Sonia M. Bartolomei-Suárez Associate Dean of Academic Affairs, School of Engineering David González-Barreto Professor, Industrial Engineering Department.

Sonia M. Bartolomei-Suárez Associate Dean of Academic Affairs, School of Engineering

David González-Barreto Professor, Industrial Engineering Department

Antonio González-QuevedoProfessor, Civil Engineering and Surveying Department

University of Puerto Rico, Mayagüez04/18/23

Using an Expected Loss Function to Identify Best High Schools for

Recruitment

Outline• Introduction• Objectives• Description of Admission Criteria• Performance of our engineering students in their high

schools• Performance of the students at UPRM’s College of

Engineering• Definition of the Performance Index Using Quadratic Loss

Function• Conclusions• Future Work• References• Acknowledgement

Using an Expected Loss Function to Identify Best High Schools for Recruitment

Introduction– A study of our entering student profile demonstrates that a large

number of them come from the Western part of the island of Puerto Rico, our geographic region [1].

– The school of engineering is interested in attracting good students from all the geographic areas of Puerto Rico.

– With this goal in mind, this study was developed to identify the best schools in the island, based on the performance of the engineering students in our university.


Objectives– An objective of the strategic plan of the University of

Puerto Rico Mayagüez (UPRM) is to identify and attract the best possible prospective students from high schools to the College of Engineering.

– To address this objective a good first step is to identify the high schools that produce, over a period of years, the students that better executed within our institution.


Description of Admission Criteria– The admission index, which is called the IGS, is composed of the

high school grade point average, the verbal aptitude, and the mathematics aptitude tests scores from the College Board Entrance Examination.

– The highest possible value of the IGS is 400. – The weight of the GPA is 50%, while the weight for each of the

two aptitude tests is 25% each. – Each academic program determines each year the minimum value

of the IGS. – In general terms, no other measurement is used to admit a

student in the first year of university studies. For the engineer class of 2004-2005, the minimum IGS fluctuated from to 313 for Surveying to 342 for Computer Engineering.


Performance of our engineering students in their high schools

– First this study presents the best high schools, private and public, from the perspective of the student performance in their high schools.

– The high schools that were included in the study have sent more than 50 students who have graduated from our School of Engineering in the past ten years (1995-2005).

– This study was generated using data obtained from the Office of Institutional Research and Planning of our university.


Performance of our engineering students in their high schools

The high schools were analyzed based type of school (private or public) and:

– The number of graduates that entered at the UPRM’s College of Engineering during the years 1995-2005 (the top fifteen).

– The average admission index (IGS) for the graduates that entered at the UPRM’s College of Engineering during the years 1995-2005 (the top fifteen).


106

106

108

109

112

112

126

127

140

143

146

149

156

182

397

0 50 100 150 200 250 300 350 400 450

Ramón José Dávila, Coamo

Domingo Aponte Collazo, Lares

Secundaria UPR, Río Piedras

Dr. Carlos González, Aguada

Luis Muñoz Marin, Añasco

Benito Cerezo, Aguadilla

Lola Rodríguez de Tió, San Germán

Miguel Meléndez Muñoz, Cayey

Luis Muñoz Marin, Yauco

Blanca Malaret, Sabana Grande

University Gardens, Río Piedras

Efrain Sánchez Hidalgo, Moca

Eugenio María de Hostos, Mayagüez

Patria Latorre, San Sebastian

CROEM, Mayagüez

Esc

uela

s Púb

licas

Cantidad de Estudiantes


Figure 1. First 15 Public High Schools with 50 or more graduates at UPRM for the College of Engineering (Years 1995-2005).

77

82

86

87

88

88

90

90

96

117

121

122

145

182

262

0 50 100 150 200 250 300

Carvin School, Carolina

Colegio Evagélico Capitán Correa, Arecibo

Colegio San Carlos, Aguadilla

Colegio María Auxiliadora, Carolina

Colegio San Antonio Abad, Humacao

Academia Santa María, Ponce

Colegio San Agustín, Cabo Rojo

American Military, Guaynabo

Colegio Marista, Guaynabo

Colegio San Antonio, Río Piedras

Academia Discípulos de Cristo, Bayamón

Colegio San Ignacio, Río Piedras

Colegio San José, Río Piedras

Academia de la Inmaculada Concepción, Mayagüez

Notre Dame High School, Caguas

Esc

uela

s

Cantidad de Estudiantes


Figure 2. First 15 Private High Schools with 50 or more graduates at UPRM for the College of Engineering (Years 1995-2005).

