Having those objectives in mind, I have decided to write a mostly non-
specialized paper to illustrate how the statistical techniques can (and should)
be used to analyze available data.
From the beginning of the PISA project, I have been interested in the results
of Spain in the published reports. It is a common feeling that Spain scores well
below than deserved with respect to the Spanish place on the international scene.
On the other hand, I think that the feeling of the population is that Spain is
good in sports. This is based on the good behavior in international competitions
of individuals like Rafael Nadal in tennis, Mireia Belmonte in swimming, or
Gemma Mengual in synchronized swimming, and on the results of teams like
the Basketball, Handball or Soccer Spanish National teams1
In order to find out the reality, I have decided, first, to carry out the con-
struction of a mathematical model which shows how the wealth of the countries
influence their results in the PISA reports and in sports. Then, given the Span-
ish wealth, check how far is Spain from the prediction made by the model. I will
also pay attention to the comparison of the Spanish results in PISA and sports.
As for sports, I also need a variable to measure the quality of the countries.
This variable can be based on the number of medals obtained in the Summer
Olympic Games. It happens that the Summer Olympic Games enclose the most
important sports in the world and all countries participate; thus, they can be
considered as a comparative evaluation of the strength of the countries. More-
over, it seems that (at least in Spain) all sport specialists consider that the result
of a given country can be measured through the number of obtained medals.
The only difference with the usual way to handle those values is that I have
measured the strength of a given country with a weighted sum of the number of
gold, silver and bronze medals obtained; while, usually, people use a lexicographic
order based on the order gold-silver-bronze.
Therefore, in this paper, I will use the results of the last publicized PISA
report and those of the last Olympic Games: The PISA 2012 and the London
2012 Olympic Games. A similar, but a bit simpler, study, using the data of
PISA 2009 is Cuesta-Albertos (2013). The results there are analogous to those
On the other hand, it is easy to obtain information on the wealth of a country.
For instance, the link
offers estimations of the per capita Gross Domestic
Product (P.GDP) of several countries made by the International Monetary Fund,
the World Bank and the Central Intelligence Agency of the United States of
America. In this paper I will use the data by the International Monetary Fund
] as of June 2, 2014, excepting the data of Liechtenstein which has been
taken from the Central Intelligence Agency list because it was not offered by the
International Monetary Fund.
This paper was written before the last Spanish fiascos in the 2014 Brazil soccer and Spain