Ratio Mathematica Volume 42, 2022

The AHPSort II to evaluate the High-level
instruction performances

Gerarda Fattoruso*
Paola Mancini†

Gabriella Marcarelli‡

Abstract

This paper proposes a model for ranking Italian high schools based on sev-
eral performance outputs. To analyze the performance of Italian public High
Schools we consider the students’ school performance and their academic
achievements; also the school characteristics may influence the performance
evaluation of high schools, although the importance of these aspects is cer-
tainly less than the results achieved by students. Data are from Eduscopio
and ScuolaInChiaro portals and refers to the 2019/20 school year. We an-
alyze a sample of 263 high schools (HS) in all Italian Regions. For each
school we consider nine outputs related to students’ school and academic
performance, and school characteristics. We assess the performance of high
schools using a multi-criteria approach. Our analysis involves a high number
of schools, so we apply the AHPSort II method which in addition to defining
the ranking of schools also defines their classification. Our results show that
scientific lyceums are all in the first class regardless of the geographic area.
Keywords: school ranking; academic performance; students’ achievements;
AHPSort II.
2020 AMS subject classifications: 90 Operations research, mathematical
programming. 1

*Corresponding author: University of Sannio, Benevento, Italy and NEOMA BS, Rouen,
France; fattoruso@unisannio.it.

†University of Sannio, Benevento, Italy; paola.mancini@unisannio.it
‡University of Sannio, Benevento, Italy; gabriella.marcarelli@unisannio.it

1Received on May 3rd, 2022. Accepted on June 12nd, 2022. Published on June 30th, 2022. doi:
10.23755/rm.v41i0.809. ISSN: 1592-7415. eISSN: 2282-8214. ©Fattoruso et al. This paper is
published under the CC-BY licence agreement.

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G. Fattoruso, P. Mancini, G. Marcarelli

1 Introduction

This paper focuses on the evaluation of Italian high schools’ performance.
In Italy, Eduscopio (Giovanni Agnelli Foundation) and ScuolaInChiaro (Ministry
of Education) represent important sources of information for such an evaluation;
they provide annually, for each school, data on students’ school careers, their aca-
demic achievements and school characteristics. In particular, Eduscopio provides
students’ and their families with a ranking of high school in the area of residence
based on university performance of school leavers; ScuolaInChiaro makes avail-
able to the community all the information relating to Italian schools of all levels,
in an organic and structured form.
This paper aims to provide the ranking of Italian high schools, taking into ac-
count the school and academic careers of students as well as the characteristics
of the school. The multi-criteria approach may be a useful tool to assess the per-
formance of high schools. By considering the above datasets, [Mancini and Mar-
carelli, 2019] derived the ranking among the typologies of schools; more recently,
[Mancini and Marcarelli, 2022] provide a ranking among the school types both
at a national level and within each geographic area. Furthermore, applying the
AHP method and comparing the results with those obtained by a further MCDM
method, PROMETHEE, they found significant differences between HS according
to criteria related to school and academic performance both within and between
geographic areas. Many studies have dealt with the application of multi-criteria
methods in the field of education [Giannoulis and Ishizaka, 2010, Goztepe, 2020,
Mancini and Marcarelli, 2022, Stamenkovic et al., 2016].
By taking into account some performance indicators used by Eduscopio and Scuo-
laInChiaro and according to the approach proposed by [Mancini and Marcarelli,
2022, 2019], this study analyzes nine performance outputs for a sample of 263
Italian high schools. However, unlike [Mancini and Marcarelli, 2022, 2019] in
which the schools were grouped into 6 different types of schools and 3 geographic
areas, we provide the ranking among all the schools. Due to the characteristics of
the problem (e.g., independence among the elements, the high number of alter-
natives) and the output required, among multi-criteria methods proposed in the
literature, this paper focuses on the Analytic Hierarchy Process Sort II (AHPSort
II) method. The available data allows us to avoid some disadvantages of the AHP.
There is no inconsistency in the judgment matrices because entries of matrices are
ratios between performance indices. Furthermore, the AHPSort II allows to an-
alyze a sorting decision problem through a feasible interaction with the decision
makers precisely because it foresees a limited number of interactions. The goal of
this paper is to obtain a ranking of high schools in Italy (we consider 251 schools
in our study) by sorting them into ordered classes.
Finally, in order to verify the impact (role) of the geographical and/or the school

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The AHPSort II to evaluate the High-level instruction performances

typology factors on the performance of a school, we compare our results with
those obtained by [Mancini and Marcarelli, 2022, 2019].

The paper is organized as follows: Section 2 reports a literature overview on
the topic; Section 3 defines the methodology; Section 4 reports the case study
and the main results; Sections 5 and 6 provide a discussion and some concluding
remarks, respectively.

