Statistics

STATISTICS. - This term derives, most probably, from the Latin status, which means state, position, condition, manner of being. It was used for the first time in Italy, in 1589, by Ghilini, and, subsequently, by Achenvall and by others to indicate the science that describes and examines the most noteworthy things of the State.

Today the term s. is commonly used to indicate a collection of numbers concerning phenomena susceptible of enumeration and measurement, as, for example, s. of the clergy, s. of production, s. of pupils, etc., but in a scientific sense s. is considered as « a technique suited to the quantitative study of mass or collective phenomena, understanding by mass or collective phenomena those phenomena (physical, biological, social) whose measurement requires a mass or collection of observations of other, simpler phenomena called single or individual phenomena » (Gini).

In this sense s. serves for the study of reality - of the natural world and of the social world - in its phenomenal aspects, understood not as single cases or facts, but as a set of cases or facts susceptible of observation. It helps to discover relations, regularities, laws, which are difficult to deduce on the basis of single or few observations.

To s. in the scientific sense mentioned, one usually gives the attribute of methodological in order to distinguish it from applied s., which studies concrete collective phenomena, with the procedures indicated by methodological s. Such a distinction has simply the value of a practical partition (as, for example, between theoretical physics and experimental physics) for the purpose of allowing an autonomous development of theoretical schemes, on the one hand, and a deeper investigation of specific phenomena, on the other.

I. HISTORICAL NOTES

Ancient documents show that ever since the formation of the first human societies, the system was used of enumerating both the elements of which those societies were composed (families, individuals, men fit for arms, etc.) and the goods they possessed (livestock, products of the hunt, etc.).

The Church herself feels the need for surveys, for her spiritual ends, and institutes, one might almost say from her origin, the registration of births and deaths. Indeed the Council of Trent (sess. XXIV, de reform., c. 1) expressly obliges parish priests to keep up to date the registers relating to births, deaths and marriages, and it is precisely to these sources that recourse is generally had today in studying the demographic conditions of past centuries (v. LIBRI PARROCCHIALI).

Enumerations were evidently at the basis of inquiries of an administrative and political character. But toward the middle of the 17th century, the description of the notable things of the State assumed an organic arrangement in studies having an autonomous interest. The scientific s. then had its origin. Vito di Seckendorff (1626-92), Hermann Conring (1600-81), Gottfried Achenwall (1719-72) may be considered the representatives of the so-called German university Statistics. At the same time in England there developed the approach known as that of the Political Arithmeticians who, from numerical data, tended to derive the empirical laws that regulate social phenomena. This approach therefore had an investigative character, contrary to the German one which had a descriptive character. The best-known representatives of this school are John Graunt (1620-74) and William Petty (1623-87) for phenomena regarding the population, Gregory King (1648-1712) and Charles Davenant (1656-1714) for economic phenomena, and the astronomer Edmond Halley (1656-1742) for the branch that today is called actuarial, having constructed a mortality table of the inhabitants of Breslau. A particularly important development in the following years was had by the s. of the population, and it may be said that it reached maturity with the work of Johann Peter Süssmilch (1707-67): L'ordine divino nelle mutazioni del genere umano. This A. attributes to the divine order the fact that births exceed deaths and that the ratio of the sexes is almost constant (amounting, in every time and place, according to subsequent studies, to around 105 or 106 males for every 100 females). Already three or four centuries earlier, however, as Villani relates in his chronicles, this phenomenon of the higher male birth rate had been observed and recorded in the baptistery of S. Giovanni in Florence by making a systematic count of the baptized.

To the approach of the English school is connected the encyclopedic-mathematical one, developed particularly in France, through the work of distinguished mathematicians such as B. Pascal (1623-62), J. Bernoulli (1654-1795), A. De Moivre (1667-1754), P. S. Laplace (1749-1827) etc., who svi-

by developing the calculus of probabilities, they provided statistics with a powerful means of investigation. A very important impulse was then given by the Belgian Adolphe Quetelet (1796-1874). He laid the foundations of modern statistical methodology and, making use of it, considerably deepened studies on population, on crimes, on suicides, on the physical development of man, etc. After him many continued in the perfecting and the broadening of statistical methodology; among the best known in Italy, Pareto, Benini, and Gini are remembered.

II. THE COLLECTION OF DATA

The starting point of statistical observation is represented by the collection of data. It consists in that set of operations by which one becomes aware of a collective phenomenon. The accuracy of the deductions to be drawn will depend on the technique used and on the care taken in carrying out the operations necessary for this, and it is for this reason that the collection of data constitutes the most delicate moment of statistical observation.

