Current Urban Studies
2013. Vol.1, No.4, 117-129
Published Online December 2013 in SciRes (http://www.scirp.org/journal/cus) http://dx.doi.org/10.4236/cus.2013.14013
Open Access 117
Socio-Spatial Inequality in Education Facilities in
the Concepción Metropolitan Area (Chile)
Helen De la Fuente1, Carolina Rojas1,2*, María Jesús Salado3, Juan Antonio Carrasco1,4,
1Centre of Urban Sustainable Development CEDEUS, Concepción, Chile
2Department of Geography, Universidad de Concepción, Concepción, Chile
3Department of Geography and Geology, Universidad de Alcalá, Alcalá de Henares, Spain
4Department of Civil Engineering, Universidad de Concepción, Concepción, Chile
5Department of Geography, Ghent University, Krijgslaan, Ghent, Belgium
Received September 13th, 2013; revised October 14th, 2013; accepted October 22nd, 2013
Copyright © 2013 Helen De la Fuente et al. This is an open access article distributed under the Creative Com-
mons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, pro-
vided the original work is properly cited.
In Concepción Metropolitan Area (CMA), the uneven geographical distribution of population, exacerbat-
ed by the recent spread of urban growth, has promoted a clear spatial inequity in the provision of quality
educational facilities. The objective of this research is to systematically compare the 493 schools of exist-
ing educational opportunities in the CMA with the aim to evaluate the spatial equity in order to improve a
most inclusive urban planning. Statistical and graphical analysis revealed that nearest units to the center
of the metropolitan area (Concepción) had better conditions than the farthest with respect to students-
teacher ratio, teaching quality and academic outcomes assessment. This center-periphery pattern shows
clearly the challenges to be faced in the CMA with respect to equitable access to quality educational re-
Keywords: Spatial Equity; Inequality; Educational Facilities; Accessibility; Concepción Metropolitan
According to recent reports by the Organization for the Co-
operation and Economic Development (OCDE), Chile is the
country where private funding has increased weight in both
primary and secondary education, and where the lowest degree
of socioeconomic inclusion of the students within a school is
found (OCDE, 2012). To this student segregation according to
income level is added, presumably, a spatial segregation that
according to free market laws, it concentrates best quality cen-
ters in urban sectors in which middle-high socioeconomic sec-
tors predominate. This situation would be feeding a growing
social polarization in which lower class groups located in pe-
ripheral areas have more difficult access to quality services and
facilities (Sabatini & Brain, 2008).
Research seems to corroborate this disparity of opportunities
of social mobility. According to data from the Chilean Ministry
of Education, for 2010 the best performance was concentrated
in urban spaces occupied by middle higher classes, whereas less
advanced schools, generally of public nature are found in
spaces with high presence of lower income economic classes.
In other words, a close relation seems to exist between the so-
cioeconomic aspects of the families and the performance of an
educational center (Ministerio de Educación, 2010; Oberty,
2007). In this situation, the question is how to describe statisti-
cally and geographically the spatial distribution of the educa-
tional centers, how to measure the accessibility of the school
population to those centers, or how to establish the degree of
spatial correlation between location of educational facilities and
population strata according to their quality and level of income,
As study case, Concepción Metropolitan Area (CMA) is pro-
posed. This city represents the second urban concentration in
Chile, located in the coastal plains of the Biobío Region and
subject to recent processes of population dispersion and urban
growth, comparable to mid-size metropolitan areas of Latin
America (Rojas et al., 2013). Despite the wide range of educa-
tional facilities in its 11 municipalities, coverage degrees and
differential levels of spatial accessibility can be identified. Ba-
sically, in the most urbanized areas (Concepción and Talca-
huano) relocation phenomena are of educational centers previ-
ously located in central sectors towards more distant places are
being produced, thus favoring the use of private transport as
mode of travel and the clustering of specific and homogeneous
groups of population. On the other hand, least populated mu-
nicipalities continue concentrating their schools in the urban
center, whereas their urban growths are increasingly peripheral
and distant, involving large displacements.
So, assuming that education represents a crucial factor to re-
duce inequities and improve the quality of life of the population
(Fundación para la superación de la pobreza, 2006), this article
pretends to be an essay on the integration of spatial distribution
measures of educational facilities, with their own quality and
H. DE LA FUENTE ET AL.
socioeconomic situation indicators of the population close to
every one of the schools. The aim is to enrich the assessment on
the spatial equity in the distribution of the education opportuni-
ties and hence facilitate better and more inclusive planning.
The present work starts by briefly presenting the state of the
issue and its geographic framework. Among the methods of
statistical and cartographic analysis, the generation of an indi-
cator of educational quality that summarizes the rate students-
teacher will be considered, as well as the learning results col-
lected by the SIMCE (Measurement System of Quality Educa-
tion of the Chilean Ministry of Education), and Moran’s Local
and Global Index, used to diagnose the spatial grouping of
schools in CMA.
Results present a spatial diagnose of the educational quality
in the area of study, as well as in the zones of low and high
concentration of facilities. Finally both strengths and weak-
nesses of the investigation are discussed in order to improve the
accessibility to a quality education, considering a more equita-
ble spatial distribution (Ministerio de Educación, 2010).
