Statistical Methods
Keywords |
Classification |
Keyword |
OFICIAL |
Mathematics |
Instance: 2024/2025 - 2S 
Cycles of Study/Courses
Acronym |
No. of Students |
Study Plan |
Curricular Years |
Credits UCN |
Credits ECTS |
Contact hours |
Total Time |
L.EIC |
355 |
Syllabus |
2 |
- |
4,5 |
39 |
121,5 |
Teaching Staff - Responsibilities
Teaching language
Portuguese
Objectives
This course unit aims to provide students with an integrated vision of the basic concepts and techniques of Statistics.
Learning outcomes and competences
At the end of this course unit, students should be capable of:
- using methods to explore, summarize and present data;
- using statistical inference methods.
Working method
Presencial
Program
- INTRODUCTION TO STATISTICS: Data and observations. Populations and samples. Statistical method.
- DESCRIPTIVE STATISTICS: Types of data and measure scales. data characterization and representation.
- PROBABILITIES: Random experiments. Sampling spaces and events. Probability, conditional probability and independence. Total Probability Theorem and Bayes Theorem.
- RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS: Random variables. Discrete and continous random variables. probability, probability density and cumulative probability functions. Population parameters. Covariance and correlation. Transformed variables.
- MAIN DISCRETE AND CONTINUOS DISTRIBUTIONS: Binomial and normal distributions. Student t distribution.
- SAMPLING AND SAMPLING DISTRIBUTIONS: Sampling and random sampling. Sampling distributions. Central Limit Theorem.
- ESTIMATION AND CONFIDENCE INTERVALS: Estimators and estimates. Confidence Interval. Confidence intervals for expected values and proportions. Sample size determination.
- STATISTICAL HYPOTHESIS TESTING: Hypothesis testing methodology. Significance level and statistical power (Type I and Type II errors). t-tests. Relationship between Hypothesis Testing and Confidence Interval. Hypothesis Testing concerning expected values and proportions. Qualitative data and Hypothesis Testing; non-parametric tests; Chi-square tests: Adjustment, homogeneity and independence tests.
Mandatory literature
A. Miguel Gomes e José F. Oliveira; Estatística - Apontamentos de Apoio às Aulas, 2018
Rui Campos Guimarães e José António Sarsfield Cabral;
Estatística, 2ª edição, Verlag Dashofer, 2011. ISBN: 978-989--642-108-3
Complementary Bibliography
Devore Jay L.;
Modern mathematical statistics with applications. ISBN: 978-1-4614-0390-6
Nathan Tintle, Beth L. Chance, George W. Cobb, Allan J. Rossman, Soma Roy, Todd Swanson, Jill VanderStoep;
Introduction to Statistical Investigations, Wiley, 2015. ISBN: 978-1-119-15430-3
Wonnacott Thomas H. 1935-;
Introductory statistics. ISBN: 0-471-51733-X
Teaching methods and learning activities
Theoretical classes: presentation of the course unit themes followed by examples and problem solving
Theoretical-practical classes: problem solving and clarification of doubts
keywords
Physical sciences > Mathematics > Probability theory
Physical sciences > Mathematics > Statistics
Evaluation Type
Distributed evaluation without final exam
Assessment Components
Designation |
Weight (%) |
Teste |
100,00 |
Total: |
100,00 |
Amount of time allocated to each course unit
Designation |
Time (hours) |
Estudo autónomo |
82,50 |
Frequência das aulas |
39,00 |
Total: |
121,50 |
Eligibility for exams
N/A
Calculation formula of final grade
The distributed assessment consists of two tests to be carried out on dates to be defined at the beginning of the semester.
In the first exam period (Normal Period), the Final Classification is the sum of the classifications obtained in the tests. The first test is worth 8 points and the second one 12 points. There is no minimum grade in any of the tests to be aproved in the Curricular Unit (UC).
Any student enrolled at UC can use the Appeal Period exam, either to pass or to improve his/her grade. This exam has two independent parts: Part I corresponds to the first test and Part II to the second one.
To be approved in the UC, it is necessary to obtain, in any of the exam periods, a Final Classification (CF) greater than or equal to 9.5 points (CF ≥ 9.5).
Any student can choose not to undergo the distributed assessment and obtain the CF by only taking the Appeal Period exam.
In the Appeal Period exam, students not yet approved in the UC may choose to take only one part of the exam while maintaining the grade of the test corresponding to the other part.
Also in this case the CF will be the sum of the two obtained classifications.
At any exam period, a student with a final grade equal to or higher than 17.5 (CF ≥ 17.5) will have to take an Extra Test (PE). The PE score varies between -1 and +3 points.
Any student who meets the conditions to take the PE, can
- choose not to take it and will have CF = 17 points, or
- choose to do it and will have CF = 17 + PE score.
Students enrolled in the UC are not subject to any conditions for accessing any assessment test/exam.
Special assessment (TE, DA, ...)
Special evaluations will be made by a written exam.
Classification improvement
Students who have passed the UC in the Normal Period and wish to improve their Final Classification may do so during the Appeal Period, or at any other period provided for this purpose by taking a global exam, that is, an exam that covers all the content taught.