Applied Statistics

Code:

M2020

Acronym:

M2020

Level:

200

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2020/2021 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:B	0	Official Study Plan	3	-	6	56	162
L:CC	3	Plano de estudos a partir de 2014	2	-	6	56	162
			3
L:F	3	Official Study Plan	2	-	6	56	162
L:G	0	study plan from 2017/18	2	-	6	56	162
			3
L:M	63	Official Study Plan	2	-	6	56	162
L:Q	0	study plan from 2016/17	3	-	6	56	162
MI:ERS	18	Plano Oficial desde ano letivo 2014	2	-	6	56	162
			3

Teaching language

Portuguese

Objectives

 It is expected that, jointly with new statistical methodologies, the students can see real applications of the concepts previously learnt in "Probability and Statistics". Theory-wise, the simplest methods of statistical inference including some theory on estimators and point estimation and hypothesis testing. 

It is also expected that the students acquire familiarity with the programing language and software environment R, in the framework of problems solving.

Learning outcomes and competences

Upon completing this course, the student should:

- have a good insight of the fundamental concepts and principles of statistics, and in particular those from basic inference statistics.

- know the common inference statistical  methods and how to apply them to concrete situations;

- be able to identify and formulate a problem, to choose adequate statistical methods and to analyze and interpret in a critical way the obtained results;

- be able to apply the studied models, and more generally to perform simple data analyses, in R

Working method

Presencial

Program

1. Statistics. Unbiased and consistent estimators. Most usual statistics, with emphasis on the sample mean and sample variance.


2. Point estimation. The method of moments. Maximum likelihood estimation. Properties of the maximum likelihood estimators.


3. Joint distributions. Bivariate gaussian and multinomial.


4. Hypothesis testing. Errors of type I and type II, test statistic, power of a test. One- and two-sample parametric tests. Relation between hypothesis tests and confidence intervals. Non-parametric tests: goodness-of-fit, location, independence and homogeneity.


5. Correlation analysis. Pearson and Spearman correlation coeficient. Hypothesis testing.

Mandatory literature

A. Rita Gaio; Apostamentos disponibilizados pelo docente
António Carvalho Pedrosa, Sílvio Marques A. Gama; Introdução Computacional à Probabilidade e Estatística, Porto Editora, 2016. ISBN: 978-972-0-01990-5

Complementary Bibliography

Casella George; Statistical inference. ISBN: 0-534-24312-6
Pestana Dinis Duarte; Introdução à probabilidade e à estatística. ISBN: 972-31-0954-9

Teaching methods and learning activities

Lectures and classes: The contents of the syllabus are presented in the lectures, illustrated with several examples. In the practical classes, exercises and related problems are solved and discussed. Several real data sets will be analyzed using the statistical software R. All resources are available for students at the unit’s web page.

 

Software

R

keywords

Physical sciences > Mathematics > Statistics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	50,00
Teste	50,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	106,00
Frequência das aulas	56,00
Total:	162,00

Eligibility for exams

Attendance to the course unit, as defined in the 
following terms, is compulsory: If a student 
is regularly enrolled, he/she cannot exceed the limit 
number of absences corresponding to 25% of the 
practical classes.

Students covered by the situations provided for by law 
are exempt from verifying the attendance conditions 
mentioned above (Art. 10, Regulamento Geral para  
Avaliação dos discentes de primeiros ciclos, 
de ciclos de estudos integrados de mestrado e 
de segundos ciclos da Universidade do Porto). 

Mandatory attendance is subject to the UP's action plan 
in view of the possible COVID-19 pandemic evolution. 

Calculation formula of final grade

The assessment will be based on two tests (T1 and T2):

• The first test, T1, will have the duration of 90 minutes, taking place in the middle of the 2nd period (10 points).
• The second test, T2, also lasting 90 minutes, will take place on the day for the examination of the normal season (10 points).

The appeal ("época de recurso") exam will have three options: exams corresponding to parts T1 and T2, and an exam on the whole syllabus. Each student must state, in advance, what their option is.

Improvement of the classification of the previous academic year is done by taking the exam on the whole syllabus.

The assessment method may change, depending on the  evolution of the COVID-19 pandemic.

Classification improvement

Improvement of the classification at the time of appeal ("época de recurso") can be made.

The marks from the tests can used in the appeal season ("época de recurso").

Observations

Jury: Ana Rita Gaio and Sílvio Gama