Principles of Equity, Equality and Spatial
Justice in the Location of Facilities
There is a way to understand these concepts beyond their
merely textual meaning, mainly applied to social sciences and
geography. These expressions arose on the basis of Radical
Geography, which illustrates the insufficiency of the theoretical
models of the Quantitative Geography, which were intended to
explain both location of activities and land uses, to move to-
wards measuring, quantifying and assessing geographic situa-
tions. It involves measuring the degree of injustice, equity or
equality of distributions or spatial configurations (Moreno,
Some authors coincide on the close relation among Equality,
Justice and Equity. Despite this, it is possible to obtain a dif-
ferentiation, as explained by Bosque (2004), who pointed out
that the meaning of equity can manifest itself as equality, but
not necessary as synonyms, because equity is understood as
justice, impartiality of treatment, opportunities, etc. Geographi-
cally, something is fair in the sense that distribution among
areas has its own proportional differences and these differences
are not seen as needs or difficulties, but acceptable for the pop-
ulation. Equality, on the other hand, starts from the basis that
everyone must have the same opportunities, same health level,
education and opportunities, creating a difficult application
both in social and geographic terms, regarding that both people
and spaces are different.
On the other hand, spatial justice can have two approaches:
one that decreases differences among areas or distances, and
one in which the required opportunity is reached. For the spe-
cific case of desirable facilities (Hospitals, Schools or other
services), spatial justice is concerned are not unevenly distrib-
uted over the space, so there are no differences or. At least, they
are not excessively big in the access of the population to these
facilities (Flores, 2009). In the case of non-desirable facilities
(industries, landfills), the issue is that the distances between
population and facilities are not too dissimilar, so some people
are not too affected, whereas others are not affected at all
(Bosque & Moreno, 2005).
Another author that recognizes similarities among terms of
equality, justice and equity is Moreno (1999), who pointed out
that justice corresponds to the “set of methods used by authori-
ties to reduce inequalities among socio-spatial classes”. On the
other hand, equality would be sustained on democratic ideas
and on egalitarian ideals of philosophy and alludes to the fact
that a person has identical rights and obligations, so individuals
must be treated in the same way, nevertheless it must be recog-
nized that not all individuals are equal. For this reason, an as-
sessment on situations, and profit sharing and disutility in a fair,
impartial and equitable way must be carried out.
It is possible to make a distinction between arithmetic and
proportional equality. Arithmetic equality is referred to a per-
fect equality, equality of treatment, where exactly the same
amount of benefits is destined to everyone, regardless of the
circumstances. Justice assumes an unequal distribution, so its
aim is to improve the situation of the most disadvantaged. As
postulated by Harvey (1977): “The geographic problem con-
sists in elaborating a spatial organization mechanism that
maximizes the perspectives of the most disadvantaged region”.
For Moreno, the terms of spatial equity and equality are almost
synonyms, being differentiated from the justice, because ideal
justice consists in the suppression of all disadvantages. In other
words, justice encompasses both equality and equity. For this
reason, justice mixes both social and spatial features. In other
words, involves public authorities to attenuate inequalities and
the notion of equality would be mixed with the scope of equity.
A similar version was presented by Pitarch Garrido (2000)
for the elaboration of planning models of educational services,
where five fundamental aspects must be considered, such as
social equity, indicating that all public activity must be ad-
dressed to whole of the society excluding any discrimination on
the basis of social differences. On this basis, education as pub-
lic service must look for social equity as a right for every citi-
zen. On the other hand, locational equity takes into account that
the space always introduces inequalities and therefore, is a con-
figurative factor, closely related to social equity.
Educational System in CMA: Institutional
and Geographic Framework
The Chilean Educational system is divided into four levels:
preschool education (4 to 5 years of age), primary education (6
to 15 years), secondary education (15 to 18 years) and higher
education. This study is focused on the evaluation of the first
In theses levels the Chilean Ministry of Education have ap-
plied a number of assessment indicators, organized in five
groups (Ministerio de Educación, 2008):
Context indicators: They reflect the potential demand for
educational services and the growth trend of such demand,
as well as the relative size of the enrolment.
Participation indicators: They are related to the access to
education, participation and internal efficiency of the sys-
tem. They are calculated by means of levels and include the
net rate enrolment (total amount of students of the official
age group in a specific level of primary or secondary educa-
tion—6 - 13 and 14 - 17 years of age, respectively, regard-
ing the total population of that age group); and gross rate
enrolment (total amount of students in a specific teaching
level of primary or secondary education, in relation to the
total amount of students for that education level). Age dis-
tribution by age and its growth rate show the trends in the
different levels and institutions. Particularly, the distribu-
tion of the enrolment reflects important variations since
H. DE LA FUENTE ET AL.
1981, due to the incorporation of the subsidized education,
which is pretending decentralizing the educational system.
Resources indicators: Supplies possessed by schools in both
monetary and human capital, i.e. teachers. They include the
proportion between students and teachers, a kind of student
load indicator assumed by the teacher. They are used to
analyze the total expense in education.
Result indicators: They measure the efficiency of the sys-
tem. They include approval rates, as well as illiteracy and
Indicators employability of students: In the workplace the
participation of the work force and the unemployment rate
are measured, because this is higher for the younger sector
of the population (25 to 29 years) than for the total popula-
tion (25 to 64 years). In addition, there is a direct relation
between the educational attainment and unemployment
(Ministerio de Educación, Departamento de Estudios y
Desarrollo de la División de Planificación y Presupuesto,
Additionally, the Chilean Ministry of Education carries out
the SIMCE tests (acronym in Spanish for the Measurement
System of the Quality of Education) in order to obtain national
data on learning outcomes in the so-called Fundamental Objec-
tives and Minimum Required Contents (OF-CMO). Table 1
presents the outcomes of SIMCE 2010, for the entire country
and for Biobío Region as a whole. It can be observed that the
regional outcomes are located around the average (slightly be-
low in the case of primary education and slightly above in the
case of secondary education). Later, in Table 2 the outcomes
for CMA can be observed, disaggregated for municipalities.
