Statistics and Data Analysis is a compulsory subject, taught in the first quarter of the Second Year of the Degree in Economics. It is part of the compact known as Economic Analysis Foundations (M02) and precedes Statistics Applied to Economics, taught in the second quarter of the same year. Both subjects jointly cover the requirements needed to tackle Econometrics (introduction to Econometrics and Applied Econometrics) in the Third Year.



Requirements for this subject include familiarity with differential and integral calculus and rudiments of linear algebra, as taught for instance in Mathematics I and II of the Degree in Economics.

This subject aims are:

(a) Provide a groundwork in Descriptive Statistics and Probability Theory, both theoretical and applied.

(b) Teach quantitative techniques for economic data interpretation.

(c) Introduce the student to the study of Probability Calculus, which will later assist him/her in the building of theoretical statistical models, bridging the gap among observable samples and unknown properties of populations

(d) Develop adequate methodology for the study of probabilities of simple results of a random experiment.

(e) From the Cross-Curricular Competences catalogue of the UPV/EHU: Social commitment (critical understanding of global socio-environmental issues).



After taking this subject the student will be have acquired the ability to:



- Apply statistical methods in the scope of economics and business.

- Identify the characteristic elements of probability distributions (probability function, moments, etc.)

- Search and summarize adequately the statistical information relevant to analyze an economic problem.

- Describe and interpret the information contained in an economic data set, using graphical analysis and the main descriptive statistics (using adequate software).

- Present in a clear and systematic form the conclusions obtained in the descriptive analysis of economic data.

I Descriptive statistics



1. Univariate statistical variables: plots and summary statistics.



Univariate statistical variables. Frequency distributions. Bar charts. Histogram. Frequency polygon. Pie chart. Simple and

weighted arithmetic mean. Median and quantiles. Mode. Variance. Standard deviation. Coefficient of variation. Range and

mean deviation. Box plot. Skewness. Kurtosis. Gini index. Lorenz curve. Centered and standardized variables. Effect of

linear transformations.



2. Bivariate statistical variables: plots and summary statistics.



Bivariate statistical variables. Frequency distributions. Marginal distributions. Conditional distributions. Scatter plot.

Covariance. Correlation coefficient. Statistics for linear combinations of statistical variables.



3. Index numbers.



Simple index numbers: properties. Average rate of change. Unweighted complex indices: simple average of indices and weighted basket index. Weighted complex indices: Laspeyres, Paasche, Fisher

indices. Changes in the base period. Deflation of statistical series: current and constant values. Applications.





II Probability



4. Principles of probability.



Introduction. Axioms. Probability allocation. Probabilities as relative frequencies. Stochastic independence. Conditional probability. Intersection theorem. Partition theorem. Bayes theorem.



5. Random variable. Probability distribution.



Random variable in R. Distribution function in R. Discrete and continuous random variables. Probability mass functions and density functions. Examples of discrete and continuous probability distributions: Bernoulli, binomial, uniform and exponential. Probability distribution of a function of a random variable. Random variable in R2. Distribution function in R2. Marginal distributions.

Conditional distributions. Stochastic independence.



6. Mathematical expectation, moments, characteristic functions.



Mathematical expectation of a function in R. Moments in R. Chebyschev's inequality. Characteristic, moment generating and cumulant generating functions. Mathematical expectation in R². Covariance. Correlation coefficient. Correlation and independence. Conditional expectation.



7. Normal distribution. Central limit theorem.



Definition and basic properties of the N(0,1) distribution. Linear transformations. General normal distribution. Linear combination of independent normally distributed random variables. Sequence of random variables. Definition of convergence in law. Continuity theorem of characteristic functions. Asymptotic normal distributions. Central limit theorem.

Teaching will be based upon formal lectures, applied lectures and seminars.

Formal lectures will be about the theoretical contents of the subject. Applied lectures will include exercise solving and examples illustrative of the theory. Seminars will involve the use of hand calculators.

• Continuous Assessment System
• Final Assessment System
• Tools and qualification percentages:
  • Solving tests (multiple choice questionnaires, exercises, problems,...) (%): 100

We offer two alternative assessment systems, one to be chosen by each student:



1. Mid-term exam plus a final exam. Students taking the mid-term exam (containing multiple choice questions, exercises, problems, ...) and getting a minimum score of 6 points out of 10 will be allowed to skip the contents assessed in that exam when sitting at the final exam in January. The final exam will just include questions on the second part of the course for them. Passing (or better) the subject will require in any case a minimun score of 5 in the final exam. For students with marks equal to 6 or over in the mid-term exam, the final score will be computed as the average of the mid-term and final exam marks. In the case that the score at the final exam is under 5 points, the final marks will be those of this final exam.



Any student having obtained 6 points or more in the mid-term exam will be able to, if he/she wishes so, attend the final exam covering the full contents of the subject (and not just the second part), in which case the final marks obtained will be those obtained in the final exam.



2. Final exam for 100% of the marks,



The final exam may contain multiple choice questions and/or problems. Should it include both, a minimum score for each of the two sections of the exam might be required.



If an on-site evaluation becomes not possible, the final examination will be celebrated on the same scheduled date, using on-line facilities available at the eGela platform. In such case, 15 days in advance of the exam date, more precise information about the exact format of this exam (just short questions, just problems or both) will be given through eGela. This exam will have to be solved individually as usual and, if considered convenient, the teaching staff might ask for an oral test in order to check the answers given, at a later date. Should this be the case, such oral test would consist on an individual conversation with the student.

2nd exam round (June)



The evaluation will be, in all cases, a final exam. The final grade will be solely dependent on that exam.



For both calls, the final exam can contain multiple choice questions and problems (open questions). Whenever the exam contains these two type of questions simultaneously, a minimum score in the two parts of the exam may be required.



If an on-site evaluation becomes not possible, the final examination will be celebrated on the same scheduled date, using on-line facilities available at the eGela platform. In such case, 15 days in advance of the exam date, more precise information about the exact format of this exam (just short

questions, just problems or both) will be given through eGela. This exam will have to be solved individually as usual and, if considered convenient, the teaching staff might ask for an oral test in order to check the answers given, at a later date. Should this be the case, such oral test would consist on an individual conversation with the student.

The use of a pocket calculator and statistical tables is required,
both in exams and in the classroom. Some projects may require the use of
a computer with adequate software: in this subject R would be used, which
may be freely downloaded from:

http://cran.es.r-project.org

R is also installed in most computer rooms across the school.

Basic bibliography

Basic reading:



1. M.J. Bárcena, K. Fernández, E. Ferreira and M.A. Garín (2023). Elementos de Probabilidad y Estadística Descriptiva. 2da edición. Servicio Editorial de la Universidad del País Vasco, UPV/EHU.

2. F.J. Martín Pliego and L. Ruiz Maya (2004). Estadística I: Probabilidad. Editorial AC, 2a edición. Madrid.

3. D. Peña (2001). Fundamentos de Estadística. Alianza Editorial, Madrid.

4. D. Peña and J. Romo, J. (1997). Introducción a la Estadística para las Ciencias Sociales. McGraw Hill.

5. S. Ross (2001). Probability and Statistics for Engineers and Scientists. Academic Press, London.

6. E. Paradis (2003). R for beginners. Institut des Sciences de l'Evolution. Université Montpellier II, France. (http://cran.r-project.org/doc/contrib/Paradis-rdebuts_en.pdf)

7. Ross, S. (2010). A first course in Probability, 6th edition. Pearson.

8. Libretext Statistics, “Introductory Statistics”, available at

https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Book%3A_Introductory_Statistics_(OpenStax), chapters 1 & 2.

9. Shafer and Zang, “Introductory Statistics”. Libretext Statistics, available at https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Book%3A_Introductory_Statistics_(Shafer_and_Zhang), chapter 2.



Exercises:

1. J. Arteche et al. (2000). Ejercicios de Estadística I. Elementos de Probabilidad y Estadística. Servicio Editorial de la UPV/EHU.

2. F.J. Martín Pliego, J.M. Montero Lorenzo and F.J. Ruiz Maya (2002). Problemas de Probabilidad. Editorial AC, Madrid.

3. F. Tusell and M.A. Garín (1991). Ejercicios de Probabilidad e Inferencia Estadística. Tébar-Flores, Madrid.

In-depth bibliography

1. Grimmett, G. and Welsh, D. (1991). Probability: an introduction. Oxford.
2. Grinstead, C.M. and Snell, J.L. (-). Introduction to Probability.
(http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/amsbook.mac.pdf)
3. Levin, S. and Rubin, S. (1994). Statistics for Management. Prentice Hall.
4. Lind, D.A. (1994). Basic statistics for Business and Economics. Irwin.
5. Newbold, P. (2003). Statistics for Business and Economics. Prentice Hall.
6. MacClave, J.T. (1994). Statistics for Business and Economics. MacMillan.
7. MacClave, J. T. (2001). A first course in business statistics, Prentice Hall.
8. Stowell, S. (2014). Using R for Statistics. Apress-Springer.
9. H. Pishro-Nik, "Introduction to probability, statistics, and random processes", available at https://www.probabilitycourse.com, Kappa Research LLC, 2014.
10. Libretext Statistics, “Probability Theory”, available at
https://stats.libretexts.org/Bookshelves/Probability_Theory (advanced)

Journals

At the introductory level of this course, direct resort to specialized journals will hardly be required. However, a good collection is available in the library, both in printed form and with on-line access.

Regarding statistical sources for Spain, the journal "Indice", http://www.revistaindice.com/, may be of interest. Concerning uses of statistics to multiple applications, the journal "Chance" may be of
use.

Web addresses

EUSTAT: http://www.eustat.es
INE: http://www.ine.es
"Indice": http://www.revistaindice.com
"Chance": http://www.springer.com/mathematics/probability/journal/144
Open Data Euskadi: http://opendata.euskadi.net

Electronic resources:

The University of the Basque Country (UPV-EHU) has entered agreements with some publishers whereas students and teaching staff can freely download books in PDF format for their personal use. More information in

http://www.ehu.es/es/web/biblioteka/liburu-elektronikoak

Software:

In applied sessions, and in general along the course, the statistical packages R and Rstudio can be used. Both are freely available in the most common platforms (MS Windows, Linux, Mac OS) and can be
downloaded from:

http://cran.r-project.org/
https://www.rstudio.com/