Using an Expected Loss Function to Identif Best High Schools for Recruitment Sonia M. Bartolomei-Suárez 1, David González-Barreto and Antonio A. González-Quevedo 3 Abstract - An objective of the strategic plan of the Universit of Puerto Rico Maagüez (UPRM) is to identif 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 identif the high schools that produce, over a period of ears, the students that better executed within our institution. The student performance (SP) at undergraduate level is currentl available in databases on the institutional research office. In this work, the SP is combined through indicators to develop an index per high school based on the performance of their students in UPRM College of Engineering. The performance index (PI) is based on the concept of the expected loss function. In this function the actual performance for each indicator is compared against an expected or targeted value. The PI includes the distance between the actual and the targeted performance for all defined indicators, thus the objective is to minimize this index. The better schools will results in indexes that are ver low, indicating ver good SP for their respective students. The PI is a tool that can be used both b the UPRM admission office and b high schools to do benchmarking among them. This paper presents a case stud for the high schools that suppl students to the UPRM engineering college for a period of six ears. The defined indicators for the case stud includes: graduation GPA, average time to degree, and graduation rate. Index Terms Prospective students, recruitment, performance index, loss function. INTRODUCTION value of the IGS is 400. The weight of the GPA is 50%, while the weight for each of the two aptitude tests is 5%. Each academic department or program determines each ear the minimum value of the IGS for the entering students. In general terms, no other measurement is used to admit a student in the first ear of universit studies. For the engineer class of 004-005, the minimum IGS fluctuated from to 313 for Surveing to 34 for Computer Engineering. PERFORMANCE OF OUR ENGINEERING STUDENTS IN THEIR HIGH SCHOOLS This stud presents the best high schools, private and public, from the perspective of the student performance at the Universit of Puerto Rico at Maagüez. The high schools that were included in the stud have sent more than 50 students who have graduated from our School of Engineering in the past ten ears (1995-005). This stud was generated using data obtained from the Office of Institutional Research and Planning of our universit. The 15 public high schools that have the greatest number of engineering graduates in the past ten ears are shown in Figure 1. The top three schools: CROEM (397 students), Patria Latorre (18 students) and Eugenio María de Hostos (158 students) are in our geographic region, the Western part of Puerto Rico. As a matter of fact, eleven of the fifteen public high schools are located in our geographic region. Onl two of the fifteen schools are located in the capital cit of San Juan, which is the largest cit in Puerto Rico. These schools are the Universit Gardens High School (146 students) and the High School of the Universit of Puerto Rico (108 students). A stud 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 stud was developed to identif the best schools in the island based on the performance of the engineering students in our universit. CROEM, Maagüez Patria Latorre, San Sebastian Eugenio María de Hostos, Maagüez Efrain Sánchez Hidalgo, Moca Universit Gardens, Río Piedras Blanca Malaret, Sabana Grande Luis Muñoz Marin, Yauco Miguel Meléndez Muñoz, Cae Lola Rodríguez de Tió, San Germán Benito Cerezo, Aguadilla Luis Muñoz Marin, Añasco 18 156 149 146 143 140 17 16 11 11 397 Dr. Carlos González, Aguada 109 DESCRIPTION OF ADMISSION CRITERIA Secundaria UPR, Río Piedras Domingo Aponte Collazo, Lares 108 106 The admission index, which is called the IGS, is composed of the high school grade point average, the verbal aptitude test score and the mathematics aptitude test score from the College Board Entrance Examination. The highest possible Ramón José Dávila, Coamo 106 0 50 100 150 00 50 300 350 400 450 Cantidad de Estudiantes FIGURE 1 FIRST 15 PUBLIC HIGH SCHOOLS WITH 50 OR MORE GRADUATES AT UPRM FOR THE COLLEGE OF ENGINEERING (YEARS 1995-005). 