of data and the extension of the number of items about which data are collected.

Tommaso Salvemini

[*Directly related are the entries*Sample Surveys; Statistics, Descriptive; Variances, Statistical Study of. *Other relevant material may be found in*Census; Genetics; Income Distribution, *article on*Size; Index Numbers; Migration; Population; *and in the biographies of*Benini; Bernoulli Family; Lexis; Pareto.]

## WORKS BY GINI

1908 *Il sesso dal punto di vista statistico: he leggi della produzione dei sessi.* Milan: Sandron.

(1912) 1955 *Memorie di metodologia statistica.* Volume 1: Variabilltà e concentrazione. 2d ed. Rome: Veschi.

1914*a Di una misura della dissomiglianza fra due gruppi di quantità e delle sue applicazioni allo studio delle relazioni statistiche.* Venice: Ferrari.

(1914*b*) 1962 *L’ammontare e la composizione della ricchezza della nazioni.* 2d ed. Turin: Bocca.

(1915–1920) 1921 *Problemi sociologici della guerra*. Bologna: Zanichelli. → A collection of previously published articles.

1921 Measurement of Inequality of Incomes. *Economic Journal* 31:124–126.

(1923) 1952 *Patologia economica.* 5th ed., rev. & enl. Turin: Unione Tipografico-Editrice Torinese.

1924 Quelques considérations au sujet de la construction des nombres indices des prix et des questions ana logues. *Metron* 4:3–162.

1927 *II neo-organicismo: Prolusione al corso di sociologia*. Catania: Studio Editoriale Moderno.

1929 Gini, Corrado; and Galvani, Luigi Di talune estensioni dei concetti di media ai caratteri qualitativi. *Metron* 8, no. 1/2:3–209.

1933 Gini, Corrado; Berardinis, L. de; and Galvani, L. Sulla selettività delle cause di morte durante l’infanzia. *Metron* 11, no. 1:163–183.

1934 Ricerche sulla popolazione. *Scientia* 55:357–373.

1937 Methods of Eliminating the Influence of Several Groups of Factors. *Econometrica* 5:56–73.

1938 Di una formula comprensiva delle medie. *Metron* 13:3–22.

1939 I pericoli della statistica. *Rivista di politica economica* 29:901–924.

1940 Sur la théorie de la dispersion et sur la vérification et l’utilisation des schémas théoriques. *Metron* 14:3–29.

1941 Alle basi del metodo statistico: II principio della compensazione degli errori accidentali e la legge dei grandi numeri. *Metron* 14:173–240.

1943 I testi di significatività. Società Italiana di Statistica, *Atti* [1943]:241–279.

1946a Actualidades demográficas. *Revista international de sociologia* 4:147–169.

1946*b* Los efectos demográficos de las migraciones internacionales. *Revista international de sociologia* 4:351–388.

1947 Statistical Relations and Their Inversions. International Statistical Institute, *Revue de I’Institut International de Statistique* 15:24–42.

1948 Evoluzione della psicologia del lavoro e della accumulazione. Banca Nazionale del Lavoro, *Moneta e credito* Whole No. 2.

1949 Vecchie e nuove osservazioni sulle cause della natalità differenziale e sulla misura della fecondità naturale delle coniugate. *Metron* 15:207–358.

1950 Metodologia statistica: La misura dei fenomeni collettivi. Volume 3, part 2, pages 245-321 in *Enciclopedia delle matematiche elementari.* Milan: Hoepli.

1951 Caractére des plus récents développements de la méthodologie statistique. *Statistica* 11:3–11.

1952 On Some Symbols That May Be Usefully Employed in Statistics. International Statistical Institute, *Bulletin* 33, no. 2:249–282.

1953 The Measurement of the Differences Between Two Quantity Groups and in Particular Between the Characteristics of Two Populations. *Acta genetica et statistica medica* 4:175–191.

1955 Sur quelques questions fondamentales de statistique. Paris, Université, Institut Henri Poincaré, *Annales* 14:245–364.

1956*a* Valutazione del lavoro e del capitale nell’ *Economia lavorista. Rivista bancaria* New Series 12:522–530.

1956*b Economia lavorista: Problemi del lavoro.* Turin: Tipografia Sociale Torinese.

(1956*c*) 1966 *Statistical Methods.* Rome: Biblioteca del Metron. → Lectures delivered at the International Center for Training in Agricultural Economics and Statistics, Rome.

1958 Logic in Statistics. *Metron* 19, no. 1/2:1–77.

1959*a Transvariazione.* Rome: Libreria Goliardica.

1959*b Ricchezza e reddito.* Turin: Unione Tipografico-Editrice Torinese.

1959*c* Mathematics in Statistics. *Metron* 19, no. 3/4:1–9.

## SUPPLEMENTARY BIBLIOGRAPHY

Castellano, Vittorio 1965 Corrado Gini: A Memoir With the Complete Bibliography of His Works. *Metron* 24; no. 1–4.

Frechet, Maurice 1947 Anciens et nouveaux indices de corrélation: Leur application au calcul des retards économiques. *Econometrica* 15:1-30, 374–375.

FrÉchet, Maurice 1947-1948 Le coefficient de con nexion statistique de Gini-Salvemini. *Mathematica* 23:46–51.

FrÉchet, Maurice 1957 Sur la distance de deux lois de probabilité. Paris, Université, Institut de Statistique, *Publications* 6:183–198.

Galvani, Luigi 1947 À propos de la communication de M. Thionet: “L’école moderne de statisticiens italiens.” Société de Statistique de Paris, *Journal* 88:196–203. → A bitter attack on the 1945-1946 article by Pierre Thionet. See pages 203-208 for Thionet’s reply to Galvani.

Goodman, Leo A.; and Kruskal, William H. 1959 Measures of Association for Cross-classifications: II. Further Discussion and References. *Journal of the American Statistical Association* 54:123–163.

Kruskal, William H. 1957 Historical Notes on the Wilcoxon Unpaired Two-sample Test. *Journal of the American Statistical Association* 52:356–360.

Neyman, Jerzy (1938)1952 *Lectures and Conferences on Mathematical Statistics and Probability.* 2d ed., rev. & enl. Washington: U.S. Department of Agri culture, Graduate School.

Salvemini, Tommaso 1943 La revisione critica di Gini ai fondamenti della metodologia statistica. *Statistica* 3:46–59.

Thionet, Pierre 1945-1946 L’école moderne de statisticiens italiens. Société de Statistique de Paris, *Journal* 86:245-255; 87:16–34.

#### More From encyclopedia.com

#### You Might Also Like

#### NEARBY TERMS

**Gini, Corrado**