Analysis of the UNAM's entrance exam

on Apr 7, 2014
The UNAM is Mexico's biggest and most important university. To enter it students must either take an exam or graduate from a high school run by the UNAM in less than 4 years with a grade point average of at least 70% (although some majors like medicine require 90% for pase directo). The admission exam is given twice a year, in February and June, and any student from any high school with at least a grade point average of 70% can take it. If the student meets the requirements for entering the UNAM, passing the exam guarantees him admission. The exam has 120 questions.

Depending on the student's choice of major, the admission exam emphasizes one of four basic areas of study. Let's say you want to study math: in addition to being tested on the topics every high school student is supposed to know, you'll get a couple of extra questions about integration by parts; if you want to study biology the extra questions will be about the the Krebs cycle; if you want to study philosophy the exam will probably include extra references to the great works of literature; and if you want to study a social science you'll be asked about the differences between a grand macchiato and a caffè latte.
Click on the chart to visit the interactive version


Apart from UNAM's main (and most prestigious) campus of Ciudad Universitaria (CU), the university has several satellite campuses in the Mexico City metro area as well as many others across Mexico. In this post I will only analyse those located in Mexico City, and only for the scholarized system (sistema escolarizado) where the students have to actually sit in a classroom (the UNAM also offers remote TV/Internet classes and under an open system). The admission exam to the UNAM is quite competitive and only a small percentage of those who apply actually get in.

Date Location Percentage
admitted
Applied Completed
Test
Admitted
2011-06  CU 8.6 30,615 27,515 2,626
2011-06  Not CU 9.1 32,215 29,667 2,916
2012-02  CU 5.2 61,262 55,793 3,192
2012-02  Not CU 6.4 56,012 52,287 3,597
2012-06  CU 5.1 30,944 28,084 1,573
2012-06  Not CU 10.1 32,741 30,354 3,299
2013-02  CU 5.4 63,562 59,425 3,424
2013-02  Not CU 6.7 56,348 53,547 3,800
2013-06  CU 6.3 29,872 26,052 1,868
2013-06  Not CU 13.8 33,744 30,403 4,656

This year Harvard sent out 2,023 offers out of 34,295 applications for an admission rate of 5.9%, which is exactly the same overall admission rate as the UNAM (CU) from June 2011 to June 2013 (though, of course, Harvard has much much lower standards in who it admits).

Admissions by major
Click on the chart to visit the interactive version

Admissions by area
Click on the chart to visit the interactive version


I scrapped all admission results from the UNAM's website from June 2011 to June 2013. There were some problems with the data at the UNAM's end since the listings didn't always match the summary statistics included in the web pages. If you visit the results for Historia del Arte you'll see that the summary statistics claim that zero students applied to take the test, but the listing includes 3 students (given the test scores of infomatics students I'm not surprised by the mistakes). Anyways, this kind of mismatch was rare and didn't involve that many students. I took the actual listing to be definitive. In addition the results sometimes include data from students whose result is Cita para aclarar situación escolar, I simply interpreted this as being a missing value.

Physical Sciences, Mathematics and Engineering


Biological Sciences and Health


Social Sciences


Humanities and Arts

Highest scoring majors in each area


Changes in median admission scores from exam to exam (first differences)
Median scores each year

(a standard deviation is 17 points)

One big problem with the admission process at the UNAM is that it doesn't use Gale-Shapley and thus students have an incentive to not reveal their true preferences:

Imagine a student who is deciding between studying ingeniería mecatrónica and ingeniería mecánica, because mechatronics is very hard to get into, and students only get to apply to one major at each exam, he decides to list mechanical engineering as his choice even when there was a chance (albeit not as big) that he would have been admitted to mechatronics.
Click on the chart to visit the interactive version

Another consequence of not using Gale-Shapley is that some students who do list their true preference are rejected in favor of lower scoring students (this is probably a really big deal).
Click on the chart to visit the interactive version

Imagine a student who lists his or her true preference but who would be willing to entertain studying at an alternative campus with a lower admission score (international relations at CU vs international relations at FES Aragón) or a similar major with lower admittance requirements (international relations vs political science for example) who is rejected from his first choice but obtains a test score higher than the minimum requirement for his alternative.
We can see in the above chart how the percentage of students admitted increases at the lower requirement campuses during the June exam, but there is no such increase at the main CU campus. This is probably a consequence of students who had been rejected after the February exam having another go at being admitted at the lower requirement satellite campuses.