In many investigations one starts from material already collected, for example, by the State (by means of its statistical offices) or by public or private bodies, but even when one uses the data of collections already made, it is advisable to have some notion of how those figures were arrived at.

In the collection of data four phases can be distinguished:

1. Determination of the collection plan

In determining the collection plan it is necessary to define precisely the object and the statistical unit of collection. This may be simple (an individual, a commodity of a given quality, a particular category of livestock, etc.) or composite (a family, as an aggregate of persons bound by particular ties; an almond grove, as an aggregate of plants of the same type, etc.), or complex, as in the case of economic censuses in which one has to deal with firms in which units of various kinds appear. In relation to the limits of time and means available for the collection, it may be complete or partial, according to whether or not it includes all the units of the field to which the investigation is meant to refer.

The set of statistical units considered in a partial collection is said to constitute a sample. The criterion for choosing the units constituting the sample is of great importance for the accuracy or representativeness of the statistical information derived from it. It is clear in fact that the implicit purpose in studying the sample is that of obtaining information as accurate as possible (with a given margin of uncertainty) about the mass of cases or universe, according to the Anglo-Saxon denomination, from which the sample is drawn.

2. Assumption or gathering of the data

In the collection plan the procedures for gathering the data are also fixed. Usually questionnaires are used (for example, household schedules, in censuses) or forms or cards in which the information to be requested is set out in the form of a question. Such a system facilitates the gathering, the forwarding and the appropriate grouping of the units collected according to homogeneous characteristics. The records of civil status (births, marriages, deaths, migrations) are brought to the knowledge of the collector by means of declarations made obligatory by legal provisions. These collections are called automatic and, in general, are transcribed into registers, while the others are called reflected, as in the case of censuses (v. POPOLAZIONE).

3. Processing of the data

As regards the processing of the information reported on questionnaires, forms, registers, etc., one first proceeds to appropriate classifications so that for each characteristic (for example, sex, age, occupation) homogeneous groups are formed, and then, if the cases are not many, one proceeds either, as was once done, to a manual enumeration of the units of each group, or, when the number of statistical units is large, one uses processing by mechanical means. Without going into their operation, it is enough to say that they consist of a punch that makes it possible to transcribe conventionally the data of the form by means of holes distributed over columns, of a special card or standard card, and then of a selector or sorter that makes the punched cards pass over two levels, causing those that present one or more holes in determined positions (corresponding to a characteristic recorded) to fall into appropriate compartments. The results of the processing are reported on special tables, called statistical tables, of which numerous examples are to be found by looking, for example, at the statistical yearbooks published by individual States.

III. GRAPHICAL REPRESENTATIONS

The statistical data obtained from a survey can be rap-

(from Compendio Statistico Ital., Rome 1958, fig. 2)
STATISTICS. - Fig. 2. --- Secular clergy and religious; --- religious; --- total, in the four Italian geographical divisions, from 1881 to 1931; Figures per every 1000 inhabitants.

presented graphically for the purpose of obtaining lines or figures that allow an immediate and simple view of the trend of the phenomenon to which the data refer. Such representations also make it possible to see more quickly whether relations exist among several phenomena that it would have been difficult to discover from an examination of the many numbers concerning each phenomenon.

Two fundamental types of graphic representations can be distinguished: a) diagrams; b) cartograms.

The principle governing the construction of diagrams is that of making a geometric figure (e.g., a segment, a rectangle, an angle, a circle, etc.) correspond to a number.

Fig. 1 is a diagram with superimposed rectangles that indicates the size of the secular clergy, of male religious and of female religious in Italy, in the census years 1911, 1921 and 1931; observing this graph, one immediately discerns which category is the most numerous and which has had the greatest variations in the two decades considered.

A diagram on orthogonal Cartesian coordinates is that of fig. 2; it shows at a glance the different variations in the numerical size of the secular clergy, of male religious and of female religious in the four Italian geographical divisions, from 1881 to 1931.

Cartograms, on the other hand, have as their base the geographical outlines of an area (continent, nation, region, etc.) with the subdivisions of interest, and in each of these subdivisions the intensity of the phenomenon represented is indicated by the more or less marked tint (or hatching) inserted therein.

The cartogram of fig. 3 indicates the number of inhabitants per sq km of surface area in the Italian provinces.

If in each geographical zone one wishes to indicate the size of several modes, one can resort to the system of inserting in each zone a figure (formed of rectangles or of circular sectors, or of other designs) so that from its size a view of the size of the various modes of the phenomenon can be deduced.