336

336

336

337

337

337

337

337

338

339

339

340

340

340

341

341

333 334 335 336 337 338 339 340 341 342

Juan Antonio Corretjer, Ciales

Asunción Rodríguez, Guayanilla

Ponce High School, Ponce

Juan Quirindongo Morell, Vega Baja

Domingo Aponte Collazo, Lares

Patria Latorre, San Sebastían

Luis Muñoz Marin, Añasco

Eladio Tirado López, Aguada

Carmen Bozello de Huyke, Arroyo

Carmen Belén Veiga, Juana Díaz

University Gardens, Río Piedras

Emilio R. Delgado, Corozal

Leonídes Morales Rodríguez, Lajas

Ramón José Dávila, Coamo

Secundaria UPR, Río Piedras

Vocacional Antonio Lucchetti, Arecibo

Esc

uela

s Púb

licas

IGS


Figure 3. Public High Schools with the highest IGS for graduates of the School of Engineering within 1995-2005.

338

339

339

339

339

339

340

340

340

340

340

340

342

343

343

335 336 337 338 339 340 341 342 343 344

Colegio San Conrado, Ponce

Colegio San Antonio Abad, Humacao

Colegio Evagélico Capitán Correa, Arecibo

Colegio San José, Caguas

Academia Santa María, Ponce

Carvin School, Carolina

Colegio Marista, Guaynabo

Cupeyville School, Río Piedras

Academia de la Inmaculada Concepción, Mayagüez

Colegio Santo Tomás de Aquino, Bayamón

Colegio San José, Río Piedras

Notre Dame High School, Caguas

Colegio San Antonio, Río Piedras

Academia San José, Guaynabo

Colegio Ponceño

Esc

uela

s

IGS


Figure 4. Private High Schools with the highest IGS for graduates of the School of Engineering within 1995-2005.

Performance of the students at UPRM’s College of Engineering

• After identifying the high schools based on the performance of their students at the high school level, it was decided to analyze the high schools based on the performance of their students at the College of Engineering.

• The high schools were analyzed based on:- the time to complete a BS in engineering - the UPRM graduation grade point average (GPA) - the UPRM graduation rate


6.12

6.09

6.04

6.03

6.00

6.00

5.97

5.97

5.97

5.87

5.83

5.79

5.79

5.65

5.59

5.30 5.40 5.50 5.60 5.70 5.80 5.90 6.00 6.10 6.20

SAN GERMAN-LOLA RODZ DE TIO

YAUCO-LUIS MUNOZ MARIN

RIO PIEDRAS-UNIVERSITY GARDENS

AIBONITO-DR JOSE N. GANDARA

LARES-DOMINGO APONTE COLLAZO

AGUADILLA-BENITO CEREZO

JUANA DIAZ-CARMEN BELEN VEIGA

CAYEY-MIGUEL MELENDEZ MUNOZ

OROCOVIS-JOSE ROJAS CORTES

ARROYO-CARMEN BOZELLO DE HUYKE

HUMACAO-ANA ROQUE

SAN SEBASTIAN-PATRIA LATORRE

COAMO-RAMON JOSE DAVILA

CIDRA-ACADEMICA ANA J CANDELAS

RIO PIEDRAS-SECUNDARIA UPR

Escu

ela

s P

úb

licas

Tiempo Promedio


Figure 5. Top 15 public high schools with the lowest average time to complete the bachelor’s degree in engineering (1991-2006).

5.90

5.88

5.87

5.80

5.78

5.76

5.75

5.70

5.67

5.66

5.66

5.62

5.55

5.52

5.48

5.20 5.30 5.40 5.50 5.60 5.70 5.80 5.90 6.00

PONCE-ACAD SANTA MARIA

CAROLINA-CARVIN SCHOOL

RIO PIEDRAS-COL SAN JOSE

GUAYNABO-COL SAGRADOS CORAZONES

MAYAGUEZ-ACAD LA INMACULADA

CAGUAS-NOTRE DAME HIGH SCHOOL

RIO PIEDRAS-COL SAN IGNACIO

SAN GERMAN-COL SAN JOSE

AGUADILLA-COL SAN CARLOS

RIO PIEDRAS-COL SAN ANTONIO

CAGUAS-COL SAN JOSE

PONCE-COL PONCENO

RIO PIEDRAS-COL ESPIRITU SANTO

PONCE-COL SAN CONRADO

HUMACAO-COL SAN ANTONIO ABAD

Escu

ela

s P

rivad

as

Tiempo Promedio


Figure 6. Top 15 private high schools with the lowest average time to complete the bachelor’s degree in engineering (1991-2006).