Concepción Metropolitan Area (CMA) located in Central
South Chile, is a functional and hierarchical territory formed by
11 municipalities, with a population of about one million in-
habitants. The main articulator centers are Concepción and Tal-
cahuano and the other municipalities or sub enters are Coronel,
Chiguayante, Hualqui, Lota, Penco, San Pedro de la Paz, Santa
Juana, Florida and Tomé. In the CMA important urban trans-
formations have been produced in the last years, such as com-
mercial and the development of facilities nuclei of regional
importance, as well as a sustained improvement in the accessi-
bility conditions and, in general, in transport infrastructures
(Figure 1). In 2011 there were 493 schools in CMA, with a
predominance of private subsidized schools (40.7%). Public
schools represent 38.5% and private schools are only 5.4%.
Table 3 presents these data along to the population size, disag-
gregated by municipality.
Regarding the general status of education in the CMA, the
municipality with the highest schooling is Concepción, with an
average of 10.7 years (CASEN, 2006). In the case of enrolment
for public, subsidized and private schools, most of them also
belong to Concepción, with 54,596 students in 2010, according
to Annual Plan of Municipal Educational Development (PA-
DEM, 2011). On the other hand, the illiteracy rate presents the
highest values in municipalities of rural environment, such as
Santa Juana and Hualqui, whereas Concepción, Chiguayante
and Talcahuano have the lowest rates, with circa 2% of the
population (CASEN, 2006).
Data and Methods
In order to describe the distribution of educational facilities
Results SIMCE, national and regional level.
National Biobío Region
level Evaluation Score
score Score Average
253 257.5 250
260 256.0 252
250 252.5 263
Note: Source: Ministry of Education, 2010.
Educational facilities in CMA (according to SIMCE results).
According to perfomance
ProvinceCommune Numbers o
schools High MediumLow
Concepción 68 26 31 8
Talcahuano 46 9 26 12
San Pedro de la Paz29 7 11 9
Chiguayante 29 5 17 4
Penco 19 1 16 1
Tomé 26 4 15 2
Coronel 35 4 23 8
Lota 17 1 10 1
Hualpén 25 13 14 6
Hualqui 17 11 5 3
Santa Juana 20 1 4 6
*High: >283 points; Medium: 237 - 282; low: <283.
in the area of study, four dimensions of interest were selected,
with indicators that could measure them: Dispersion (standard
deviation ellipse), concentration (neighborhood index), spatial
inequality (Sargent Florence Quotient) and supply-demand rela-
tion (indicator of accumulated opportunities). Second, a syn-
thetic indicator of educational quality composed of variables
considered representative is proposed: students-teacher ratio,
teacher evaluation and SIMCE results. Both indices and indi-
cators used in the study are detailed as follows:
Standard Deviation Ellipse
It allows assuming the main spatial characteristics of a set of
geographic entities: central tendency, dispersion and directional
trends. Its core shows the central tendency of that set of entities;
its major axis is extended towards the maximum dispersion
direction and its minor axis indicates the degree of linearity of
the distribution. Given the fact that it can be mathematically
demonstrated that the maximum dispersion axis in a dot struc-
ture always forms a straight angle with the minimum dispersion
xis, an ellipse constitutes an adequate representation form for a
Open Access 119
H. DE LA FUENTE ET AL.
Census districts CMA.
Code Name Code Name Code Name Code Name
0 Intendencia 39 Bannen 20 Plaza Perú 59 San Vicente
1 Liceo de Hombres 40 Lota Bajo 21 Observatorio 60 Estadio
2 La Cárcel 41 Cementerio 22 Larenas 61 Huachipato
3 Plaza España 42 Colcura 23 Pedro de Valdivia 62 Ramuntcho
4 Estación Central 43 Penco 24 Palomares 63 Hualpencillo
5 Cerro Amarillo 44 Fábrica 25 Lo Pequén 64 Carriel
6 Plaza Cruz 45 Lirquén 26 Municipalidad 65 Las Salinas
7 Cementerio 46 Margaritas 27 Villa Mora 66 Barranquilla
8 Laguna Redonda 47 Batro 28 Schwager 67 Zunico
9 Pajonal 48 Boca Sur 29 Buen Retiro 68 Estadio Higueras
10 Manuel Rodríguez 49 Los Acacios 30 Corcovado 69 San Miguel
11 Escuela Argentina 50 San Pedro 31 Escuadrón 70 Club Hípico
12 General Cruz 51 Lomas Coloradas 32 Lonco 71 Bremen
13 Estación Tucapel 52 Santa Juana 33 Matadero 72 Cerro Verde
14 Lo Méndez 53 El Portón 34 Fábrica 73 El Puerto
15 La Toma 54 Valdivieso 35 Chiguayante 74 Ralihue
16 La Pólvora 55 Cerro Fuentes 36 La Leonera 75 El Morro
17 Población Baquedano 56 La Aduana 37 Hualqui 76 Dichato
18 Plaza Condell 57 Cerro Buenavista 38 Lota Alto
19 Hospital 58 Tumbes
Note: Source: INE 2002.
such dispersion by providing a perceived “mean” location and
thus it allows perceiving the whole systematic delocation of the
Neighborhood index or nearest neighbor analysis is simply
the calculation of the average distance divided by the expected
average distance to the nearest neighbor, in the case of a ran-
dom disposition. If the index is greater than 1, dispersion is the
tendency. On the contrary, the pattern will show a conglomer-
ate distribution and its calculation results from the following:
where R is the neighborhood index, obs
is the observed dis-
tance to the nearest neighbor and ran
is the expected average
distance to the nearest neighbor, in a random dot arrangement.
