Rational Maps and Parameters of Geographical-Statistical Data - article ; n°3 ; vol.7, pg 337-348

Roberto Bachi

Description

Espace, populations, sociétés - Année 1989 - Volume 7 - Numéro 3 - Pages 337-348
Cartographie et « paramètres géostatistiques»
L'auteur décrit ici les activités de l'Institut Central Statistique d'Italie qui tendent à obtenir les buts suivants :
a) la publication d'un Atlas statistique incluant à peu près 400 cartogrammes qui représentent la distribution territoriale des phénomènes démographiques, économiques et sociaux,
b) la préparation d'un volume qui décrit les caractéristiques de ces distributions en employant des « paramètres géostatistiques »,
c) la standardisation des procédures graphiques-statistiques.
A description is given of activities of the Central Institute of Statistics of Italy directed toward:
a) the publication of an Atlas including some 400 «Rational» maps representing the territorial distribution of demographic, economic and spatial phenomena,
b) the preparation of a volume summarizing the characteristics of those distributions by means of «geostatistical parameters»,
c) standardisation of graphical statistical procedures.
12 pages
Source : Persée ; Ministère de la jeunesse, de l’éducation nationale et de la recherche, Direction de l’enseignement supérieur, Sous-direction des bibliothèques et de la documentation.

Sujets

• Sociologie, société et politique

Informations

• Publié par: ESPACE-_POPULATIONS-_SOCIETES
• Publié le: 01 janvier 1989
• Nombre de lectures: 7
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