2 Literature overview

The literature on school ranking is vast. Past studies have mainly focused on
the school quality and its student achievements [Eide and Showalter, 1998], some
other on school’s contribution to student academic performance [Jamelske, 2009,
Kelly and Downey, 2010] or on the question of “school accountability” affecting
the school choice [Burgess et al., 2013, Hart and Figlio, 2015, Nunes et al., 2018].
Many factors may influence students’ achievements, such as their socioeconomic
status, family background, geographical area of residence and the type of school
attended [Agasisti and Murtinu, 2012, Lauer, 2003] as far as school and class size,
students’ features and school management and resources [Giambona and Porcu,
2018, Masci et al., 2018]. As regards the impact of secondary school on academic
performance, recently, Aina et al. [2011] and Aina et al. [2021] have demonstrated
that differences in university students’ achievements across high schools cannot be
limited to the first-year and have to consider the geographic differences. In recent
study, several authors used multi-criteria methods for analysed school ranking and
their performance. Bana e Costa and Oliveira [2012] use the Measuring Attrac-
tiveness by a Categorical Based Evaluation Technique (MACBETH) which allows
a multi-criteria evaluation of the different scientific areas within high schools in
order to offer an accurate evaluation for each range of activities proposed by the
school. Blasco-Blasco et al. [2021] analyze the performance of high schools with
a particular focus on student achievement indicators. The authors analyze the
student support policies of the schools with the use of Technique for Others Pref-
erence by Similarity to Ideal Solution (TOPSIS). Yendra et al. [2018] also use
TOPSIS integrated with AHP for the analysis of the quality of the training offer
of the high school and higher level. Recently, Mancini and Marcarelli [2019] an-
alyzed the performance of Italian high schools, and derived a ranking among dif-
ferent typologies of schools based on the students’ academic achievements, their
school performance and the school characteristics. Then, Mancini and Marcarelli
[2022] made an in-deep analysis taking into account the geographic areas. Using
AHP and Promethee methods they derive a ranking among the school typologies
both at a national level and within each geographic area.

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G. Fattoruso, P. Mancini, G. Marcarelli

3 Methodology
AHPSort II is a Multi-Criteria Decision Analysis (MCDA) method for solving

sorting problems. This method allows you to use several criteria and a very large
number of alternatives [Ishizaka et al., 2012]. Furthermore, it is a method that
provides for a limited interaction with the decision maker [Fattoruso et al., 2022].
The procedure can be repeated or easily automated. The AHPSort II method
is described below. We consider a set of alternatives A=(a1, . . . , ai) evaluated
respect a set of criteria G=(g1, . . . , gj); therefore, gj(ai) represents the evaluation
of alternative ai on criterion gj. Moreover, we consider a set of classes C=(C1, . . . ,
Co); the construction of the classes requires the definition by the Decision Maker
(DM) of the limiting profiles lpij or of the central profiles cpij for each considered
gj criterion [Ishizaka et al., 2020]. The lpij are defined by the DM when he is able
to clearly separate the classes from each other, therefore they represent thresholds
that separate the classes from each other; alternatively, when this is not possible,
the DM opts to define the cpij which represent the centroids of each class for all
the considered criteria. The AHPSort II allows you to analyze a large number
of alternatives by using representative profiles rpsj = (rp1j, . . . , rpsj). The rp
are points homogeneously distributed in the observed data for each gj criterion.
Once all the elements that constitute the decision problem have been defined,
AHPSort II foresees the evaluation of local priorities: wj for gj; psj for rpsj; and,
poj alternatively for lpij or cpij. The local priorities are determined using Pairwise
Comparison Matrices (PCMs) with the eigenvalue method [Ishizaka et al., 2020].
The determination of the local priority of the alternatives pij is instead defined
through the following linear interpolation formula:

pij = psj +
ps+1j − psj
rps+1j − rpsj

· (gj(ai) − rpsj). (1)

The global priority of the alternative ai is defined as follow:

pi =
J∑

j=1

pij · wj. (2)

while the global priority pk of lpij or cpij is defined as:

pk =
J∑

j=1

poj · wj (3)

The sorting of ai to a C class takes place considering the final global priority;
therefore, considering the proximity of pi to pk.

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The AHPSort II to evaluate the High-level instruction performances

4 Case study

4.1 Data
Our case study concerns the evaluation of the performance of schools in Italy.

In particular, our reference sample is composed of 56 scientific lyceums (SL),
38 classical high schools (CL), 39 linguistic high schools (LL), 26 high schools
of human sciences (HSL), 43 commercial technical high schools (CTHS), 49
High School Technological Technician (TTHS). Figure 1 shows the percentage
of schools considered in this study divided by typology.

Figure 1: Typologies of high schools in Italy

Each school is evaluated against criteria that determine the performance of the
school among these are: Maturity score (g1) defined as the weighted average score
between the high school graduation score of enrolled students e non-enrolled stu-
dents; INVALSI test score (g2) defined as the average of each student’s math,
reading and foreign language test scores; Percentage of graduates in good stand-
ing (without failures) (g3); Students enrolled in the academic year (g4). In addition
to the school performance criteria, schools are evaluated for the academic perfor-
mance of their students; this type of criteria include: the percentage of students
who pass the first year (g5); percentage of academic credits achieved at the end
of the first year (g6); average exam score (g7). Finally, the evaluation of schools
also takes into account criteria that consider the characteristics of each school,
including the average number of students per class (g8) and the percentage of
teachers employed part-time (g9). The data was collected by the Eduscopio and
ScuolaInChiaro portals for the 2019-2020 academic year.

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4.2 Results
In our paper we consider a set of alternatives A = (a1, . . . , a251) evaluated

respect the criteria set G = (g1, . . . , g9); the evaluation table of gj(ai) is reported
in Appendix A.

The decision-makers involved in the construction of our study are school man-
agers of the different typology of schools considered which from here on we will
generically call DMs.

