Applied Statistics

Code:

2MADSAD04

Acronym:

EA

Keywords
Classification	Keyword
OFICIAL	Statistics

Instance: 2020/2021 - 1S

Active?	Yes
Responsible unit:	Agrupamento Científico de Matemática e Sistemas de Informação
Course/CS Responsible:	Master in Modeling, Data Analysis and Decision Support Systems

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MADSAD	4	Bologna Official Syllabus	1	-	7,5	56	202,5

Teaching language

English

Objectives

The purpose of Applied Statistics is to provide the student statistical analysis techniques applied to some areas. It is intended to provide the tools necessary for inferential approach through parametric and non-parametric hypothesis testing (for location).
Some fitting distribution tests as well as parametric and non-parametric methods of analysis of variance are studied in detail.
Some simulation techniques are also provided, as well as some methods and techniques related to statistical quality control.

Learning outcomes and competences

The skills that the student intends to acquire are such that the student should be able to:
- use of the most appropriate hypothesis test (parametric or non-parametric), including the fititng distribution and  the analysis of variance tests,  and to distinguish clearly its application and conclusions that can be drawn;
- use the main simulation methods in statistics and program them in R;
- use the techniques of statistical quality control and know how to take the most appropriate conclusions;
- determine the parameters of the sampling plans associated to fixed risk levels;
- compare single and double sampling plans through the usual performance measures (operating characteristic curve, average outgoing quality curve, average number of items inspected by lot assuming a 100% rectifying process, average sample size in a double sampling plan);
- implement Shewhart control charts for monitoring processes associated to quantitative and qualitative variables;
- implement Shewhart control charst for monitoing the process mean and the process variability, namely the sample mean chart, the sample range chart, the sample standard-deviation chart and the sample variance chart, when the in-control process nominal values are known or unknown;
- implement Shewhart control charts for monitoring the proportion or the number of defectives (non-conforming) in a given number of production itens, as well as to monitor the number of non-conformities in a given number of production itens;
- implement FSI and VSI versiosn of the previous control charts;
- evaluate the performance of the contorl charts by using the common indicators: ARL, ATS, false alarm rate, power function;
- by analogy with the implementation of the previous charts, must be able to implement Shewhart control charts of individual observations and charts for other process paremeters;
- describe and justify the advantages of implementing EWMA and CUSUM control charts.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

N.A.

Program

Topic 1 Statistical models: discrete and continuos

Topic 2 Simulation
2.1. Generation of random variables
2.1.1. Introduction: Motivation
2.1.2. univariate distributions
2.1.2.1. Discrete random variables
2.1.2.2. Continuous random variables
2.1.3. multivariate distributions
2.2. Integration by Monte Carlo method

Topic 3 Parametric and non-parametric (location) tests
3.1.Parametric tests
3.1.1 Tests for the mean
3.1.2 Tests for the variance
3.1.3 Tests for comparison of means and variances
3.1.4 Tests for proportions
3.2 Non-parametric location tests
3.2.1 Test of the signs
3.2.2 Wilcoxon
3.3.3 Mann - Whitney - Wilcoxon


Topic 4 Fitting tests
4.1 Chi-Square
4.2 Kolmogorov-Smirnov
4.3 Adequacy of the statistical model
4.3.1. Graphical method (QQ plot)

Topic 5 Analysis of variance: parametric and non-parametric tests
5.1 With one factor
5.1.1 ANOVA Model
5.1.2 Kruskal - Wallis
5.2 With two factors
5.2.1 ANOVA Model
5.2.2 Friedman Test


Topic 6 Statistical Quality Control
6.1. Introduction
6.1.1. The main objective of statistical quality control
6.1.2. Usual statistical techniques in quality control
6.2. Acceptance quality control
6.2.1. Single and double Sampling plans. Operating characteristic curve
6.2.2. Rectification of lots. Average outgoing quality. Average number of itens inspected by lot. Average sample size in a double plan.
6.2.3. Producer's and consumer's risk
6.3. Statistical Process Monitoring
6.3.1. Brief introduction to control charts
6.3.2. Policies sampling FSI and VSI
6.3.3. Parameters associated with the "performance" of letters FSI and VSI
6.4. Shewhart control charts
6.4.1 Control Charts usual for quantitative variables
6.4.2 Control Charts usual for qualitative variables
6.5 CUSUM and EWMA control charts.