1 Sonia M. Bartolomei-Suárez, Associate Dean of Academic Affairs, School of Engineering, Universit of Puerto Rico, Maagüez, sonia@ece.uprm.edu David González-Barreto, Associate Professor, Industrial Engineering Department, Universit of Puerto Rico, Maagüez, davidg@ece.uprm.edu 3 Antonio González-Quevedo, Professor, Civil Engineering and Surveing Department, Universit of Puerto Rico, Maagüez, agonzalez@rectoria.uprm.edu Coimbra, Portugal September 3 7, 007 International Conference on Engineering Education ICEE 007
The top 15 private high schools that send more than 50 students to the College of Engineering at UPRM who graduate are shown in Figure. The top private high school is Notre Dame in the cit of Caguas with 6 graduates. In second place is Immaculate Conception High School in Maagüez with 18 graduates, followed b Colegio San José in San Juan with 145 graduates. Eight of the 15 schools are located in the metropolitan area of San Juan. Notre Dame High School, Caguas Academia de la Inmaculada Concepción, Maagüez 18 6 The top 15 private high schools with the highest admission index (IGS) for students of the College of Engineering at UPRM from 1995-005 whom graduate are shown in are shown in Figure 4. The top two schools are tied with and IGS of 343 and the are Colegio Ponceño in the cit of Ponce and San José Academ in the cit of Guanabo. Following is Colegio San Antonio with an average IGS of 34. The cities represented in these 15 schools are Caguas (3), Ponce (3), Guanabo (), San Juan (), and Baamón, Maagüez, Carolina, Arecibo, Humacao all with one school. Colegio San José, Río Piedras 145 Colegio Ponceño 343 Colegio San Ignacio, Río Piedras 1 Academia San José, Guanabo 343 Academia Discípulos de Cristo, Baamón 11 Colegio San Antonio, Río Piedras 34 Colegio San Antonio, Río Piedras 117 Notre Dame High School, Caguas Colegio Marista, Guanabo American Militar, Guanabo Colegio San Agustín, Cabo Rojo 90 90 96 Colegio San José, Río Piedras Colegio Santo Tomás de Aquino, Baamón Academia de la Inmaculada Concepción, Maagüez Academia Santa María, Ponce Colegio San Antonio Abad, Humacao Colegio María Auxiliadora, Carolina 88 88 87 Cupeville School, Río Piedras Colegio Marista, Guanabo Carvin School, Carolina Colegio San Carlos, Aguadilla 86 Academia Santa María, Ponce Colegio Evagélico Capitán Correa, Arecibo 8 Colegio San José, Caguas Carvin School, Carolina 77 Colegio Evagélico Capitán Correa, Arecibo 0 50 100 150 00 50 300 Cantidad de Estudiantes FIGURE FIRST 15 PRIVATE HIGH SCHOOLS WITH 50 OR MORE GRADUATES AT UPRM FOR THE COLLEGE OF ENGINEERING (YEARS 1995-005) The top 15 public high schools with the highest admission index (IGS) for students of the College of Engineering at UPRM from 1995-005 whom graduate are shown in Figure 3. The top public high schools are Antonio Luchetti Vocational School in Arecibo followed b the UPR High School (both with the same IGS of 341 points). Following these two schools are Ramón José Dávila in Coamo, Leonides Morales Rodríguez in Lajas and Emilio R. Delgado in Corozal with an average IGS of. These fifteen top public high schools are distributed throughout Puerto Rico. Vocacional Antonio Lucchetti, Arecibo Secundaria UPR, Río Piedras Ramón José Dávila, Coamo Leonídes Morales Rodríguez, Lajas Emilio R. Delgado, Corozal Universit Gardens, Río Piedras Carmen Belén Veiga, Juana Díaz Carmen Bozello de Huke, Arroo Eladio Tirado López, Aguada Luis Muñoz Marin, Añasco Patria Latorre, San Sebastían Domingo Aponte Collazo, Lares Juan Quirindongo Morell, Vega Baja 338 341 341 Colegio San Antonio Abad, Humacao Colegio San Conrado, Ponce 338 335 338 341 34 343 344 FIGURE 4 PRIVATE