We report in Table 1 the weights wj of criteria defined with the eigenvalue
method.

g1 g2 g3 g4 g5 g6 g7 g8 g9
wj 0,10 0,15 0,10 0,10 0,15 0,15 0,15 0,05 0,05

Table 1: Criteria weights wj

For each gj criterion considered, we have defined three priority classes C1,
C2 and C3 to which we have associated for simplicity the labels of LOW (C1),
MEDIUM (C2), and HIGH (C3). Classes define the performance of high schools.
Therefore in the High (C3) the schools with the best performances will be sorted,
in the Low class (C1) those with the worst performances. In Table 2, we report the
central profiles cpij defined by the DMs, for each class C and each criterion gj.

g1 g2 g3 g4 g5 g6 g7 g8 g9
Low (C1) 65,79 1 17,4 0,33 0,2 21,26 20 10 1
Medium (C2) 75,71 4 53,8 0,64 0,55 54,4 24,44 19 26,14
High (C3) 80 6 80 0,8 0,8 80 28 26 50

Table 2: Central profiles cpij for each criterion gj

As suggested by Abastante et al. [2019], we have built the reference profiles
rpsj = (rp1j, . . . , rp6j). We report in Table 3 the rpsj for each criterion gj.

g1 g2 g3 g4 g5 g6 g7 g8 g9
rp1j 0 0 0 0 0 0 0 0 0
rp2j 17,12 1,4 18,04 0,192 0,18 17,50 4 5,6 10,25
rp3j 34,25 2,8 36,08 0,384 0,36 35,01 8 11,2 20,51
rp4j 51,38 4,2 54,12 0,576 0,54 52,52 12 16,8 30,77
rp5j 68,50 5,6 72,16 0,768 0,72 70,03 16 22,4 41,03
rp6j 85,63 7 90,2 0,96 0,9 87,54 20 28 51,29

Table 3: Reference profiles rpsj for each criterion gj

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Moreover, we have defined in Table 4 the local priorities psj and in Table 5 the
local priorities poj.

ps1 ps2 ps3 ps4 ps5 ps6 ps7 ps8 ps9
rp1j 0,020 0,032 0,030 0,025 0,023 0,022 0,027 0,023 0,030
rp2j 0,031 0,045 0,043 0,038 0,034 0,034 0,038 0,034 0,042
rp3j 0,041 0,058 0,054 0,067 0,063 0,059 0,051 0,062 0,055
rp4j 0,069 0,090 0,092 0,088 0,089 0,087 0,065 0,085 0,090
rp5j 0,104 0,197 0,187 0,155 0,147 0,156 0,086 0,150 0,154
rp6j 0,280 0,234 0,259 0,267 0,297 0,298 0,128 0,300 0,261

Table 4: Local priorities psj

po1 po2 po3 po4 po5 po6 po7 po8 po9
C1 0,084 0,036 0,033 0,046 0,045 0,042 0,128 0,042 0,032
C2 0,174 0,091 0,083 0,108 0,104 0,102 0,193 0,103 0,084
C3 0,196 0,217 0,218 0,205 0,198 0,198 0,282 0,200 0,252

Table 5: Local priorities poj

After, define the local priority pij with the use of (1), we calculate the global
priority pi. In Figure 2, in Appendix, we report the ranking of the high school.

Finally, we obtained the classification of the high schools in terms of perfor-
mance; the results are shown in Table 6.

North Center South Italy
High 27 26 23 76
Medium 57 52 60 169
Low 2 3 1 6

Table 6: Schools performance sorted in geographical areas

In Figure 3, in Appendix, it’s shown how the different typologies of high
schools have been sorted into the different performance classes.

5 Discussion
As shown by the results obtained, it emerges that the schools that obtain the

best performance throughout Italy are the SLs and the CLs with the best positions
for those in the south follow. A portion of CL is positioned in medium-sized per-
formances mainly in northern and central Italy. In the medium classes the LL,

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HSL, CTHS and TTHS converge in order. A few CL from the north, south and
center are included in the performance of the lower class. SL have the best perfor-
mance regardless of the geographical area. Moving from North to South the first
class is almost exclusively composed by SL, in the North, by a great number of SL
and a few CL, in the Center, and fifty-fifty by SL and CL, in the South. Comparing
the results with those obtained by Mancini and Marcarelli [2019] and Mancini and
Marcarelli [2022], an inversion of ordering emerges in the first positions between
SL and CL. The other positions are confirmed. It should be noted that in the works
of Mancini and Marcarelli [2019] and Mancini and Marcarelli [2022] the initial
data are represented by the average performance values by type of school for each
criterion considered. In this paper, however, the performances are evaluated for
individual schools. In this sense, the difference in the overall results may be due
to the influence of anomalous values in the calculation of the average values by
type of school. For a more detailed comparison, we also checked the ranking of
schools for each criterion. Figure 4, in Appendix, shows in particular the ranking
of the SL and CL for each criterion, geographical area and class considered. As
can be seen in the Figure 4, SLs obtain higher performances for all the criteria
except for the g3 criterion for the CLs of northern Italy.

6 Conclusions
This paper investigates the performance of Italian high schools in order to de-

rive a ranking considering the typology and the geographic area. Using AHPSort
II, we obtain a classification of Italian high schools into different categories. The
results show that the ranking among the types of schools does not vary moving
from North to South: scientific lyceums are all in the first class regardless the
geographic area. However, the limit of this work is the lack of a model valida-
tion. The model may assist students in selecting the type of school to attend; the
information makes it possible to make an appropriate choice according to their
academic perspectives.