The easiest way to remedy this would be to copy the COMIPEMS exam —which the UNAM helped design— and allow students to list more than one major/campus when applying. Obviously there are a lot of variations and complications the UNAM could use to make its admission process better, for example they could start admitting students from different areas than their first choice major if they had really high test scores. I'm sure the applied math and computing international relations students are up to the task of designing an admittance mechanism that satisfies Gale-Shapley.

There's also a positive correlation between average test scores and the starting salaries of university graduates (of any university in Mexico City, not just the UNAM) in a poll conducted by Reforma in Mexico City.


P.S. I bet the Escuela Nacional de Artes Plásticas is full of rich kids
P.P.S. Visit the companion website full of interactive charts
P.P.P.S. Source code

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5 comments:

Hectorsaurio Perdomo said...

Muy interesantes las gráficas. Ojalá que muchos estudiantes consideren los resultados antes de aplicar.

María GH said...

Todos los que tomamos este examen alguna vez pensamos en estos datos y estas relaciones. Felicidades por ser la primera persona que de verdad toma en serio estas visualizaciones e interpretaciones, ¡muy interesante!

Edo said...

Especialmente en el tema del desperdicio de talento, a mi parecer el problema sigue siendo el pase directo de las preparatorias a la universidad. Muy pocas veces una persona que vive fuera del DF tiene oportunidad de ingresar a la UNAM desde la preparatoria y estos tienen mas del 70% de la ocupación de lugares. Por otro lado los exámenes de admisión son totalmente genéricos y no estás lo suficientemente orientados a los áreas por lo que una persona puede ser muy talentosa en su área y no verse reflejado en el examen de admisión.

Diego Valle-Jones said...

Edo,

Creo el pase directo no es un gran problema ya que las prepas de la UNAM son de las mejores en México (según la COMIPEMS y ENLACE). El examen de la UNAM debe de tener una muy alta correlación con el de la COMIPEMS y de hecho los alumnos de las prepas del IPN, que también obtienen calificaciones muy altas en el COMIPEMS, tienden a ser aceptados a la UNAM en mayor proporción (p. 49) que alumnos de otras escuelas. Obviamente todo esto es en el campo de lo teórico, en lo práctico no veo como quitar el pase automático sin quitarle la autonomía a la UNAM y un buen de policías

Edo said...

Es cierto que las prepas de la UNAM son de las mejores en el grupo de las públicas y dentro del área metropolitana, mas no figuran dentro del estudio de los aspirantes por examen de selección por lo que es complicado medir su desempeño en comparación con el resto de los aspirantes. Por otro lado creo que si aquellos por ejemplo de las escuelas vocacionales que aparecen como favoritos en las encuestas de la COMIPEMS deberían tener un peso estadístico mayor en el estudio que presentas (Las puertas del ingreso a la educación superior) y se descartaría la conclusión a la que llega el autor diciendo "mediante procedimientos de selección académica se ponen en juego mecanismos de selección social".
En base a esta hipótesis, me temo que al abrir el ingreso a la UNAM a un esquema de selección basado únicamente en el examen de admisión, éste se vuelva un mecanismo de exclusión social (aun mayor) a los sectores de menor nivel socio-económico principalmente en la Ciudad de México.
De cualquier modo como lo mencionas, muchas presiones políticas harían imposible hacer dicho cambio por lo que únicamente nos queda como un buen ejercicio hipotético.

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Thank you for your interesting and insightful comments. I truly look forward to reading them.