HIGH SCHOOLS WITH THE HIGHEST IGS FOR GRADUATES OF THE SCHOOL OF ENGINEERING WITHIN 1995-005 It can be concluded that the first four charts show high school students characteristics as the enter the universit. In the next section, the student performance in the College of Engineering will be analzed. PERFORMANCE OF THE STUDENTS AT THE COLLEGE OF ENGINEERING The top fifteen public high schools with the shortest time to graduate with a bachelor s of science degrees in engineering from 1991-006 are shown in Figure 5. The top school in this categor is the UPR High School in San Juan with 5.59 ears. In second place is Ana J. Candelas School in Cidra with 5.65 ears. In third place there is a tied with 5.79 ears for Ramón José Dávila in Coamo with Patria Latorre School in San Sebastián. Among the fifteen top public high schools in this categor, two are from the metropolitan area of San Juan, five are from the Western region, three are from the Southern region, four are from the Central region, and one from the Eastern region. IGS Ponce High School, Ponce Asunción Rodríguez, Guaanilla Juan Antonio Corretjer, Ciales 333 334 335 338 341 34 IGS FIGURE 3 PUBLIC HIGH SCHOOLS WITH THE HIGHEST IGS FOR GRADUATES OF THE SCHOOL OF ENGINEERING WITHIN 1995-005 Coimbra, Portugal September 3 7, 007 International Conference on Engineering Education ICEE 007
RIO PIEDRAS-SECUNDARIA UPR CIDRA-ACADEMICA ANA J CANDELAS 5.59 5.65 5.79 5.79 5.83 Domingo Aponte Collazo School in Lares with an average GPA of 3.07. Among the 15 public high schools with the highest UPRM graduation GPA, two are from the metropolitan area of San Juan, eight are from the Western region, two are from the Southern region, two are from the Central region, and one from the Eastern region. ARROYO-CARMEN BOZELLO DE HUYKE 5.87 RIO PIEDRAS-SECUNDARIA UPR 3. E s c u e la s P ú b lic a s OROCOVIS-JOSE ROJAS CORTES CAYEY-MIGUEL MELENDEZ MUNOZ JUANA DIAZ-CARMEN BELEN VEIGA 3.07 3.06 3.13 AIBONITO-DR JOSE N. GANDARA 6.00 6.00 6.03 6.04 MAYAGUEZ-JOSE DE DIEGO YAUCO-LUIS MUNOZ MARIN 6.09 ANASCO-LUIS MUNOZ MARIN 6.1 MAYAGUEZ-CROEM 3.03 5.30 5.40 5.50 5.60 5.70 5.80 5.90 6.00 6.10 6.0 Tiempo Promedio CAYEY-MIGUEL MELENDEZ MUNOZ SABANA GRANDE-BLANCA MALARET 3.01 3.0 FIGURE 5 TOP 15 PUBLIC HIGH SCHOOLS WITH THE LOWEST AVERAGE TIME TO COMPLETE THE BACHELOR S DEGREE IN ENGINEERING (1991-006) The top fifteen private high schools with the shortest time to graduate with a bachelor s of science degrees in engineering from 1991-006 are shown in Figure 6. The shortest time belongs to Colegio San Antonio Abad in Humacao with 5.48 ears. In second place is Colegio San Conrado in Ponce with 5.5 ears and in third place is Colegio Espiritú Santo in San Juan with 5.55 ears. Among the fifteen top private high schools in this categor, six are from the metropolitan area of San Juan, three are from the Western region, three are from the Southern region, two are from the Central region, and one from the Eastern region. RIO PIEDRAS-COL ESPIRITU SANTO PONCE-COL PONCENO CAGUAS-COL SAN JOSE AGUADILLA-COL SAN CARLOS SAN GERMAN-COL SAN JOSE RIO PIEDRAS-COL SAN IGNACIO 5.48 5.5 5.55 5.6 5.66 5.66 5.67 5.70 5.75 AIBONITO-DR JOSE N. GANDARA ARROYO-CARMEN BOZELLO DE HUYKE 3.00 3.01.85.90.95 3.00 3.10 3.15 3.0 3.5 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 (1991-006) The top seventeen private high schools that showed the highest UPRM graduation grade point average (GPA) for students who entered the Facult of Engineering and graduated from it (1991-006) are shown in Figure 8. The top private school in this categor is Colegio Espiritú Santo in San Juan with an average GPA of 3.3. In second place for this categor is Colegio San Carlos in Aguadilla tied with Immaculate Conception Academ in Maagüez with an average UPRM graduation GPA of 3.1. Among the 17 private high schools with the highest UPRM graduation GPA, six are from the metropolitan area of San Juan, five are from the Western region, three are from the Southern region, two are from the Central region, and one from the Eastern region. RIO PIEDRAS-COL ESPIRITU SANTO 3.3 5.76 AGUADILLA-COL SAN CARLOS 3. 