Our future works will address a comparative analysis to test the model pro-
posed: ELECTRE TRI [Corrente et al., 2016] may provide a classification of
high schools into different categories such as ‘over-performing schools’, ‘average-
performing schools’ and ‘weak-performing schools’; then we may compare re-
sults with those obtained by our model. Furthermore, if the decision makers are
not sure about the correct level of reference profiles, it could be interesting to per-
form a sensitivity analysis with several limiting profiles to test the robustness of
the process. Finally, when applied to small territorial districts, our model may be a
useful tool to help public administrations distribute additional financial resources
to public schools based on their performance rank.

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The AHPSort II to evaluate the High-level instruction performances

Declarations
Conflict of interest . The authors declare that they have no conflict of interest.

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T S Area g1 g2 g3 g4 g5 g6 g7 g8 g9
SL a1 North 80,20 6 61,9 0,94 0,88 80,2 27,33 27 9,7
SL a2 North 78,61 3 67,9 0,90 0,80 74,6 26,62 21 18,7
SL a3 North 76,47 4 59,2 0,90 0,81 69,1 25,89 23 16,3
SL a4 North 74,87 4 59,2 0,92 0,74 48,2 24,91 24 27,2
SL a5 North 72,85 4 38,0 0,83 0,68 52,4 24,07 24 25,2
SL a6 North 77,94 7 65,6 0,94 0,89 87,2 28,62 26 16,3
SL a7 North 80,68 7 59,3 0,93 0,87 85,6 28,62 23 7,8
SL a8 North 77,29 6 62,8 0,95 0,89 82,0 27,57 26 11,7
SL a9 North 75,02 4 59,1 0,93 0,84 74,2 26,20 22 14,5
SL a10 North 75,70 4 40,7 0,88 0,76 67,1 25,02 21 17,3
SL a11 North 72,22 4 44,0 0,91 0,80 66,5 24,73 22 23,7
SL a12 North 70,66 4 46,9 0,78 0,61 46,3 25,53 21 27,7
SL a13 North 78,54 3 68,2 0,92 0,86 75,8 27,09 22 24,6
SL a14 North 76,10 5 67,6 0,87 0,79 67,6 26,55 21 5,8
SL a15 North 78,91 7 69,1 0,94 0,90 87,5 28,81 22 12,2
SL a16 North 76,66 4 52,1 0,92 0,84 75,8 26,71 24 11,7
SL a17 North 68,76 4 37,7 0,86 0,72 55,7 23,56 22 39,0
SL a18 North 79,52 5 74,6 0,93 0,90 87,2 28,89 24 22,3
SL a19 North 75,18 5 57,4 0,91 0,86 76,1 27,51 19 38,5
SL a20 North 75,54 4 46,3 0,92 0,84 62,6 25,04 23 11,8
SL a21 Center 81,37 5 70,3 0,84 0,80 77,2 27,61 22 14,3
SL a22 Center 78,38 6 62,9 0,93 0,86 72,1 26,81 23 19,8
SL a23 Center 78,03 4 60,0 0,90 0,83 70,7 26,59 21 20,6
SL a24 Center 80,23 6 76,6 0,93 0,87 76,7 27,92 25 6,2
SL a25 Center 81,64 5 72,6 0,92 0,85 71,5 27,57 20 17,9
SL a26 Center 81,01 6 56,3 0,90 0,84 82,7 28,47 25 7,1
SL a27 Center 77,34 5 56,6 0,93 0,86 78,1 27,59 22 7,5
SL a28 Center 77,44 3 65,4 0,90 0,81 76,6 27,51 24 10,6
SL a29 Center 77,35 5 60,2 0,93 0,86 77,4 27,10 24 16,7
SL a30 Center 77,78 2 62,4 0,91 0,82 71,3 26,56 23 15,6
SL a31 Center 78,45 6 65,8 0,91 0,83 73,1 26,27 23 23,0
SL a32 Center 76,15 6 66,1 0,90 0,81 73,5 26,21 22 12,9
SL a33 Center 77,36 5 57,1 0,91 0,85 73,0 26,01 23 7,6
SL a34 Center 77,11 2 49,9 0,90 0,76 71,1 26,15 24 20,5
SL a35 Center 73,94 5 53,1 0,84 0,71 56,1 24,99 24 20,5
SL a36 Center 77,02 3 59,9 0,89 0,76 64,3 25,18 22 9,7
SL a37 Center 75,24 3 53,2 0,80 0,68 55,0 25,33 22 18,2
SL a38 Center 75,8 4 65,1 0,88 0,74 59,9 25,23 23 18,1
SL a39 South 81,32 4 76,9 0,90 0,81 66,7 25,87 22 9,6
SL a40 South 82,01 6 74,6 0,93 0,85 68,4 26,09 22 4,9