Roberto Bachi
Rational Maps and Parameters of Geographical-Statistical Data
In: Espace, populations, sociétés, 1989-3. Spécial numéro vingt - Special twentieth issue. pp. 337-348.
Résumé
Cartographie et « paramètres géostatistiques»
L'auteur décrit ici les activités de l'Institut Central Statistique d'Italie qui tendent à obtenir les buts suivants :
a) la publication d'un Atlas statistique incluant à peu près 400 cartogrammes qui représentent la distribution territoriale des
phénomènes démographiques, économiques et sociaux,
b) la préparation d'un volume qui décrit les caractéristiques de ces distributions en employant des « paramètres géostatistiques
»,
c) la standardisation des procédures graphiques-statistiques.
Abstract
A description is given of activities of the Central Institute of Statistics of Italy directed toward:
a) the publication of an Atlas including some 400 «Rational» maps representing the territorial distribution of demographic,
economic and spatial phenomena,
b) the preparation of a volume summarizing the characteristics of those distributions by means of «geostatistical parameters»,
c) standardisation of graphical statistical procedures.
Citer ce document / Cite this document :
Bachi Roberto. Rational Maps and Parameters of Geographical-Statistical Data . In: Espace, populations, sociétés, 1989-3.
Spécial numéro vingt - Special twentieth issue. pp. 337-348.
doi : 10.3406/espos.1989.1340
http://www.persee.fr/web/revues/home/prescript/article/espos_0755-7809_1989_num_7_3_1340'I.ATIONS. SOC
Roberto BACHI Hebrew University,
Jerusalem 92225
19 Hovevei Zion Street
Israël
Rational Maps and Parameters
of Geographical-Statistical Data
1. INTRODUCTION
This Institute-like most official statistical This paper deals with progress in methods
agencies of other countries - publishes in which utilize sets of data detailed by small
its censuses and current reports enormous areas, by presenting them over «rational
amounts of data specified by small areas maps» (1) and summarizing them by
« geostatistical parameters» (2). General (such as by 8086 « comuni » or municipal
characteristics to which the various sets of circumscriptions). These data are of great
data refer can thus be evidenced and comp utility for local administration, for
ared. Those methods appear to be of business, for microgeographic research,
etc. However, there are difficulties in the use in many fields. Recent large scale ap
plications of these methods include : a) a direct utilization of these data for the aim
volume in preparation (by R. Bachi, S. of obtaining quick, meaningful and com
Delia Pergola, S. Ever-Hadani, V. Klaff) parable overviews of the characteristics of
on comparative urban ecology of Jewish the territorial distributions to which the
minority populations in cities of Europe, data refer. These difficulties stem, inter
the Americas and Africa; b) a « Statistical alia, from the great length of the sets of
Atlas of Italy» published by the Central data considered, and from the fact that the
Statistical Institute of that country, from «comuni» are very different in size and
which examples quoted in this paper are shape and they do not constitute conve
taken. nient statistical units for comparative
(1) See Bachi 1968, 1981, 1988, 1989 in the ritories (see, for example, for centrography and its
bibliography appended to this paper. evolution Neft 1966). The name of « geostatistics »
(2) Objectives of geostatistical methods are describ has been suggested by F. Hart (1954) and largely us
ed in section 3. These methods have evolved out of ed by R. Bachi and other researchers. Later, the term
a body of tools which are sometimes designated in the geostatistics has been used, independently, for in
literature as «centrography», as centers have been the dicating various types of research in geological
first type of parameters used for summarizing statistics.
characteristics of distributions of populations over 338
analysis of the territorial-statistical data. These applications have been made possi
Preparations are made at present for the ble by a program package for the prepara
tion of maps and calculation of publication of a companion volume to the
geostatistical parameters (compiled by Atlas which will present and analyze in a
S. Ever Hadani in consultation with comparative way parameters summarizing
the main characteristics of each of the R. Bachi).
distributions displayed in the Atlas.
2. RATIONAL MAPS
2.1. «Simple» Rational Maps. Examples 10,000). Values KcFi are rounded to the
from the Statistical Atlas of Italy nearest integer (Kj - KcFj). We thus ob
Rational maps are based on the following tain a distribution «equivalent» to the
principles : original, which indicates the number Kj of
population elements (out of a total of (a) We start by identifying the « gross ter
ritorial container»: in our case, this is K = 10,000) found in each cell i.
predetermined, being the territory of Ita (d) Each Kj is represented on the map by
a «Graphical Rational Pattern» (see Bachi ly. In other cases, and «endogenous»
1 968 , 1 988) . GRP is a device enabling us definition of territory may be preferred,
to represent any integer n = lOt + u includsuch as a convex hull around the popula
tion distribution or its major ed between 1 and 100 by a symbol formed
clusters (Bachi, 1981). by u unitary marks of area a (which in
(b) The gross container is subdivided into dicate the units) and t marks of area 10a
a convenient number (in our case, which indicate the tens. As the GRP re
N = 1,000) of cells i of regular hexagonal quires little space on the map, a GRP
shape and of constant area A = A/N representing Kj can be put on the map in
(where A = area of the gross cont correspondance to cell i. GRP can be
designed in different ways. ainer). In the specific example of Italy,
A = 301 sq. km. In the maps of this paper, the symbols
The graphical-geostatistical program shown by the scale of Graph 1 have been
used : any Kj is represented by a GRP with transforms frequencies Fj by tracts j into
value n = Kj. For values of K[ of 100 and frequencies cFi by cells i, pooling together of small «comuni», the centers over (indicating concentrations of over 1 %
of which fall within cell i, and subdivising of the population in a cell) a square of area
frequencies Fj of large « comuni » between 100a is used. Map 2 shows, as an examp
le, the distribution of the population of the cells included in j, etc. The method
Italy in 1987. of substituting the original network of i
rregular regions j by a network of regular Any symbol n = Kj in a map (which can be
cells i, more suitable for comparisons, is distinguished according to the scale of
not new. However, in most current ap Graph 1) represents K; (F/K) = cFi
elements of the original population in plications, a network of square cells is
used. Here we have preferred hexagonal cell i.
cells, in order to take advantage of the fact While no claim is made that the method of
that the center of each hexagonal cell has implementation of the GRP used here is
equal distance from the center of all the six wholly satisfactory from a visual view
adjacent cells. point, considerable advantages of the GRP
system over usual statistical maps can be (c) In order to facilitate comparisons be
suggested (see Bachi 1989 a, 1989 b). In tween the distributions of various populat
particular, it can be emphazised that the ion groups, all distributions have been
same GRP map represents absolute frstandardized by calculating relative fr
equencies cFi, relative frequencies cfj, equencies cfi = cFj/F (where F= £Fj =
equivalent frequencies Kjjand densities per E cFj) and multiplying them by a conve
sq. km. in each cell Fj/A. The passage nient coefficient K (here K = 339
90+
80+
70+
60+
50+
40+
■ ■
30+
20+
10+
m m ■ • * • • ■■ •■■ :.: :.:
12 3 4 5 6 7 8 10
Graph 1. Scale of Graphical Rational Patterns, showing integers from 1 to 100.
from one type of scale to the other is im sons in the actual population, to K/N =
mediate and can be shown, if so required, 10 units of the equivalent population, to
in the key to the map. For example, as (F/K)/(A/N) = 1/10 (F/A) = about 19
the population of Italy is 57,290,000 a unit persons per sq. km.
of GRP corresponds to F/K = 5729
The cross given in Maps 2, 3, 4 (as in all generally, ellipses drawn around the hands
maps of the Atlas of Italy) represents im of the cross would include a high propor
portant parameters of the distributions tion of the population (see Bachi, 1981).
shown (which are discussed below). The The crosses help in the appraisal of import
cross is centered at the mean center of the ant features of each distribution and in
set considered. Its hands indicate disper comparing the various maps. They also
sion in the two directions along which this help to create a bridge between detailed
is respectively maximal and minimal. analysis o