3.00

3.01

3.01

3.02

3.03

3.04

3.04

3.04

3.04

3.05

3.05

3.06

3.07

3.13

3.22

2.85 2.90 2.95 3.00 3.05 3.10 3.15 3.20 3.25

ARROYO-CARMEN BOZELLO DE HUYKE

AIBONITO-DR JOSE N. GANDARA

SABANA GRANDE-BLANCA MALARET

CAYEY-MIGUEL MELENDEZ MUNOZ

MAYAGUEZ-CROEM

ANASCO-LUIS MUNOZ MARIN



HUMACAO-ANA ROQUE

MAYAGUEZ-JOSE DE DIEGO






Escu

ela

s P

úb

licas

GPA Promedio


Figure 7. Top fifteen public schools with highest UPRM Graduation Grade Point Average (GPA)for students from public high schools who entered the Faculty of Engineering (1991-2006).

3.04

3.04

3.04

3.04

3.05

3.06

3.07

3.08

3.09

3.12

3.15

3.19

3.20

3.21

3.21

3.22

3.23

2.90 2.95 3.00 3.05 3.10 3.15 3.20 3.25

CAROLINA-COL MARIA AUXILIADORA

GUAYNABO-AMERICAN MILITARY

PONCE-COL PONCENO

CABO ROJO-COL SAN AGUSTIN

ISABELA-COL SAN ANTONIO


CAROLINA-CARVIN SCHOOL


GUAYNABO-COL SAGRADOS CORAZONES

CAGUAS-COL SAN JOSE

SAN GERMAN-COL SAN JOSE





AGUADILLA-COL SAN CARLOS

RIO PIEDRAS-COL ESPIRITU SANTO

Escu

ela

s P

rivad

as

GPA Promedio


Figure 8. Top seventeen private schools with highest UPRM Graduation Grade Point Average (GPA)for students from private high schools who entered the Faculty of Engineering (1991-2006).

64.91

65.00

68.33

68.63

68.97

70.00

70.59

71.67

72.09

72.73

73.21

76.06

80.00

82.46

83.56

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00


SABANA GRANDE-BLANCA MALARET


CIDRA-ACADEMICA ANA J CANDELAS

OROCOVIS-JOSE ROJAS CORTES

HUMACAO-ANA ROQUE

MAYAGUEZ-CROEM


MAYAGUEZ-EUGENIO M DE HOSTOS



YAUCO-LUIS MUNOZ MARIN

MOCA-EFRAIN SANCHEZ HIDALGO



Es

cu

ela

s P

úb

lic

as

Tasa de Graduación


Figure 9. Top fifteen public high schools with the highest UPRM graduation rates for students who entered the School of Engineering in the cohorts of 1991-1997.

58.70

66.67

68.29

73.58

75.56

76.26

78.05

78.05

80.33

81.16

82.22

82.50

90.18

93.02

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00

CAROLINA-COL MARIA AUXILIADORA

GUAYNABO-AMERICAN MILITARY

BAYAMON-ACAD DISCIPULOS DE CRISTO

RIO PIEDRAS-COL SAN JOSE




ARECIBO-COL EVANG CAPITAN CORREA

RIO PIEDRAS-COL SAN IGNACIO

CABO ROJO-COL SAN AGUSTIN

BAYAMON-COL DE LA SALLE




Escu

ela

s P

rivad

as

Tasa Graduación


Figure 10. Top fourteen private high schools with the highest UPRM graduation ratesfor students who entered the School of Engineering in the cohorts of 1991-1997.

Performance of the students at UPRM’s College of Engineering

• Looking at the figures, we realized that the list of schools that meet the different criteria, were not the same.

• We saw a need to develop a function that include all the criteria. This function is based on the quadratic expected loss function.

• Therefore, these three indicators were combined to develop a performance index (PI) that will allow standard ratings of these high schools.


Definition of the Performance Index Using Quadratic Loss Function

– The concept of quadratic loss function has been proposed by Phadke [2] to approximate quality losses.