Appendix A

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T S Area g1 g2 g3 g4 g5 g6 g7 g8 g9
SL a41 South 77,97 5 66,1 0,94 0,84 74,9 28,12 18 16,7
SL a42 South 81,79 5 57,1 0,93 0,87 80,0 27,29 24 6,8
SL a43 South 79,05 2 62,4 0,94 0,87 76,3 26,67 23 16,5
SL a44 South 78,65 6 61,1 0,90 0,75 61,6 25,44 21 3,4
SL a45 South 81,41 5 55,7 0,78 0,68 65,8 25,42 18 5,9
SL a46 South 79,16 6 59,2 0,89 0,79 68,3 25,95 22 10,0
SL a47 South 79,86 2 52,6 0,87 0,77 67,9 25,94 21 5,2
SL a48 South 74,06 3 20,6 0,80 0,60 43,3 22,65 14 21,2
SL a49 South 81,07 4 84,6 0,93 0,85 74,9 26,15 27 2,7
SL a50 South 79,60 2 61,7 0,96 0,87 68,9 25,57 23 10,0
SL a51 South 82,32 5 77,9 0,93 0,85 74,1 25,89 21 4,3
SL a52 South 78,27 5 62,3 0,91 0,85 76,5 26,57 24 4,3
SL a53 South 77,21 4 50,5 0,83 0,79 69,4 25,18 21 6,4
SL a54 South 72,66 1 39,8 0,80 0,66 53,3 23,32 21 0,0
SL a55 South 78,94 4 51,3 0,91 0,84 74,5 26,88 20 9,9
SL a56 South 74,99 4 50,3 0,84 0,72 58,5 25,38 21 11,9
CL a57 North 78,96 6 66,9 0,95 0,86 75,0 28,31 22 16,9
CL a58 North 79,47 5 67,3 0,86 0,77 67,7 26,48 24 30,8
CL a59 North 79,26 6 61,9 0,93 0,88 80,2 27,89 24 14,0
CL a60 North 79,90 6 68,2 0,94 0,88 78,5 28,41 22 10,1
CL a61 North 74,10 5 55,5 0,91 0,81 64,8 26,41 23 34,4
CL a62 North 65,79 2 73,3 0,86 0,73 55,1 26,08 19 25,0
CL a63 North 75,87 3 74,6 0,88 0,80 66,8 26,88 22 24,6
CL a64 North 80,86 4 65,3 0,87 0,79 68,9 27,76 21 14,7
CL a65 North 80,55 5 72,2 0,95 0,88 72,7 27,73 21 29,6
CL a66 North 78,82 5 68,8 0,92 0,84 64,6 26,63 22 21,2
CL a67 North 79,53 6 72,7 0,93 0,87 71,3 28,29 23 7,7
CL a68 Center 81,30 6 60,1 0,92 0,84 71,4 28,27 21 24,6
CL a69 Center 79,34 5 69,4 0,91 0,82 60,3 26,98 22 14,3
CL a70 Center 83,12 7 75,9 0,92 0,86 67,7 26,80 24 7,0
CL a71 Center 84,57 6 88,5 0,95 0,86 65,8 27,62 23 31,9
CL a72 Center 81,25 6 59,4 0,92 0,85 76,0 28,86 24 13,3
CL a73 Center 78,85 6 62,6 0,90 0,85 73,1 28,23 24 7,0
CL a74 Center 82,45 6 73,9 0,93 0,86 78,5 27,54 23 8,6
CL a75 Center 82,77 3 62,6 0,95 0,82 69,3 27,28 23 8,6
CL a76 Center 82,4 4 64,4 0,87 0,77 68,5 27,19 23 13,1
CL a77 Center 81,29 2 72,4 0,93 0,83 69,5 27,07 23 15,0
CL a78 Center 81,41 2 78,9 0,79 0,74 56,7 25,80 23 15,5
CL a79 Center 80,06 2 66,5 0,90 0,77 55,2 25,09 23 20,8
CL a80 Center 75,70 3 67,5 0,86 0,71 50,7 24,62 23 15,8

295



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T S Area g1 g2 g3 g4 g5 g6 g7 g8 g9
CL a81 Center 81,39 4 83,9 0,95 0,90 66,2 27,06 23 5,4
CL a82 South 83,77 5 90,2 0,95 0,88 68,0 26,30 22 8,5
CL a83 South 83,78 5 72,2 0,94 0,87 80,0 27,77 25 9,9
CL a84 South 81,21 6 78,3 0,95 0,89 77,3 27,41 22 6,8
CL a85 South 79,67 6 57,1 0,88 0,74 68,7 26,36 21 3,4
CL a86 South 74,90 3 73,0 0,83 0,68 55,9 25,83 19 12,4
CL a87 South 79,90 3 80,5 0,76 0,62 42,3 25,69 23 26,4
CL a88 South 82,55 6 83,4 0,91 0,83 67,4 26,12 23 0,0
CL a89 South 85,2 4 80,0 0,96 0,82 60,5 26,23 14 3,7
CL a90 South 84,13 5 86,7 0,93 0,84 63,0 24,70 20 3,2
CL a91 South 80,54 5 71,3 0,88 0,80 69,4 26,63 22 3,4
CL a92 South 79,32 5 63,30 0,75 0,62 53,0 24,78 17 23,0
CL a93 South 81,20 3 67,5 0,88 0,79 64,4 26,71 19 2,7
CL a94 South 77,03 3 45,6 0,84 0,73 46,8 23,38 19 14,4
LL a95 North 80,33 5 50,8 0,86 0,77 66,3 26,31 23 0,0
LL a96 North 77,98 4 55,4 0,78 0,72 58,6 25,08 19 11,1
LL a97 North 73,42 6 63,7 0,7 0,56 41,0 24,09 22 37,2
LL a98 North 75,23 4 59,5 0,83 0,76 69,9 26,06 23 10,8
LL a99 North 76,91 7 75,4 0,78 0,74 64,0 25,46 23 11,6
LL a100 North 73,4 4 40,6 0,75 0,65 40,6 24,12 21 27,7
LL a101 North 78,8 3 53,5 0,78 0,63 48,2 24,04 21 33,8
LL a102 North 78,78 4 67,6 0,76 0,70 65,0 24,15 24 20,8
LL a103 North 79,1 4 64,8 0,8 0,71 61,4 26,39 21 14,7
LL a104 North 80,05 4 70,3 0,73 0,61 51,3 24,05 24 7,4
LL a105 North 82,81 4 77,9 0,78 0,74 73,6 26,19 24 21,1
LL a106 North 78,27 3 54,4 0,75 0,64 50,8 24,96 23 17,2
LL a107 Center 81,49 5 66,4 0,79 0,71 64,9 26,87 22 14,3
LL a108 Center 78,25 5 44,3 0,74 0,66 54,9 25,73 22 12,5
LL a109 Center 75,69 3 35,3 0,63 0,50 43,5 25,54 20 25,8
LL a110 Center 80,3 4 63,5 0,72 0,64 59,0 25,22 23 4,5
LL a111 Center 78,86 5 60,0 0,74 0,65 55,2 24,93 20 17,9
LL a112 Center 80,25 3 56,0 0,79 0,71 62,2 26,00 23 15,8
LL a113 Center 76,92 6 52,5 0,72 0,66 64,6 25,49 23 14,66
LL a114 Center 76,42 4 56,1 0,73 0,65 67,9 24,78 21 13,01
LL a115 Center 82,52 4 66,7 0,8 0,62 53,3 25,33 24 20,95
LL a116 Center 76,91 4 70,8 0,76 0,63 52,7 24,63 23 16,13
LL a117 Center 78,09 6 63,0 0,67 0,56 54,2 25,27 24 26,35
LL a118 Center 75,51 4 47,3 0,71 0,60 44,9 23,91 22 28,24
LL a119 Center 73,76 3 55,2 0,7 0,55 37,1 24,55 21 23,36
LL a120 Center 74,28 3 41,8 0,64 0,51 41,4 23,01 20 26,32

