Applied Statistics

Code:

2MADSAD04

Acronym:

EA

Keywords
Classification	Keyword
OFICIAL	Statistics

Instance: 2019/2020 - 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	43	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 non-parametric hypothesis testing as a complement to parametric hypothesis testing, known by students. It also provides some simulation and sampling techniques, 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) and to distinguish clearly its application and conclusions that can be drawn;
- use the main simulation methods in statistics and program them in R;
- choose between the sampling process more accurate, or possible to apply;
- after selecting the most adequate sampling plan for a given problem, must determine the minimum sample size that guarantees a pre-defined precision, and select the most efficient estimator among several possible estimators;
- 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

Program

Module 1 Non-parametric tests
1. Fitting tests
1.1 Chi-Square
1.2 Kolmogorov-Smirnov
1.3 Adequacy of the statistical model
1.3.1. Graphical method (QQ plot)
2. Localization testing
2.1 Test of the signs
2.2 Wilcoxon
2.3 Mann - Whitney - Wilcoxon
3. Analysis of variance
3.1 With a factor
3.1.1 ANOVA Model
3.1.2 Kruskal - Wallis
3.2 With two factors
3.2.1 ANOVA Model
3.2.2 Friedman Test

Simulation Module 2
1. statistical models
2. Generation of random variables
2.1. Introduction: Motivation
2.2. univariate distributions
2.2.1. Discrete random variables
2.2.2. Continuous random variables
2.3. multivariate distributions
3. Integration by Monte Carlo method


Module 3 Sampling
1. introduction
2. Sampling methods empirical or non probabilistic
2.1. Quota method
2.2. Purposive sampling method
2.2.1. Method of individuals-type
2.2.2. Snowball sampling method
2.3. Convenience sampling method
2.4. Random-route (random itineraries)
3. Probabilistic sampling methods
3.1. Simple random sampling
3.2. Stratified random sampling
3.3. Sampling in bunches

Module 4 Statistical Quality Control
1. Introduction
1.1. The main objective of statistical quality control
1.2. Usual statistical techniques in quality control
2. Acceptance quality control
2.1. Single and double Sampling plans. Operating characteristic curve
2.2. Rectification of lots. Average outgoing quality. Average number of itens inspected by lot. Average sample size in a double plan.
2.3. Producer's and consumer's risk
3. Statistical Process Monitoring
3.1. Brief introduction to control charts
3.2. Policies sampling FSI and VSI
3.3. Parameters associated with the "performance" of letters FSI and VSI
3.4. Shewhart control charts
3.4.1 Control Charts usual for quantitative variables
3.4.2 Control Charts usual for qualitative variables
3.5 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
Vic Barnett; Sample Survey – Principles and Methods, 3rd edition, Hodder and Arnold, 2003
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
Reis, Elizabeth, Vicente, Paula e Ferrão, Fátima. Sondagens. ; A amostragem como factor decisivo de qualidade. Edições Sílabo, 1998
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	63,00
Frequência das aulas	42,00
Trabalho escrito	15,00
Total:	120,00

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 module 2.

Students can also do three tests (each one with a  score of 20), one for each module (1,3 e 4), and a practical work (with a score of 20) for module 2, and in this case the final classification of the distributed evaluation corresponds to the simple average of the marks obtained in the four modules, since that the minimum mark in each module 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 modules marks, since that the minimum mark in each module is greater or equal to 6.0. 

Test 1 focuses on all the contents of Module 1.

Pratical assigment with all the contents of Module 2.

The students will be evaluated on all the contents of Modules 3 and 4 in the tests that will take place in the day of the exam (normal season)

Each Module evaluation has a maximum score of 20.

Students can do the exam with all the contents of the 3 Modules 1, 3 and 4 (The classification of the Test 1 is forgotten).

Examinations or Special Assignments

The contents of Module 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.

Classification improvement

Improving classification can only be done by making all modules 1, 3 and 4 by final exam.

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