# Statistical Analysis

## Objectives

This curricular unit aims at supplying to the students the theoretical and practical knowledge about methodologies on parametric and nonparametric statistical inference. Students will explore the core principles of statistics, from both the conceptual and applied perspectives. The students will acquire competences related to random variables, estimators, sampling distributions, point and interval estimation and hypothesis testing. Additionally, some issues of asymptotic distributions are addressed. Moreover, the analysis of variance is introduced, as well as several nonparametric statistical tests. The students will clearly understand the conditions of applicability of each procedure. The concepts and principles will be illustrated using real-world concepts applicable to many industries, including medical, business, sports, insurance, etc.

## General characterization

200185

7.5

##### Responsible teacher

Ana Cristina Marinho da Costa

##### Hours

Weekly - Available soon

Total - Available soon

##### Teaching language

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

### Prerequisites

Teaching language: English.

### Bibliography

Newbold, P., Carlson, W. L., Thorne, B. (2013). Statistics for Business and Economics. 8th edition, Boston: Pearson, https://ebookcentral.proquest.com/lib/novaims/detail.action?docID=5174169 (full text available after login in NOVA IMS network or through VPN connection).

Conover, W. J. (1999). Practical Nonparametric Statistics. 3rd edition. New York: Wiley.

Mariappan, P. (2019). Statistics for Business. New York: Chapman and Hall/CRC, https://doi.org/10.1201/9780429443244 (full text available after login in NOVA IMS network or through VPN connection).

Wilks, S. (1948). Elementary Statistical Analysis. Princeton, New Jersey: Princeton University Press. https://www.jstor.org/stable/j.ctt183q2d4 (full text available after login in NOVA IMS network or through VPN connection).

Hogg, R. V., Tanis, E. A. (2001). Probability and Statistical Inference. 6th edition, New Jersey: Pearson/Prentice-Hall.

Murteira, B., Ribeiro, C.S., Silva, J.A., Pimenta, C. (2010). Introdução à Estatística. Lisboa: Escolar Editora.

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

### Teaching method

The curricular unit is based on theoretical and practical lessons. A variety of instructional strategies will be applied, including lectures, slide show demonstrations, step-by-step applications (with and without software), questions and answers. 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

REGULAR PERIOD (1st call): test (30%; about LU1-LU5), exam (50%; about all topics, but more focused on LU6-LU8), Assignment Report (20%; mandatory for approval).

RESIT PERIOD (2nd call): final exam (100%).

RULES:
To complete the test/exam, students must provide themselves with the form and statistical tables disclosed in Moodle, and also with a scientific calculating machine. Graphic calculating machines are not allowed.
The Assignment Report is mandatory for approval in the regular examination period. The report must be prepared individually, in Portuguese or English, using a set of artificial data. Detailed information and the data set of the assignment are disclosed in Moodle. Reports submitted after the deadline will have a penalty of 0.5 points for each day of delay. The maximum delay allowed is 3 days. Reports not submitted in the Moodle platform will be rejected.

## Subject matter

The curricular unit is organized in 8 Learning Units (LU):

1. RANDOM VARIABLES
- Probabilistic models
- Discrete r.v.
- Continuous r.v.

2. PROBABILITY DISTRIBUTIONS
- Binomial, Poisson, Normal
- Approximation of Binomial to Normal
- t, Chi-square, F

3. SAMPLING DISTRIBUTIONS
- Sampling statistics & sampling distributions
- Distribution of sampling mean and sampling proportion

4. POINT ESTIMATION
- Unbiasedness, efficiency, consistency

5. INTERVAL ESTIMATION
- CI for mean, proportion, variance
- CI for difference between means and between proportions
- Sample size determination

6. HYPOTHESIS TESTING
- Concepts
- Tests for mean,proportion, variance, difference between means and between proportions, ratio between variances
- Tests for correlation coefficient

7. ANALYSIS OF VARIANCE
- One-way ANOVA with fixed effects
- Multiple comparison tests
- Tests to the equality of k variances

8. NONPARAMETRIC TESTS
- Introduction
- Distribution fitting tests
- Comparing independent and paired-samples
- Spearman's rank correlation test

## Programs

Programs where the course is taught: