COMPETENCIES

-M03CM02: Be familiar with the main probability distributions and the usual data analysis and statistical inference techniques.

-M03CM03: Correct use of terminology related to random phenomena and data analysis.

-M03CM04: Correct modeling of typical situations related to random phenomena and data processing.

-M03CM05: To be familiar with appropriate computer resources for the treatment of the above situations and to handle correctly some of them.

-M03CM06: Select the appropriate statistical analysis technique, depending on the objective defined in the study.

-M03CM07: Correct performance of the calculations and / or graphical visualizations that require such situations, using the appropriate theoretical and/or computational resources.

-M03CM08: Critical interpretation of the results of the performed analyses.



LEARNING RESULTS

- Knowledge of how to perform estimation and hypothesis contrasts from samples.

- Knowledge of how to interpret the results of the performed statistical analyses.

- Knowledge of how to make estimates of significant quantities (probabilities, means, etc.) when their exact calculation is not feasible.

- Knowledge of how to make a reasoned choice of the most appropriate method to perform estimation and hypothesis contrasts from samples.

- Correct use of appropriate computer resources for the calculations or graphical visualizations required by the statistical analysis of a project.

THEORETICAL CONTENTS

1. SAMPLING AND ESTIMATION

- Introduction to Sampling

- Point estimation. Different methods to obtain estimators. Properties of estimators.

- Interval estimation. Definition of confidence interval. Classical confidence intervals for one population. Classical confidence intervals for two populations.

2. HYPOTHESIS TESTING

- Introduction and fundamentals of hypothesis testing. Classification of the tests. Probability of error of type I and type II. Significance level. p-value.

- Uniformly more powerful contrasts (UMP). Neyman-Pearson's lemma.

- Control of error probabilities and sample size.

- Likelihood ratio test.

- Classical hypothesis tests for one and two populations.

3. ANALYSIS OF VARIANCE

- Introduction

- Analysis of variance for a single classification or a single factor (ANOVA).

- Multiple comparisons.

4. NON-PARAMETRIC TESTS

- Introduction

- Goodness-of-fit tests.

- Independence and homogeneity tests.

- Location test for one, two or more samples.



PRACTICAL CONTENTS

Data analysis with R Software

- Reading and manipulation of data.

- Script code for Probability-Calculus and Statistical Inference.

- Interpretation of results.

The notes of the course will be published in the eGela platform at the beginning of the term, along with the distribution tables that will be used throughout the course. The students will also be provided with a manual to help them with the computer labs and the list of problems that will be solved, at least in part, in practical classes.



The theoretical contents will be presented in lecture form, following the basic references that appear in the Bibliography and the compulsory material. These lectures will be complemented with problem classes (classroom practices) in which students will be asked to solve questions in which the previously acquired theoretical knowledge will be applied. The seminars will be dedicated to examples based on significant questions related to the contents. In general, an assignment will be proposed by the lecturer to the students and the session will be devoted to reflection and open discussion. Computer labs will be for the application of the different statistical inference techniques that have been studied to a specific dataset using computer resources. This will allow the students to answer the questions posed by the professor using the appropriate technique.



Students will have individual and group assignments on theory and problems, for which they will have the support of the professor in the classroom, the online platform and tutorials.

The lecturer will guide the students' work and will stimulate that it is done with regularity and dedication. They will also be encouraged to use personal tutorials where they can clarify any doubts or difficulties that may arise in the course.

EVALUATION CRITERIA



Written exam: 65%.

Computer exercises: 15%

Seminars: 5%.

Group assignments: homework, exercises or statistical report: 15%



A minimum grade of 4 (out of 10) in each of the evaluation sections is required in order to pass the course.



If the student declines the continuous evaluation, choosing the final evaluation method, he or she must notify the lecturer in writing form between the first and the 9th week of the term. Even so, giving up the continuous evaluation does not exempt the student from demonstrating the ability and knowledge to carry out the activities that have been graded on that form. Therefore, the final evaluation will include a part that will ensure the evaluation of these contents and it will be considered for the final grade in the same proportion as in continuous evaluation. The test can be an oral presentation, a computer exercise or a written description of the subject knowledge addressed in the supplementary activities.



WITHDRAWAL:

The students that have carried out the activities throughout the course, but do not attend the ordinary call, will be qualified as Not Presented.

Notes and materials published on the eGela platform.

Basic bibliography

Basic references (in alphabetical order):

- Casella G, Berger RL. (2008). Statistical Inference. Duxbury Press. Belmont, California.

- Kerns GJ. (2018). Introduction to Probability and Statistics Using R. Third Edition. Libre distribución. Disponible en: https://cran.r-project.org/web/packages/IPSUR/vignettes/IPSUR.pdf.

- Peña Sánchez de Rivera D. (1992). Estadística. Modelos y Métodos. Fundamentos. Alianza Universidad. Madrid.

- Rohatgi VK. (2003). Statistical Inference. John Wiley & Sons. New York.

- Zuur AF, Ieno EN, Meesters EHWG. (2009). A Beginner's Guide to R. Springer Science+Bussines Media LLC. New York.

In-depth bibliography

Supplementary references (in alphabetical order):
- Chihara LM, Hesterberg TC. (2018). Mathematical Statistics with Resampling and R, 2nd Edition.
John Wiley & Sons. New York.
- Kickinson J and Chakaborti S. (1992). Non Parametric Statistical Inference. Dekker Inc.
- Lehman EL. (1983). Theory of point Estimation. John Wiley & Sons. New York.
- Lehman EL. (1986). Testing Statistical Hypothesis. 2nd Edition. John Wiley & Sons. New York.
- Rohatgi VK. (2000). An Introduction to Probability Theory and Mathematical Statistics. John Wiley & Sons. New York.
- Walpole RE, Myers RH, Myers SL, Ye K. (2012). Probabilidad y Estadística para Ingeniería y Ciencias.
Pearson Educación, México.