Course: 2021/2022

Statistical inference methods II

(13706)

Requirements (Subjects that are assumed to be known)

Exploratory data analysis
Elementary statistical theory I
Elementary statistical theory II
Statistical inference techniques I

SPECIFIC COMPETENCES
1. Understand the methodology in the construction of parametric hypotheses tests.
2. Understand nonparametric hypotheses tests and their applications in different situations.
3. Basic notions of the Analysis of Variance.
4. Acquire handling of the different association measures.
5. Computer skills related to the previous points.
CROSS COMPETENCES
1. Decision making.
2. Analyzing and summarizing information.
3. Organizing facts.
4. Understand a real problem and define it as a statistical problem.

Description of contents: programme

1. Basic concepts in hypothesis testing
2. One-sample parametric hypothesis testing
2.1. Tests for a single normal population mean
2.2. Tests for a single normal population variance
2.3. Large sample tests for a population mean
3. Two-sample parametric hypothesis testing
3.1 Tests for two independent samples.
3.2. Tests for two paired samples.
3.3. Large sample tests
4. Analysis of Variance
4.1. Model assumptions
4.2. ANOVA table
4.3. Two sample comparisons
4.4. Two-way ANOVA and interactions.
5. Nonparametric goodness of fit tests
5.1. Chi-square tests.
5.2. Kolmogorov-Smirnov tests.
5.3. Kolmogorov-Smirnov-Lilliefors tests for normality.
6. Nonparametric one-sample location tests
6.1. Sign test
6.2. Wilcoxon signed-rank test
7. Non parametric multiple-group tests
7.1. Chi-square tests
7.2. Kolmogorov-Smirnov tests
7.3. Mann-Whitney-Wilcoxon tests
7.4. Kruskall-Wallis tests
8. Association measures
8.1. Pearson linear correlation coefficient
8.2. Spearman rank correlation coefficient
8.3. Kendall rank correlation coefficient

Learning activities and methodology

Theory (4 ECTS). Lectures will be taught face-to-face mode with available material posted in internet. Problems (2 ECTS) Problem Solving classes. Computational exercises using the statistical software R. Work assignments in groups. Weekly office hours to assist students on an individual and group basis.

Assessment System

- % end-of-term-examination 40
- % of continuous assessment (assigments, laboratory, practicals...) 60

Basic Bibliography

- Casella, G. y Berger, R. L.. Statistical Inference. Wadsworth and brooks.
- Dalgaard, Peter. Introductory statistics with R . Springer. 2008
- Gibbons, J.D: y Chakraborti, S.C.. Nonparametric Statistical Inference. Marcel Dekker.
- Ugarte, María Dolores. Probability and statistics with R . CRC Press. 2008

Additional Bibliography

- Mukhopadhayay.. Probability and Statistical Inference. Marcel Dekker.
- Rohatgi, V.K.. An introduction to probability theory and mathematical statistical.. Wiley.

**More information: **http://www.est.uc3m.es/amalonso/esp/tie2.html