Neighborhood index can have values between 0, which indi-
cates a fully grouped structure and 2.15, which indicates a fully
disperse structure. This indicator provides a very useful de-
scriptive measure of specific structures, especially for identify-
ing the increase or decrease of both dispersion or grouping of a
structure (Ebdon, 1982). The index has used the centroid points
of each census unit population.
Sargent Florence Quotient
This index basically measures the degree of inequality
among territories. The interpretation considers with value 1 to
an egalitarian country condition. On the other hand, values
higher than 1 correspond to a surplus of schools. Finally, values
lower than 1, correspond related to a deficit of educational in-
stitutions. In the study carried out by Fuenzalida (2010) on dis-
tribution of hospitals, it is concluded that this index is an un-
avoidable complement for the comprehension of the spatial
inequalities. Table 4 clarifies its interpretation, being estab-
lished the numerical thresholds to facilitate the assessment of
The index is applied in the following equation:
where CLi = location quotient of the territorial i subunit; i··· n =
subunits of the j set; Oi = educational service offering in i sub-
unit and di = educational service demand in i.
In this case, i subunits are represented by the census districts
H. DE LA FUENTE ET AL.
Concepción Metropolitan Area.
of every municipality of CMA, in which Oi educational offer-
ing corresponds to the sum of the students registered by the
Ministry of Education that attend each school in the i district.
On the other hand, the demand variable is referred to the poten-
tial population to attend, whereas the demand variable is related
to the potential population that attends to an educational facility
in the subunit. In other words, they correspond to people be-
tween 0 to 17 years, according to data from Census (2002).
Subsequently, results obtained from the index are plotted in five
main categories. These are: important deficit, moderate deficit,
moderate surplus, important surplus and country condition (Ta-
Hence, a value close to 1 will mean that the proportion of the
offering in the i subunit respect to the total CMA is similar to
the proportion of demand in i respect to the total. Values higher
than 1 indicate that in the i subunit there is a relative oversupply
respect to the resident demand; and values lower than 1 indicate
that there is a deficit in the supply respect to the demand regis-
tered in I, which is greater as farther away from the unit.
Resident Population Indicator in an Area of Specific
Radius/Indicator of Accumulated Opportunities
Although several limitations and possible improvements
have been pointed out (Bisonnette et al., 2012; Chen et al.,
2012; Langford et al., 2008), the method called Two Step Float-
ing Catchment Areas (2SFCA) has been frequently used in the
recent literature on the assessment of spatial inequities in the
Qualitative and quantitative classification of educational quality indi-
Low quality Medium quality High quality
−1 0 1
Teacher ratio2 >34 students 17 - 34 students <17 students
evaluation 3 Satisfactory and
Sargent Florence assessment.
Level of locator coeffciencient Value
Important deficit <0.49
Moderate deficit 0.50 - 0.99
Moderate surplus 1.01 - 1.87
Important superplus 1.88 - 2.73
Country situation 1
Note: Source: Fuenzalida, 2010.
distribution of public facilities (Cervigi et al., 2008; Chen et al.,
2012; Gualiardo, 2004; Luo, 2004; Luo & Qi, 2009; Luo &
Whippo, 2012; Wang, 2012). The first step establishes a buffer
around every supply center and it counts how much population
resides inside them. The second step the buffer is sketched from
every point of demand and the centers or facilities located in-
side the center are added.
Both start from the delimitation of an influence area of de-
termined extent from these points. If these points represent the
supply, it can be accounted the volume of resident population
within such area, besides quantifying the population covered by
the service. In this case, the service is educational. The Geo-
graphic accessibility of the facility is also measured (Gutiérrez
& García, 2002). If the points that originate the influence area
represent the demand, the number of available schools or hos-
pital beds can be quantified within that range of distance from
each demand point, an indicator of accumulated opportunities
will be used as an accessibility measure (Salado, 2012).
In any case, in order to use one and another, it is necessary to
consider at least three elements: points of supply, distribution
of population (potential demand) and the gap among the poten-
tial demand of the points of supply, according to areas of influ-
In order to determine the areas of influence, two methods
that consider the location of educational centers have been
taken into account. The first method consists in modeling dif-
ferent areas of influence or buffers of 500 and 1000 m, ranges
commonly used as more accessible (Ramírez, 2008; Villanueba,
2010; Sabuda, 2007; Yi, 2004) and Pizzolato, Broseghini, &
Noguera, 2002). The second method uses areas of influence
from the análisis through Thiessen polygons. It must be noted
that both GIS operations are carried out by means of the ArcGis
Open Access 121
H. DE LA FUENTE ET AL.
software. Later, buffers are intersected with the area of influ-
ence from Thiessen polygons (geometric construction of the
For the calculation of the population variable within the
range of geographic accessibility (buffers intersected with Thi-
essen polygons), an inconvenient is presented by how deter-
mining the amount of potential population between 0 and 17
years, because of its irregular distribution, which many times
covers not completely the census blocks. This information is
required to determine the approximate number of people cov-
ered by the educational service. Therefore, for the solution to
this problem the method proposed by Gutiérrez, Pinto &
Gómez (2000) is used. This method is nothing but the ratio
between the total population of the block and the population
covered by the area of influence, as detailed in the following
Being P = total population estimated in the area of influence
of any facility; i··· n = sectors entirely included in the coverage
area; pi = population entirely included in the coverage area; j··· m
= sectors partially included in the coverage area; pj = population
of the j sector; aj = area of the j sector which is within the area of
influence; and aj = area of the j sector.