5.78 3.1 GUAYNABO-COL SAGRADOS CORAZONES 5.80 3.1 RIO PIEDRAS-COL SAN JOSE 5.87 3.0 CAROLINA-CARVIN SCHOOL 5.88 3.19 5.90 SAN GERMAN-COL SAN JOSE 3.15 5.0 5.30 5.40 5.50 5.60 5.70 5.80 5.90 6.00 Tiempo Promedio FIGURE 6 TOP 15 PRIVATE HIGH SCHOOLS WITH THE LOWEST AVERAGE TIME TO COMPLETE THE BACHELOR S DEGREE IN ENGINEERING (1991-006) CAGUAS-COL SAN JOSE GUAYNABO-COL SAGRADOS CORAZONES CAROLINA-CARVIN SCHOOL ISABELA-COL SAN ANTONIO 3.09 3.08 3.07 3.06 3.1 The top fifteen public high schools that showed the highest UPRM graduation grade point average (GPA) for students who entered the Facult of Engineering and graduated from it (1991-006) are shown in Figure 7. In first place is the UPR High School with an average GPA of 3.. In second place is Lola Rodríguez de Tió School in San Germán with an average GPA of 3.13 and in third place is CABO ROJO-COL SAN AGUSTIN PONCE-COL PONCENO GUAYNABO-AMERICAN MILITARY CAROLINA-COL MARIA AUXILIADORA.90.95 3.00 3.10 3.15 3.0 3.5 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 (1991-006) Coimbra, Portugal September 3 7, 007 International Conference on Engineering Education ICEE 007
The top fifteen public high schools with the highest UPRM graduation rates for students who entered the Schools of Engineering in the cohorts of 1991-1997 are shown in Figure 9. The first public high school in this categor is Patria Latorre School in San Sebastián with a graduation rate of 83.56%. In second place is the UPR High School in San Juan with a graduation rate of 8.46%. In third place is Efraín Sánchez Hidalgo School in Moca with a graduation rate of 80%. Among the top fifteen public high schools with highest graduation rates, two are from the metropolitan area of San Juan, nine are from the Western region, one is from the Southern region, two are from the Central region, and one from the Eastern region. RIO PIEDRAS-SECUNDARIA UPR MOCA-EFRAIN SANCHEZ HIDALGO 8.46 80.00 83.56 93.0 90.18 8.50 BAYAMON-COL DE LA SALLE 8. CABO ROJO-COL SAN AGUSTIN 81.16 RIO PIEDRAS-COL SAN IGNACIO 80.33 ARECIBO-COL EVANG CAPITAN CORREA 78.05 78.05 76.6 75.56 RIO PIEDRAS-COL SAN JOSE 73.58 BAYAMON-ACAD DISCIPULOS DE CRISTO 68.9 GUAYNABO-AMERICAN MILITARY 66.67 CAROLINA-COL MARIA AUXILIADORA 58.70 0.00 10.00 0.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00 Tasa Graduación YAUCO-LUIS MUNOZ MARIN MAYAGUEZ-EUGENIO M DE HOSTOS MAYAGUEZ-CROEM OROCOVIS-JOSE ROJAS CORTES CIDRA-ACADEMICA ANA J CANDELAS SABANA GRANDE-BLANCA MALARET 76.06 73.1 7.73 7.09 71.67 70.59 70.00 68.97 68.63 68.33 65.00 FIGURE 10 TOP FOURTEEN PRIVATE HIGH SCHOOLS WITH THE HIGHEST UPRM GRADUATION RATES FOR STUDENTS WHO ENTERED THE SCHOOL OF ENGINEERING IN THE COHORTS OF 1991-1997 The previous six charts are related to time to graduate, graduation grade point average and graduation rate. These three indicators will be combined in the next section to develop a performance index (PI) that will allow ratings of these high schools. 64.91 0.00 10.00 0.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 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 The top fourteen private high schools with the highest UPRM graduation rates for students who entered the Schools of Engineering in the cohorts of 1991-1997 are shown in Figure 10. In first place in this categor is Colegio San Conrado in Ponce with a graduation rate of 93.0%. In second place is Immaculate Conception Academ in Maagüez with a graduation rate of 90.18% and in third place is Santa María Academ in Ponce with a graduation rate of 8.50%. Among these fourteen private schools with highest UPRM graduation rates, seven are from the metropolitan area of San Juan, one is from the Western region, two are from the Southern region, one is from the Central region, and one from the Eastern region. PERFORMANCE INDEX USING QUADRATIC LOSS FUNCTION The concept of quadratic loss function has been