# Statistics

## Objectives

This curricular unit aims to supplying to the students the theoretical and practical knowledge about methodologies on parametric and nonparametric statistical inference. The contents of the curricular unit include inference tools such as statistics, estimators, sampling distributions, point and interval estimation and hypothesis testing. Additionally, some issues of asymptotic distributions are addressed. The students will acquire competences related to the point estimators and their properties, and will learn how to construct confidence intervals and perform hypothesis testing on population parameters, such as the mean, the variance, the difference between means, the ratio of variances, the proportion, the difference between proportions and the correlation coefficient. Moreover, the analysis of variance is introduced, as well as several nonparametric statistical tests. The students should clearly understand the conditions of applicability of each procedure.

## General characterization

##### Code

200046

##### Credits

7.5

##### Responsible teacher

##### Hours

Weekly - Available soon

Total - Available soon

##### Teaching language

Portuguese. If there are Erasmus students, classes will be taught in English

### Prerequisites

Not applicable.

### Bibliography

Afonso, A., Nunes, C. (2011). Estatística e Probabilidades. Aplicações e Soluções em SPSS, Escolar Editora.

Conover, W. J. (1999). Practical Nonparametric Statistics. 3rd ed., Wiley.

Hogg, R. V., Tanis, E. A. (2010). Probability and Statistical Inference. 8th Edition, New Jersey: Pearson/Prentice-Hall.

Newbold, P., Carlson, W. L., Thorne, B. (2012). Statistics for Business and Economics. 8th Edition, Boston: Pearson.

Murteira, B., Ribeiro, C.S., Silva, J.A. e Pimenta, C. (2002). Introdução à Estatística, McGraw Hill.

### Teaching method

The curricular unit is based on theoretical and practical lessons. The sessions include presentation of concepts and methodologies, solving examples, discussion and interpretation of results. The practical component is geared towards solving problems and exercises, including discussion and interpretation of results. A set of exercises to be completed independently in extra-classroom context is also proposed.

### Evaluation method

1st call: individual project work (40%) and final exam (60%).

2nd call: final exam (100%).

## Subject matter

The curricular unit is organized in six Learning Units (LU):

**LU1. Sampling distributions**

- Statistical inference concepts

- Definitions and notation

- Introduction to the sampling distributions

- Sampling statistics

- Distribution of the sampling mean

- Distribution of the difference between means

- Distribution of the sampling variance

- Distribution of the ration between sampling variances

- Distribution of the sampling proportion

- Distribution of the difference between sampling proportions

**LU2. Point estimation**

- Notation and concepts

- The method of maximum likelihood

- Properties of the estimators

**LU3. Interval estimation**

- Confidence intervals for the mean

- Confidence intervals for the difference between means

- Confidence intervals for the variance

- Confidence intervals for the ration between variances

- Confidence intervals for the proportion

- Confidence intervals for the difference between proportions

**LU4. Hypothesis testing**

- Concepts and methodology

- Hypothesis testing for the mean

- Hypothesis testing for the difference between means

- Hypothesis testing for the variance

- Hypothesis testing for the ration between variances

- Hypothesis testing for the proportion

- Hypothesis testing for the difference between proportions

- Correlation coefficient

**LU5. Analysis of variance (ANOVA)**

- Analysis of variance with one factor and fixed effects

- Multiple comparison tests

**LU6. Nonparametric tests**

- Distribution fitting tests

- Comparing independent samples

- Comparing paired-samples

- Comparing multiple samples