Educational Quality Indicator (EQI)
This synthetic indicator summarizes three partial indicators.
From these results, a qualitative evaluation scale was carried
out (low, middle and high quality), as well as a quantitative
scale (between −1 and 1). Both balance of these partial indica-
tors and the definitive classification are presented in Table 5.
Student-Teacher ratio: It is equivalent to the number of
students in relation to the total amount of teachers accord-
ing to education level, administrative dependency, region
and geographic area. Carried out by the Chilean Ministry of
Education, it allows studying the endowment of teacher per
student and outlines the school situation per school.
Teacher evaluation: The Ministry of Education carries out
the performance evaluation of school teacher, establishing
four degrees: outstanding (it indicates a professional per-
formance that clearly and consistently stands out with re-
spect to expected), competent (proper professional perform-
ance, it fulfils the requirements), basic (it fulfils with what
is expected in the indicator, but irregularly), and unsatis-
factory (it presents clear weaknesses in the teaching per-
SIMCE results (of learning outcomes in Fundamental
objectives and Minimum Required Contents): Disag-
gregated results are presented in Table l. This is the indica-
tor granted with the greatest weight, because it counts on a
methodologically solid system, it is widely used as tool for
education policies and it has been in use for long time.
From every variable, a qualitative evaluation scale is per-
formed, with variables such as: High, Medium and Low quality.
On the other hand, a quantitative sale was also performed, as-
signing minimums that range from −1 to 1 as maximum. The
evaluation scale used to measure the descriptive correlation
statistics of variables is presented in Table 5. This scale fulfills
with the condition of being a scale of comparable values that
allows assessing different factors, variables or criteria, inde-
pendently of the method to be used (Moreno, 1999).
The assessment favors the fact that all values are expressed
in a comparable scale of values (−1 to 1). Therefore, by means
of a simple calculation procedure the proportion applied
through maximum and minimum values of each variable under
study is applied, as observed as follows:
where X corresponds to the value assigned by the scale, Xmin is
the minimum value of the data set, Xmax is the maximum value
of the data set, and Y represents the data value to convert.
By means of this equation it is possible to convert all con-
tinuous data into a scale of values between −1 and 1. Thus, a
data matrix or basic input for the construction of educational
quality index is obtained.
The synthetic index, product if every one of the dimensions
(Teacher evaluation, SIMCE test and teacher student ratio)
gives more weight to the SIMCE results, then to the teacher
evaluation and finally to the student teacher ratio. This propor-
tional order is given to the fact that for the Chilean Ministry of
Education. SIMCE has greater “legitimacy and credibility”.
This test has allows focusing the attention of the public opinion
and the teachers into the learning results, by means of a meth-
odologically solid system , as well as widely used tool for edu-
cational policies, making clear that this is a reliable indicator in
time. In Table 6 three indicators of educational quality and
their different relative weights for obtaining the synthetic index
of educational quality can be observed. The index allows a first
approach to the distribution of the phenomenon under study,
assuming that every spatial unit have weighted values of each
variable, being 10 the maximum value of the scale and repre-
senting an educational quality of excellent level. On the other
hand, −10 is the minimum value, demonstrating the opposite
situation, i.e. an education with multiple deficiencies (Table 6).
The result from the previous indicators was later assigned to
cells in a 100 × 100 m grid (the size of the grid has been estab-
lished regarding that the average size of a census block, in the
CMA fluctuates around 10,000 m2). The aim of this assignment
was to find out if the distribution of the results corresponded to
a condensed, scattered or random pattern by GeoDa Software.
In order to achieve this, a spatial auto-correlation analysis that
studies the variation mode of the thematic values among the
different points of the space is carried out (Góngora Gómez,
Spatial auto-correlation reflects the degree in which objects
or activities in a geographic unit are similar to other objects or
Weighting of quality indices.
Evaluación docente 3
Tasa Alumno profesor 2
H. DE LA FUENTE ET AL.
activities in close geographic units (Goodchild & Haining,
1992). Basic property of spatial auto-correlated data is that val-
ues are not random in space. In other words, data values are
spatially correlated each other and become redundant (Lee &
Wong, 2001). This kind of models supposes that finding a spe-
cific observation in a point of an area it is possible to find simi-
lar observations in points close to it. On the contrary, distant
points would have totally dissimilar characteristics.
Specifically, the Moran’s Statistical Global index (I Moran)
was applied. This index determines the kind of grouping exist-
ing between neighbor spatial units in order to obtain some
known distribution model, or to study the spatial segregation of
a characteristic. The complexity of the problem increases as a
result of possible multidirectional interdependencies that may
arise in the space. Its formulation is as follows:
where n is the number of geographic observation units, wij are
the elements of a binary contiguity matrix, x is the attribute of
this variable and the mean of the cross product.
The measurement of a correlation with the same variable has
in different spatial contiguous units in a horizontal perspective,
originates one out of these three possibilities:
Positive spatial auto-correlation: neighbor spatial units pre-
sent close values and indicate for the spatial units a ten-
dency to grouping.
Spatial negative correlation: Neighbor spatial units present
very dissimilar values and indicate for the spatial units a
tendency to dispersion.
No correlation: any of the above situations take place.
Therefore, values of neighbor spatial units present values
Moran’s index is grounded in an auto-covariance model and,
after the mean and the variance, is the most important property
of any geographic variable. Unlike the previous ones, it is ex-
plicitly linked to spatial patterns. These observations can be
discrete or continuous and they may be associated to a point on
a specific surface, or associated to a surface on which a parti-
tion has been performed. This partition may be regular or ir-
regular and commonly recognized as reticule (López Her-
nández & Palacios Sánchez, 2000).