296



The AHPSort II to evaluate the High-level instruction performances

T S Area g1 g2 g3 g4 g5 g6 g7 g8 g9
LL a121 Center 79,18 4 69,4 0,72 0,64 53,9 24,88 23 5,41
LL a122 South 80,26 5 67,8 0,77 0,75 74,8 25,95 22 9,17
LL a123 South 79,24 4 74,5 0,86 0,78 64,3 26,10 21 13,73
LL a124 South 80,25 3 39,6 0,72 0,67 67,6 25,53 22 7,95
LL a125 South 78,5 4 54,6 0,8 0,66 51,3 25,82 28 3,97
LL a126 South 79,12 3 60,0 0,7 0,58 56,8 24,71 22 13,43
LL a127 South 72,71 4 30,0 0,52 0,41 37,8 24,12 20 2,70
LL a128 South 81,31 5 40,0 0,56 0,44 40,5 23,43 18 5,94
LL a129 South 76,84 4 54,7 0,49 0,35 43,0 25,21 16 4,23
LL a130 South 78,93 5 62,9 0,83 0,72 53,4 24,27 20 6,67
LL a131 South 85,63 6 71,3 0,76 0,72 61,1 24,97 20 7,29
LL a132 South 78,32 3 67,3 0,52 0,49 69,8 24,12 21 19,72
LL a133 South 74,38 4 41,3 0,56 0,47 40,9 23,39 18 29,89

HSL a134 North 78,25 5 63,9 0,76 0,65 55,8 24,11 19 18,62
HSL a135 North 76,15 4 65,0 0,76 0,59 39,8 23,62 23 27,2
HSL a136 North 75,85 4 46,7 0,75 0,65 62,2 25,74 23 24,81
HSL a137 North 75,31 4 68,0 0,84 0,64 37,4 23,04 21 28,57
HSL a138 North 72,69 4 59,5 0,61 0,52 53,3 24,46 24 20,8
HSL a139 North 73,27 3 46,2 0,71 0,56 46,7 24,60 19 26,94
HSL a140 North 76,43 4 51,7 0,73 0,69 59,6 24,48 23 11,8
HSL a141 North 73,01 2 47,0 0,76 0,65 46,5 24,43 22 36,80
HSL a142 Center 74,40 5 58,8 0,77 0,71 54,7 24,65 22 14,29
HSL a143 Center 77,24 4 59,5 0,77 0,67 50,9 24,37 23 4,5
HSL a144 Center 79,55 6 65,7 0,77 0,65 45,1 24,67 23 31,9
HSL a145 Center 75,58 4 64,2 0,8 0,68 52,2 24,70 23 16,13
HSL a146 Center 78,21 4 42,8 0,67 0,58 50,3 23,55 23 13,1
HSL a147 Center 73,24 4 56,6 0,69 0,59 52,1 23,40 22 28,24
HSL a148 Center 75,46 3 61,8 0,55 0,43 45,2 23,12 23 21,43
HSL a149 South 76,32 6 81,6 0,64 0,57 43,0 23,88 19 16,43
HSL a150 South 75,13 4 70,3 0,83 0,66 34,3 24,25 23 5,41
HSL a151 South 73,61 3 56,3 0,55 0,47 54,4 25,53 22 13,43
HSL a152 South 77,02 4 61,8 0,80 0,65 44,9 23,58 21 13,73
HSL a153 South 78,46 5 55,1 0,49 0,35 51,6 22,87 18 5,94
HSL a154 South 73,78 3 34,3 0,44 0,33 33,7 23,59 18 13,6
HSL a155 South 77,18 4 66,9 0,52 0,44 53,9 24,67 20 4,82
HSL a156 South 78,76 3 65,9 0,80 0,70 56,1 24,42 22 0,00
HSL a157 South 80,11 6 70,0 0,69 0,61 54,7 23,84 20 7,29
HSL a158 South 74,91 4 52,9 0,67 0,54 47,7 24,02 20 16,45
HSL a159 South 78,07 4 32,4 0,57 0,43 22,1 21,22 18 29,89