– One can develop a performance index (PI) to compare high schools through the execution of their students at the high level institutions.



– The quadratic loss function is given by

– Usually in quality control applications, a tolerance Δ is defined such that if the y characteristic is within T + Δ (two sided tolerance) the characteristic is acceptable.


Loss(y) = k (y – T)2 (1)

where k is a proportionality constant and T is the target value for the y characteristic.


– The quadratic loss function penalizes the behaviors that deviate from the target T.

– A challenge with the function is the definition of the constant k.

– Artiles-León [3] defined this value to assure that the loss function is not sensitive to the system of units used to measure the quality characteristic y.



– For the two sided tolerance problem this definition becomes: (2)

– Using k results in a “standardized” loss function. Since the standardized version of the loss function is dimensionless, if several quality characteristics are considered, their correspondent loss functions can be added.


2

2

2

k


– The quality characteristics or critical indicators that we are considering are:

• the average time to complete the BS degree

• the average graduation GPA

• the graduation rates for the high schools under consideration




• These characteristics are not suited for the two sided tolerance approach.

• The first one, average time to degree, can be described better as an smaller-the-better characteristic, while the other two average GPA, and graduation rate of a higher-the-better characteristic form.

• Expanding the standardized concepts to one-sided tolerance characteristics the following two equations can be derived for smaller-the-better (3) and higher-the-better (4).

(3)

(4)

2

2

)(

y

ySLoss

2

2

)(y

ySLoss


Definition of the Performance Index Using Quadratic Loss Function• A total standardized loss (TSLoss) for our case study can be defined

as:

(5)

where yi, and Δi corresponds to the characteristic and tolerance for the critical indicators.

23

23

22

22

21

21

yy

yTSLoss

Table 1. Ratings of High Schools Basedon Performance of Index


High School Performance Index

Colegio San Conrado, Ponce 3.250182

Academia de la Inmaculada Concepción, Mayagüez 3.376351

Secundaria UPR, Río Piedras 3.569336

Colegio San Antonio Abad, Humacao 3.737924

Patria Latorre, San Sebastian 3.74815

Academia Santa María, Ponce 3.796827

Colegio San Antonio, Río Piedras 3.893357

Notre Dame High School, Caguas 3.995966

Ramón José Dávila, Coamo 4.195212

Benito Cerezo, Aguadilla 4.237077

University Gardens, Río Piedras 4.326681

Ana Roque, Humacao 4.376365

Lola Rodríguez de Tió, San Germán 4.440817

Domingo Aponte Collazo, Lares 4.711063

Conclusions– Identifying the best high schools in the country allows

us to fulfill our mission of attracting the best possible prospective students to the College of Engineering.

– This is only a first step in fulfilling our mission. There are other strategies that we have to develop to enroll the best students.

– The loss function provides a scientific way to combine different criterion of performance to identify the best schools.


Future Work

– The suggested performance index, based on the TSLoss, should include additional critical indicators.

– We suggest exploring the following indicators, average GPA in math courses, average GPA in science courses, average GPA in language courses, attempted credits, among others.

– A limitation of the described performance index is that it does not take into account the correlations among the critical indicators variables considered.

– Techniques such as the Mahalanobis Distance to incorporate such relationships should be considered.


References

[1] González-Barreto, D. and González-Quevedo, A.,“Attracting a More Diverse Student Population to the School of Engineering of the University of Puerto Rico at Mayagüez”, Proceedings of the 9th International Conference on Engineering Education. July 23-28, 2006. San Juan, PR, pp. R4E21, R4B25.

[2] Phadke, M. S., Quality Engineering using Robust Design, Prentice-Hall, Englewood Cliffs, NJ, 1989.

[3] Artiles-León, N., “A Pragmatic Approach to Multiple-Response Problems using Loss Functions”, Quality Engineering, 9,2, 1996-1997, pp. 213-220.


Acknowledgement

The authors want to acknowledge the assistance provided by Leo I. Vélez and Irmannette Torres from the Office of Institutional Research and Planning of the University of Puerto Rico at Mayagüez for providing and validating the data used in this study.



Sonia M. Bartolomei-Suárez Associate Dean of Academic Affairs, School of Engineering David González-Barreto Professor, Industrial Engineering Department.

Documents

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high schools performance

best schools

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expected loss function

civil engineering

recruitment slide

computer engineering