In general, geographic data are presented in a continuous
map. The contiguity respect to the central location (e) can be
defined in three ways, by means of chess terminology:
1) Rooks criteria: cells b, d, f and h are considered adjacent
to the location of “e”.
2) Bishops criteria: cells a, c, g and i would be considered
neighbors to the location “e”.
3) Queen criteria: It combines the above two and thus cells a,
b, c, d, f, g, h and i would be considered contiguous to “e”.
The kind of contiguity on which the work was carried out
was Rooks, one of the most used, because of its simplicity
Outcomes from this index vary from −1 to 1, representing
minimum (maximum dispersion) and maximum (maximum
concentration) correlations, respectively. Zero means totally
random spatial pattern. In order to know if an auto-correlation
is significant, a null hypothesis test is carried out, checking
whether the spatial configuration of the variable occurs ran-
domly or it responds to a spatial pattern. In other words, if the
assumptions of model whether or not are satisfied from the
estimation if a sampling statistic significantly differs from the
randomly expected. This test is carried out by locating Moran’s
coefficient inside a normal probability curve (Buzai & Baxen-
In order to perform this kind of tests, both null and alterna-
tive hypotheses must be clearly formulated. When working on
socio spatial projects, as null hypothesis the following claim is
considered: “The spatial configuration is randomly produced
and as alternative hypothesis, the opposite claim: the spatial
configuration is NOT randomly produced” (Celemin, 2009).
Once both hypotheses have been established, the significance
level (α) must be defined. This indicates the probability for the
null hypothesis to be rejected. In other words, if the occurrence
probability of a particular value obtained in a test is equal or
lower than α, the null hypothesis is rejected and the alternative
hypothesis is accepted. Habitually, the significance level is
chose according to the importance of the problem. In the socio-
spatial analysis is usually 5% (0.05) and 1% (0.01) (Buzai &
P-value is the result reported by the hypothesis test. Then, if
a significance level of 0.05 is established in general, p-value
presents values lower than 0.05. This allows rejecting the null
hypothesis and accepting the alternative hypothesis, taking into
account that with this decision there is a risk of making a mis-
take in 5% of the cases. On the contrary, if the p-value presents
results over 0.05, the alternative hypothesis is not accepted,
because the risk on the decision exceeds the established limit,
and the null hypothesis must be accepted. In other words, the
“spatial configuration is occurs randomly”.
Moran’s I value represents the spatial correlation degree ei-
ther univariate or bivariate of variables and every point of the
diagram represents a specific different spatial unit, with X and
Y coordinates. In the case of a univariate correlation, on the X
axis of the diagram, standardized values of the considered
variables and on the Y axis standardized values of “average”
values of the neighbor spatial units for such variable will be
placed. Moran’s I index value is equivalent to the slope of the
regression line. The slope of the line represents the association
degree between the variable considered on the horizontal axis
and the values of the variable on the vertical axis, in relation to
the location of their neighbors (Sabuda, 2007).
Description and Analysis of Results
Spatial Distribution of the Educational Facilities
The standard deviation ellipses reveal a location model con-
centrated in every column due to a greater proportion of schools
in urban centers consolidated in the cities of the CMA (Figure
2). This map evidences that out of the ellipses area lower qual-
ity schools are found, especially in the cities of San Pedro de la
Paz, Coronel and Penco. Regarding the directional tendency of
the ellipses, these are ruled by a linear organization pattern
(Penco, Talcahuano, Coronel and Chiguayante), providing an
elongated and disperse shape leaned towards the most hierar-
chic urban center, which corresponds to Concepción.
In relation of the spatial indicators, the neighborhood analy-
sis, the average distance observed between centers is 369.2
meters, a short distance indeed that represents no obstacle to
access to a school by walking (Gutiérrez & García, 2002). The
main difficulty is given by values far from average. Values far
rom average are constituted by distances among private f
Open Access 123
H. DE LA FUENTE ET AL.
Distribution of educational quality index and Sargent Florence Quotient in CMA (Source: Own).
schools, due to their tendency of being located in peripheral
areas. On the contrary, minimum distances are given among
municipal schools. The expected distance, product of the den-
sity of points in a specific area is 369.4 meters. Therefore, the
neighborhood index offers a result of 1005 m that can be inter-
preted as a random pattern far from both ends (0 and 2.15).
Index of accumulated opportunities (Table 7) shows the
population represented by centroids of census blocks which are
covered by three ranges of buffers distance:
Less than 500 meters (Pedestrian proximity distance to fa-
cilities (Gutiérrez García, 2002) low density census block are
found (50 inhabitants). Exceptions are presented in Hualpén,
Chiguayante Sur and in Agüita de la Perdiz sector in Concep-
ción. Total population grouped in this range reaches 201,438
inhabitants for CMA (40.9% coverage). When people between
0 and 17 years of age, the coverage increases up to 213,869
In the second service ring (500 to 1000 meters) census blocks
with more than 50 inhabitants are located, reaching more than
100 inhabitants per sample unit (census blocks). Most distant
sectors are Collao Sector, Barrio Norte, Tucapel Bajo, Chepe
Hill and Agüita de la Perdiz. These places are located approxi-
mately 1 km from the nearest school and in some cases, the
acilities are low quality. In San Pedro de la Paz the disadvan- f
H. DE LA FUENTE ET AL.
Index of accumulative opportunities.