CTHS a160 North 72,22 5 42,4 0,51 0,41 43,6 24,14 19 18,62

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T S Area g1 g2 g3 g4 g5 g6 g7 g8 g9
CTHS a161 North 73,57 5 38,9 0,56 0,44 42,1 24,18 18 27,41
CTHS a162 North 73,75 3 32,1 0,50 0,42 44,1 22,47 19 23,97
CTHS a163 North 75,78 6 54,4 0,48 0,37 32,0 23,52 21 13,50
CTHS a164 North 74,27 3 27,2 0,42 0,36 61,0 24,47 21 22,92
CTHS a165 North 74,13 4 34,7 0,47 0,42 57,0 24,33 21 28,57
CTHS a166 North 74,98 4 37,0 0,45 0,34 52,0 23,41 21 27,71
CTHS a167 North 73,82 4 53,5 0,51 0,37 41,4 24,28 19 26,39
CTHS a168 North 71,55 2 35,0 0,52 0,40 35,2 22,30 21 22,22
CTHS a169 North 70,75 4 36,6 0,38 0,27 23,7 22,98 25 20,69
CTHS a170 North 76,60 2 60,1 0,39 0,33 47,9 24,13 20 12,96
CTHS a171 North 74,22 3 34,5 0,47 0,38 47,5 24,33 18 0,00
CTHS a172 North 74,99 4 58,3 0,61 0,50 54,5 23,94 24 7,41
CTHS a173 North 72,10 3 35,1 0,47 0,27 24,1 23,29 17 50,29
CTHS a174 North 74,51 5 55,1 0,55 0,45 58,5 24,02 21 38,5
CTHS a175 North 74,55 4 49,6 0,64 0,54 46,8 23,47 22 26,00
CTHS a176 Center 75,49 3 42,9 0,63 0,53 51,3 25,73 22 37,14
CTHS a177 Center 74,04 4 44,8 0,56 0,42 34,5 23,27 21 25,81
CTHS a178 Center 74,71 5 49,6 0,54 0,49 60,7 24,57 20 24,24
CTHS a179 Center 78,75 5 52,6 0,64 0,61 56,4 25,03 20 17,86
CTHS a180 Center 73,78 3 47,0 0,36 0,30 57,3 24,67 21 24,66
CTHS a181 Center 75,37 4 32,6 0,45 0,36 52,5 24,72 21 20,39
CTHS a182 Center 75,27 2 49,4 0,42 0,28 47,2 24,57 19 9,93
CTHS a183 Center 72,25 4 57,4 0,50 0,30 34,3 24,37 15 25,30
CTHS a184 Center 73,75 2 57,7 0,43 0,38 53,0 21,91 22 13,16
CTHS a185 Center 75,93 5 37,9 0,35 0,22 32,0 22,22 20 27,97
CTHS a186 Center 71,22 3 58,3 0,36 0,23 30,2 21,72 21 34,52
CTHS a187 Center 71,99 5 53,8 0,53 0,40 32,6 20,95 26 20,55
CTHS a188 Center 80,18 4 75,8 0,67 0,50 35,1 24,75 19 17,47
CTHS a189 South 73,81 3 61,5 0,47 0,42 53,8 24,17 20 11,82
CTHS a190 South 76,48 2 43,2 0,43 0,34 50,7 24,35 20 15,38
CTHS a191 South 74,61 4 27,2 0,43 0,33 44,5 23,95 20 16,67
CTHS a192 South 73,44 3 36,1 0,40 0,31 42,0 22,98 20 21,58
CTHS a193 South 75,22 3 50,4 0,38 0,29 36,8 23,24 22 10,58
CTHS a194 South 76,45 4 38,4 0,36 0,26 25,7 23,32 17 9,70
CTHS a195 South 69,12 2 33,8 0,38 0,26 31,0 20,00 15 0,00
CTHS a196 South 73,76 5 59,5 0,48 0,39 52,8 24,27 22 6,40
CTHS a197 South 76,97 4 49,9 0,53 0,43 52,7 23,90 20 9,40
CTHS a198 South 73,45 5 49,9 0,58 0,48 49,6 22,36 16 6,67
CTHS a199 South 76,37 5 62,0 0,49 0,42 47,4 22,60 18 17,20
CTHS a200 South 74,49 5 36,0 0,56 0,50 60,5 22,89 16 0,00