In fig. 4 there is represented, for example, the number of pupils of each kind of Italian secondary school in the various regions.

IV. MEASURE OF THE INTENSITY OF A COLLECTIVE PHENOMENON

The data obtained from statistical surveying do not always lend themselves to giving a synthetic idea of the phenomenon or to allowing a comparison of that phenomenon with others. For example, the differing prices obtained, in the many Italian markets of a region, for the same quantity of goods do not lend themselves, as they stand, to making a synthetic comparison with the prices of other goods or to studying the variations that the price of that quality of goods undergoes over the course of time. It is therefore necessary to be able to synthesize all these raw figures into a single value that measures the intensity of the phenomenon: this is called the average value. Even our mind, in certain circumstances, summarizes various impressions into a more synthetic one: the mathematical method has the advantage of making this determination more objective. Only that one can proceed in different ways, each of which corresponds to specific requirements, obtaining different average values, with likewise different names, of which the main ones are: simple arithmetic mean, weighted arithmetic mean, simple and weighted geometric mean, harmonic mean, median, normal value or mode or prevailing value, power means, etc.

Once the average intensity of a collective phenomenon has been determined, it may be of practical and scientific interest to measure the variability, that is, the tendency that phenomena have to assume different modes. It is clear, in fact, that many times it is not enough to know the average wealth of the inhabitants of two regions, but it may be of interest to know the inequality existing among these inhabitants. In two countries A and B the average wealth may be identical, but it may happen that the distribution of this wealth among the inhabitants is very different in A and B. The same can be said for wages, for heights, etc., which in A may be almost equal among all persons, while in B they may differ greatly from individual to individual.

Statistics has elaborated appropriate measures that are called indices of variability. The main ones are: range of variation, mean simple deviation, mean square deviation, mean difference, concentration ratio. This last measure is very important in the field of economic and social field for comparing the different degree of inequality existing in the distribution of income, wealth, property, etc. of different regions.

V. STATISTICAL RATIOS AND RELATIONS

When a logical connection exists between two collective phenomena or between a collective phenomenon and a non-collective one (as, for example, between wealth and population, between legitimate births and married women, between population and territory, between deaths from a certain cause and deaths in general, etc.), a statistical ratio can be established between the intensities of the two phenomena, which is expressed, in general, as a percentage.

The principal ones are: ratio of composition or of part to whole, ratio of derivation, index ratio or index number, ratio of coexistence, ratio of duration, ratio of repetition. At times, however, it is of interest to see whether the modalities of one phenomenon are sensitive to the quantitative or qualitative manifestations of another phenomenon. For example, it is of interest to see whether the modalities of stature depend on the modalities of profession, whether the modalities of income are related to those of wealth, etc. The study of this aspect goes under the name of investigation of the relation between two phenomena (more precisely, between the modalities of two phenomena). It can be carried out from various points of view. For example, by comparing two distributions as a whole one can observe concomitance, transvariation, dissimilarity, asymmetry, abnormality, etc. By comparing individual modalities, on the other hand, one can measure the degree of connection or dependence, the degree of concordance or correlation, for which statistics has elaborated various appropriate indices.

Other important chapters of statistics are those concerning: the integration of data (elaborating methods to eliminate or correct gaps, errors, causes of non-representativeness of the data, etc.); the comparability of data (to eliminate the intrinsic and extrinsic causes that sometimes make direct comparisons between statistical data erroneous); finally the logic of statistics which, through a thorough examination of the various phases of scientific research and of the symptomatology of causes, arrives at the formulation of laws and at the prediction in the future of collective phenomena, this being the ultimate aim of statistics.

VI. APPLIED STATISTICS

The application of the statistical method to the study of particular classes of phenomena gives rise to separate disciplines such as demographic statistics or demography, biometry, anthropometry, physical statistics, economic statistics or economics, social statistics, which in turn comprises judicial statistics, moral statistics, health statistics, labor statistics, intellectual statistics, religious statistics, etc.

A brief account is given here of some of these branches, referring to the respective entries for demographic statistics or demography (v.), biometry (v.) and anthropometry.

1. Physical statistics

A decisive contribution has been made by statistics to modern physics, where it has enabled enormous progress unthinkable before its introduction into this science. The branches that have benefited most from it are the kinetic theory of gases, thermodynamics (v.), quantum theory (v.) and the theories on the nature of the structure of the atom.