Less than 500 m 500 to 1000 m More than 1000 m
Commune Covered population
population from 0
to 17 years of age
population from 0
to 17 years of age
out of range)
population from 0
to 17 years of age
Concepción 40786 55 16169 22 16574 23
Talcahuano 42231 68 6947 11 12900 21
San Pedro de la Paz 20181 52 5694 15 12893 33
Chiguayante 21753 53 6042 15 13017 32
Penco 10318 58 2720 15 4837 27
Tomé 9515 68 2489 18 2026 14
Coronel 28455 76 4114 11 4786 13
Lota 12643 69 2455 13 3190 17
Hualpén 22353 66 2520 7 8985 27
Hualqui 3665 62 748 13 1535 26
Santa Juana 1979 64 526 17 587 19
AMC 213879 62 50424 15 81330 24
taged sectors are Candelaria, San Pedro de la Costa and Boca
Sur. Population between 0 and 17 years of age covered in this
ring is significantly lower (81,330 inhabitants for the CMA),
totaling a coverage of 81,330 people.
Population without coverage (outside the 1000 meters thresh-
old) is represented by 139,549 people, or 38.02%. Per munici-
palities, Coronel leads with the greatest amount of people out-
side the coverage area, followed by Concepción and San Pedro
de la Paz.
The exercise of quantifying the population between 0 - 17
years of age covered the educational service shows the greatest
population concentration around the main rings (206,303 in-
habitants), which represents 76.46% of the total population.
This number is encouraging, because most of the people have
access to a school, but the obstacles lie on imbalances in the
educational unit, motivating the students to both search and
mobility in order to access to better opportunities. In other
words, students within the immediate fringes can cover dis-
tances over than 1000 meters, product of these differences in
education. This lack of opportunities makes the spatial equality
conditions more difficult, originating unacceptable imbalances
(Escolano et al., 2005).
As we have mentioned in the previous section, Sargent Flor-
ence Quotient estimates deficit or surplus of the educational
service according to the supply offer proportion. As it can be
seen in the map from Figure 3, districts with greater facilities
deficit (values lower than 0.49) belong to the municipalities of
Talcahuano, Penco, Lota and Coronel, in which schools with
lower academic performance predominate (Table 6). On the
other hand, the surplus (values greater than 1.88) is presented in
districts within the municipalities of Talcahuano and Concep-
ción, which have a correspondence of values lower values of
Definitively, in CMA districts that lack educational facilities
and in a situation of important or moderate deficit correspond to
31% and 18% of the population, respectively, whereas the mod-
erate surplus corresponds to 24% and the important surplus is
27%. The highest number corresponds to districts within the
“important deficit” category (0.001), which indicates a notori-
ous spatial inequity, because the contrast between the district
with the highest deficit and the district with the greatest surplus
has amplitude of 14.7 units.
Spatial Distribution of the School Quality
Once the results of the educational quality indicator have
been placed on the 100 × 100 m grid (Figure 3) it can be ob-
served with greater clarity the tendency to concentration of the
highest values in the areas close to the urban nucleus Concep-
ción—Chiguayante—San Pedro de la Paz, in contrast to the rest
of the urban sectors of the CMA.
The spatial auto-correlation analysis corroborates the previ-
ous qualitative interpretation. In Figure 3 it can be seen how
clusters that concentrate good quality education (represented in
live red) are found in the following sectors: Lomas de San
Andrés, Santa Sabina, new Chiguayante, airport Sector, road to
Penco, Huertos Familiares and Villa San Pedro. All of them
have high-high value. In other words, high proportion of the
indicator in the reference grid close to other spatial unit that
also counts on high proportion of the same indicator. In an op-
posite situation are the low-low clusters (deep blue areas in
Figure 4), that group low quality education and located in areas
such as: San Pedro de la Costa, Boca Sur, Michaihue, Cande-
laria, parte de Lomas Coloradas, Cerro Cornou and Hualpen-
cillo, along to the industrial zone, much of Coronel, Lota, Santa
Juana, Hualqui and the Frutillares sector in Tomé. Places in
white represent an absence of auto-correlation of the variable.
Therefore, they are not significant to the study.
Open Access 125
H. DE LA FUENTE ET AL.
Distribution of educational quality in the CMA (Source: Own).
Cluster of educational quality in the CMA (Source: Own).
Regarding the significance degree of the analysis, this is jus-
tified with the map that represents the distribution of the p
value in the CMA (Figure 4). This map reveals a significance
of 0.05, so the null hypothesis on the random distribution of the
variable in the territory is rejected and the alternative hypothe-
sis is accepted (this variable does not present a random distri-
bution, but it corresponds to a particular spatial pattern).
The index clearly shows how the best schools are located in
zones of high economic level. The spatial evidence is enhanced
with results from the Chilean Ministry of Education, where in
both reading and math tests, the percentage of students with
scores over 300 points increases as the socioeconomic level
increases. However, in all groups there are students with scores
over 300 points. For instance, from the students of the low
group that undertakes both reading and Math tests, 5% and 4%,
respectively obtain scores that exceed 300 points.
Results from every one of the variables analyzed by means of
Moran’s univariate spatial auto-correlation show the relation
between educational quality and location. Specifically, results
from Moran global index indicate excellent correlation degrees
of the variables, all close to 0.9. Namely, there is a strong rela-
tion, considering that 1 is the perfect correlation value. SIMCE
variable is the one that obtains the highest correlation, followed
by Teacher Evaluation and finally, Student-Teacher ratio that
equally have a good correlation degree (Table 8).