Mandatory literature

Conover,W. J.; Practical nonparametric statistics, John Wiley, 1999
Fishman, G. S.; Monte Carlo. Concepts, Algorithms and Applications, Springer, 1996
Ross, S. M.; Simulation, Academic press, (DM 62-443), 1997
Montgomery, D.C.; Introduction to Statistical Quality Control, John Wiley and Sons, 1997

Complementary Bibliography

Guimarães, R. C. e Cabral, J. A.; Estatística, McGraw-Hill, 1997
Figueiredo Fernanda Otília de Sousa 070; Inferência estatística. ISBN: 978-972-592-501-0
Ivette Gomes, Fernanda Figueiredo e Maria Isabel Barão; Controlo Estatístico da Qualidade, Edições SPE, 2010
Bento Murteira, Carlos Silva Ribeiro, João Andrade e Silva, Carlso Pimenta; Introdução à Estatística, Escolar editora, 2010
Kleijnen, J. e Van Groenendaal, W.; Simulation: A statistical perspective, J. Wiley & Sons, 1992
Ripley, B. D.; Stochastic Simulation John Wiley & Sons, 1987
Bratley, P., Fox, B.L. e Schrage, L.E. ; A Guide to Simulation, Springer-Verlag, 1987
Hjorth, J.S.U. ; Computer Intensive Statistical Methods. Validation, Model Selection and Bootstrap, Chapman & Hall, 1994

Comments from the literature

Slides used on lessons will de available to the students on Moodle.

Teaching methods and learning activities

Theoretical and practical classes:
The lectures will focus the theoretical aspects of the theory but also include the discussion of exercises.
The methods are presented and discussed in class in the context of practical problems and exercises. There is a discussion on the applicability condtions of the methods and emphasis is given to the interpretation of the results.

Support of R software.

Software

R (http://www.r-project.org)

keywords

Physical sciences > Mathematics > Statistics

Evaluation Type

Distributed evaluation without final exam

Assessment Components

Designation	Weight (%)
Teste	75,00
Trabalho escrito	25,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	80,00
Frequência das aulas	42,00
Trabalho escrito	40,00
Total:	162,00

Eligibility for exams

All registered students can be evaluated by exam (if gave up the evaluation by tests), provided they complete the practical work of topic 2.

Students can also do three tests (each one with a  score of 20): one for topics 1 and 3; another for topics 4 and 5; and another for topic 6. And a practical work (with a score of 20) for topic 2. In this case the final classification of the distributed evaluation corresponds to the simple average of the marks obtained in the four assessments, since that the minimum mark in each assessment is greater or equal to 6.0.
The average must be greater or equal to 9.5 to be approved.

Calculation formula of final grade

Final classification is the simple average of the 4 assessment marks, since that the minimum mark in each assessment is greater or equal to 6.0. 

Test 1 focuses on all the contents of Topics 1 and 3.

Pratical assigment with all the contents of Topic 2.

Test 2 focuses on all the contents of Topics 4 and 5.

Test 3 focuses on all the contents of Topic 6.

Each assessment (test 1, test 2, test 3 and pratical assigment) has a maximum score of 20.

Students can also do the exam with all the contents of topics 1, and 3 to 6.

Examinations or Special Assignments

The contents of Topic 2 will be evaluated by an individual pratical assigment.
If no assigment is delivered, the mark will be zero, and therefore the student will be not approved.
The grade of pratical assigment is not possible to be improved.

Internship work/project

N.A.

Special assessment (TE, DA, ...)

N.A.

Classification improvement

Improving classification can only be done by making all topics 1 and 3 to 6 by final exam.

The grade of pratical assigment is not possible to be improved.

Observations

N.A.