2. Economic statistics or economics

It studies with the statistical method the phenomena of production, exchange and consumption. Accordingly, it provides for the collection and analysis of data concerning industrial, mining and agricultural production, wholesale and retail trade, both domestic and international, the prices of goods and services, family budgets, the cost of living, wages, the financial and banking market, rail, road, maritime and air traffic, income, wealth, etc., so as to have exact knowledge of the phenomena that originate from the activity that men carry out to satisfy their needs. Such phenomena are often related to demographic and social phenomena in order to illustrate the life and economic evolution of a country.

3. Social statistics

It studies various classes of phenomena connected with the social life of human groups. Some of these classes of phenomena tend to form subjects of separate discipline, and brief accounts of them are given: a) Judicial statistics. - Its object is the quantitative study both of the activity of state organs aimed at the restoration of a right violated by an unlawful act or disturbed by a dispute, and of the persons, matters and acts to which that activity refers (Spallanzani). It distinguishes: a) criminal judicial statistics (crimes against the person, against property, against morality, criminality, reformatories, etc.); b) civil judicial statistics (litigiousness, personal separations of spouses, notarial acts, etc.); c) commercial judicial statistics (bankruptcies, bill protests, etc.). b) Moral statistics. - It studies quantitatively those phenomena that relate to custom and morality in general. Such, for example, are alcoholism, prostitution, begging, etc.). c) Health statistics. - It comprises that complex of research connected with those morbid forms of a social character (tuberculosis and other infectious diseases, the mentally ill, etc.). Health and hospital care, centers for the diagnosis and treatment of malignant tumors, health services, etc. d) Labor statistics. - It studies those phenomena concerning the employment and unemployment of workers, the remuneration of labor, strikes and lockouts, internal migrations for the purpose of work, trade-union associations, etc. e) Intellectual statistics. - It concerns: a) the phenomena of the school field, such as enrollees, those examined, those promoted, graduates, degree-holders, teachers of every kind and order of schools; b) the activity of academies, libraries, picture galleries, archives, etc.; c) performances and radio; d) the press, copyrights, etc.

4. Religious statistics

It concerns the quantitative study of phenomena that are directly or indirectly connected with religion. Accordingly, it comprises on the one hand the phenomena deriving from the spiritual and social activity of the individual Churches, and, on the other, all those social phenomena, not properly religious, which are subject in varying measure to the influence of religion. The very different characteristics of these two groups of phenomena lead to a division of religious statistics into two parts: ecclesiastical statistics and confessional statistics.

5. Ecclesiastical statistics

Among the branches of social statistics it may be said that this was, until not long ago, the most neglected, above all for lack of documentary material. Certain proposals made by the Giunta centrale di statistica in 1872 and in 1879 to carry out an extensive survey: a) of the persons devoted to worship and of the population; b) of the things devoted to worship such as buildings, sacred furnishings, the property of ecclesiastical bodies, tithes, quests, oblations, etc.); c) of the acts pertaining to worship, were not implemented because it is evident that to survey phenomena pertaining to the life of the Church, to its exercise, to religious practices, an organ directly dependent on the Holy See is required.

An important flourishing of studies in ecclesiastical statistics occurred in Italy around 1940. The most important subjects on which studies are available concern: the numerical consistency of the secular clergy, of religious men and women in Italy from 1881 to 1936; the average age of missionaries and of the clergy resident in the homeland; the longevity of the Princes of the Church, the parish farm land; the age of children at Baptism, the frequency of the Sacraments, etc.

The Annuario Pontificio, having begun in 1944 and thereafter the publication of several statistical data, opens the way to a more organic and systematic statistical knowledge of the phenomena that more properly concern the field of ecclesiastical statistics.

6. Confessional statistics

It studies particularly the demographic and economic-social aspects of confessional groups and could also be called, more properly, statistics of confessional groups. Its importance is greatest in countries with a strong religious mixture, while it is minimal in countries that, from the religious point of view, present a high degree of homogeneity. From the demographic aspect, the study of their numerical consistency is interesting. For example, around 1936, out of 2,084,000,000 inhabitants of the earth, 35.3% were Christian, 59.8% non-Christian and the rest of unknown religion or without religion. Very important, moreover, are the comparisons with regard to the dynamic characteristics of confessional groups. Such, for example, are the natural movement (births, deaths, marriages), the religious movement given by conversions; the migratory movement that has modified in some countries the composition of the existing confessional groups. From the economic-social aspect, important too is the study of their occupational composition, of their degree of culture, of well-being and of wealth, of their hygienic and health conditions, of their morality, of the frequency of suicides, etc.

From such studies it is clear that religion has a marked influence on the moral and social conduct of individuals.

Tommaso Salvemini