Discussion and Conclusions: Characterization
of the Spatial Inequity in the CMA
Results already presented seem to confirm that there are sig-
nificant differences in the spatial distribution of the pre-univer-
sity schools in the CMA area and, therefore, notable contrasts
in the access to this kind of facilities, especially if we consider
the access to quality schools. Moran’s I spatial auto-correlation
analysis has become a valuable method to know and prove the
situation of every territorial unit, in relation to the other geo-
graphic surrounding entities, indicating the dissimilar spatial
configuration of the educational facilities within the territory.
Identifying spatial inequity patterns in educational issues is
generally grounded on a specialized description of both cover-
age and quality of the service (estimated on teacher competence
indicators and/or academic performance). Nevertheless, in
many studies the correlation between these indicators and those
of environmental quality and/or socioeconomic level is ignored
(Talen, 2001). Likewise, the location of such schools is appar-
ently unresponsive to a logical inclusive territorial planning
(Pitarch Garrido, 2000).
In the CMA, educational quality is presented unequally. Spe-
cifically, the most disadvantaged places are located in Tomé,
Hualpén, some places in San Pedro de la Paz, Coronel, Lota
and Santa Juana. The singularity of this case is that most of its
population belongs to low socioeconomic classes. Thus, the gap
among different zones has a strong spatial relation between
geographic distance and educational quality, as well as a noto-
rious downtown—periphery spatial pattern and providing
clearly differentiated social benefits. Distance becomes in a
factor that clearly determines the access to quality facilities,
especially damaging lower socioeconomic strata and moving in
detriment to a desirable equity and social cohesion.
From the methodological point of view, the analyses used
have allowed us to describe both distribution and spatial cov-
erage of these facilities and their relation with the distribution
of the demand and with some parameters of quality usually
used by the Chilean Ministry of Education. However, this first
approach opens gates to multiple questions. We could ask, for
example: What other components and factors would be relevant
H. DE LA FUENTE ET AL.
Moran variables of educational quality.
Indicator I Moran
Teacher evaluation 0.9554
Student-teacher ratio 0.9531
to the performance of a full diagnose that was the basis of a
solid spatial and sectoral planning? Are the gross enrolment
rates, the amount of square meters built, the computer resources
per facility, the origin of students or the transportation the way
to reach downtown···?
Without a doubt it would be of interest to know the distance
travelled (such as average, maximum and minimum distances
and typical deviations), point of origin and destination of the
students in order to allow drawing spider-maps for the different
municipalities and kind of school (per type of financing and/or
educational quality indices) and establish, thus, the deficits in
certain areas or the degree of competence among centers (Ta-
If the weight of private funding seems to be behind of an
important part of the unequal spatial distribution of the re-
sources and schools, it would be advisable to enquire into the
most appropriate way of establishing a correlation between
characteristics of the centers and the surrounding socioeco-
nomic conditions (Tolen, 2001).
Because the distribution pattern of the cities always locates
low socioeconomic strata in degraded sectors, it is precisely
those places which exhibit a greater amount of low quality
educational facilities. This highlights the presence of a socio-
spatial problem, much more complex than the shortcomings
presented by an educational facility, but closely related to the
recovering of social and economic gaps that originate inequali-
Undoubtedly, it is extremely difficult to establish a balance
between supply and demand of services established by the in-
habitants of a territory. However, the posed analyses even hav-
ing an exploratory nature conforms a useful tool for the territo-
rial planning, because educational facilities have in the city an
integrative and space structuring role (Salado, 2012).
The case of spatial equity as inspiring principle that pretends
that the whole population can have the same opportunities to
access an educational service or at lest, these opportunities are
excessively big, is truncated by the same public administration,
generating a differential accessibility by different population
groups, namely an unequal spatial distribution due to the con-
centration of good quality educational service in specific zones
of the CMA. By uncovering the socio-spatial inequality in the
CMA by means of the distribution of the educational facilities,
this kind of analysis can become a useful tool for urban plan-
ning, because facilities have an integrative and space structur-
ing role in the city. Educational institutions include organized
actions of scientific and professional nature in order to reach
the harmonic and sustainable development of the territory.
Therefore, we must consider diagnosis as the basis of the terri-
torial planning. This clarifies the past, present and future terri-
torial system features, as well as their possibilities of evolution
as a result of maintaining current conditions.
Therefore, as it has previously indicated, it becomes funda-
mental to carry out the analysis of the SIMCE results taking
Population and schools by commune, according to financing type.
Municipal Subsidized Particular
(inhabitants) Nº % Nº % Nº %
Concepción214.234 42 35.9 61 52.1 14 12.0117
Talcahuano150.881 37 52.9 31 44.3 2 2.970
San Pedro de
la Paz 121.655 10 23.3 28 65.1 5 11.643
Chiguayante84.880 10 23.3 27 62.8 6 14.043
Penco 46.261 1562.5 9 37.5 0 0.024
Tomé 54.508 3489.5 4 10.5 0 0.038
Coronel 108.855 27 48.2 29 51.8 0 0.056
Lota 48.687 15 55.6 12 44.4 0 0.027
Hualpén 92.530 1565.2 7 30.4 1 4.323
Hualqui 23.030 2278.6 6 21.4 0 0.028
Santa Juana13.201 2395.8 1 4.2 0 0.024
Note: Source: INE 2012 and MINEDUC data base, 2011.
into account the socioeconomic group, because it represents
one of the main variables associated to learning achievements
of the students.
The authors are grateful for funding provided by the Centro
de Desarrollo Urbano Sustentable (CEDEUS), Conicyt/Fondap/
This research has benefited from a collaboration within the
framework of the “TRANSendaNC” project, an International
Research Staff Exchange Scheme (IRSES) under the FP7 pro-
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