298



The AHPSort II to evaluate the High-level instruction performances

T S Area g1 g2 g3 g4 g5 g6 g7 g8 g9
CTHS a201 South 73,75 4 21,8 0,35 0,29 44,4 22,77 17 5,00
CTHS a202 South 74,72 4 31,3 0,49 0,37 36,1 23,14 17 4,39
TTHS a203 South 71,06 3 31,6 0,52 0,37 50,6 25,04 19 23,97
TTHS a204 North 71,6 4 32,0 0,45 0,36 55,0 24,15 23 27,23
TTHS a205 North 73,32 4 39,9 0,70 0,58 49,4 24,52 20 11,11
TTHS a206 North 73,78 4 37,1 0,36 0,27 35,7 22,47 22 29,81
TTHS a207 North 74,79 6 39,4 0,37 0,26 43,7 22,99 21 22,40
TTHS a208 North 74,99 4 36,5 0,77 0,67 68,8 25,97 21 27,69
TTHS a209 North 69,93 5 38,8 0,37 0,27 46,2 26,39 21 3,64
TTHS a210 North 67,97 4 30,3 0,41 0,35 58,4 24,64 19 28,28
TTHS a211 North 72,2 4 43,9 0,50 0,37 41,9 24,59 20 35,00
TTHS a212 North 70,51 5 26,8 0,48 0,35 51,3 23,42 21 17,65
TTHS a213 North 69,62 4 34,7 0,35 0,24 39,5 23,62 20 24,81
TTHS a214 North 70,55 4 52,4 0,36 0,20 30,4 25,26 19 26,39
TTHS a215 North 73,92 4 28,3 0,40 0,28 39,6 23,93 21 15,61
TTHS a216 North 76,79 6 48,4 0,65 0,57 64,6 26,16 23 23,26
TTHS a217 North 74,27 3 48,6 0,33 0,25 46,7 24,91 18 36,46
TTHS a218 North 79,65 6 73,2 0,37 0,24 42,4 24,86 10 40,38
TTHS a219 North 72,53 4 32,1 0,61 0,49 53,0 25,41 23 32,82
TTHS a220 North 73,00 3 55,6 0,45 0,32 39,3 25,17 18 23,40
TTHS a221 North 73,55 4 43,0 0,51 0,43 56,6 26,87 22 26,00
TTHS a222 North 74,49 4 39,5 0,44 0,37 60,1 25,41 22 29,72
TTHS a223 Center 71,38 4 30,2 0,43 0,37 62,1 25,65 21 21,71
TTHS a224 Center 73,81 3 33,8 0,49 0,38 47,4 24,36 21 25,84
TTHS a225 Center 73,48 6 39,4 0,44 0,30 39,9 23,52 20 10,29
TTHS a226 Center 77,89 3 41,9 0,68 0,59 53,5 24,47 19 20,00
TTHS a227 Center 75,76 4 54,8 0,58 0,47 52,7 25,36 18 28,42
TTHS a228 Center 71,09 3 46,0 0,33 0,23 48,9 26,39 19 8,85
TTHS a229 Center 72,35 4 45,8 0,50 0,38 52,4 25,59 16 19,53
TTHS a230 Center 73,03 3 28,3 0,45 0,33 54,7 24,67 22 24,66
TTHS a231 Center 70,88 3 47,9 0,53 0,36 33,7 24,48 20 36,36
TTHS a232 Center 72,64 3 30,7 0,41 0,29 38,4 23,84 20 20,35
TTHS a233 Center 71,8 5 46,1 0,50 0,32 40,4 23,50 20 11,67
TTHS a234 Center 68,81 5 31,8 0,33 0,21 36,9 23,11 21 18,60
TTHS a235 Center 73,21 5 50,5 0,42 0,24 26,1 22,66 19 25,81
TTHS a236 Center 70,51 3 23,8 0,37 0,31 49,5 23,32 18 8,48
TTHS a237 South 71,06 3 70,8 0,35 0,32 65,0 25,87 20 11,82
TTHS a238 South 79,55 3 46,7 0,51 0,44 70,8 24,43 20 21,58
TTHS a239 South 77,18 3 42,3 0,40 0,24 39,9 25,48 17 21,70
TTHS a240 South 77,84 5 48,4 0,36 0,23 43,3 24,63 19 14,86

299



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T S Area g1 g2 g3 g4 g5 g6 g7 g8 g9
TTHS a241 South 76,68 4 26,0 0,34 0,26 48,7 24,03 22 16,17
TTHS a242 South 74,62 3 31,7 0,63 0,47 48,5 23,42 16 6,06
TTHS a243 South 74,07 4 35,9 0,39 0,26 37,3 23,39 20 6,09
TTHS a244 South 80,27 3 24,5 0,47 0,27 41,5 21,07 18 21,24
TTHS a245 South 74,97 3 35,2 0,38 0,29 50,5 24,48 19 9,65
TTHS a246 South 72,50 4 40,8 0,48 0,39 54,3 24,08 17 0,73
TTHS a247 South 76,93 4 48,2 0,53 0,40 48,2 23,44 18 8,33
TTHS a248 South 71,41 3 25,8 0,34 0,29 49,8 26,01 19 9,33
TTHS a249 South 72,75 4 17,4 0,50 0,42 43,0 22,34 17 5,00
TTHS a250 South 75,08 5 24,7 0,36 0,30 58,6 23,12 16 27,91
TTHS a251 South 76,04 4 31,7 0,52 0,26 21,3 22,60 17 29,89

Table 7: Evaluation table of gj(ai).
Legend: T=Type; S=School; Area=Geo-position.

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The AHPSort II to evaluate the High-level instruction performances

Figure 2: Ranking of school defined by pi

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Figure 3: Performance of School sorted for typology and geographical areas

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The AHPSort II to evaluate the High-level instruction performances

Figure 4: Performance of SLs and CLs sorted for criteria and geographical areas

303