proposed b Phadke [] to approximate qualit 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 b Loss() = k ( T) (1) where k is a proportionalit constant and T is the target value for the characteristic. Usuall in qualit control applications a tolerance is defined such that if the characteristic is within T + (two sided tolerance) the characteristic is acceptable. The quadratic loss function in (1) penalizes the behaviors that deviate from the target T. A challenge with (1) is the definition of constant k. Artiles- León [3] defined this value to assure that the loss function is insensitive to the sstem of units used to measure the qualit characteristic. For the two sided tolerance problem this definition becomes: = k () Using k in () results in a standardized loss function. Since the standardized version of the loss function is dimensionless if several qualit characteristics are considered their correspondent loss functions can be added. In our case stud, the qualit characteristics or critical indicators that we are considering are: the average Coimbra, Portugal September 3 7, 007 International Conference on Engineering Education ICEE 007
time to degree, the average graduation GPA and 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 higherthe-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). SLoss ( ) = (3) SLoss( ) = (4) A total standardized loss (TSLoss) for our case stud can be defined as: TSLoss 1 1 + + 3 3 = (5) where i, and i corresponds to the characteristic and tolerance for the critical indicators. The TSLoss in (5) could be generalized to m characteristics and can combine one and two sided tolerance characteristics. TLoss can be viewed as a performance indicator for high schools as represented b their students execution The lower performance index the better the students performance at the universit, the better the high school. Appling (5) to institutional research data for high schools that provide the largest number of students to our engineering college for the last 10 ears the following estimates in Table 1 are obtained. exploring the following indicators, average GPA math courses, average GPA science courses, average GPA 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. Future work should consider techniques such as the Mahalanobis Distance to incorporate such relationships. ACKNOWLEDGMENT The authors want to acknowledge the effort b Leo I Vélez and Irmannette Torres from the Office of Institutional Research and Planning of the Universit of Puerto Rico at Maagüez for providing and validating the data used in this stud. REFERENCES [1] González-Barreto, D. and González-Quevedo, A., Attracting a More Diverse Student Population to the School of Engineering of the Universit of Puerto Rico at Maagüez, Proceedings of the 9 th International Conference on Engineering Education. Jul 3-8, 006. San Juan, PR, pp. R4E1, R4B5. [] Phadke, M. S., Qualit Engineering using Robust Design, Prentice- Hall, Englewood Cliffs, NJ, 1989. [3] Artiles-León, N., A Pragmatic Approach to Multiple-Response Problems using Loss Functions, Qualit Engineering, 9,, 1996-1997, pp. 13-0. TABLE 1 RATINGS OF HIGH SCHOOLS BASED ON PERFORMANCE OF INDEX High School Performance Index Colegio San Conrado, Ponce 3.5018 Academia de la Inmaculada Concepción, Maagüez 3.376351 Secundaria UPR, Río Piedras 3.569 Colegio San Antonio Abad, Humacao 3.73794 Patria Latorre, San Sebastian 3.74815 Academia Santa María, Ponce 3.79687 Colegio San Antonio, Río Piedras 3.893357 Notre Dame High School, Caguas 3.995966 Ramón José Dávila, Coamo 4.1951 Benito Cerezo, Aguadilla 4.37077 Universit Gardens, Río Piedras 4.36681 Ana Roque, Humacao 4.376365 Lola Rodríguez de Tió, San Germán 4.440817 Domingo Aponte Collazo, Lares 4.711063 FINDINGS AND CONCLUSIONS FUTURE WORK The suggested performance index, based on the TSLoss, should include additional critical indicators. We suggest Coimbra, Portugal September 3 7, 007 International Conference on Engineering Education ICEE 007