Statistics
Keywords |
Classification |
Keyword |
OFICIAL |
Quantitative Methods |
Instance: 2016/2017 - 1S
Cycles of Study/Courses
Acronym |
No. of Students |
Study Plan |
Curricular Years |
Credits UCN |
Credits ECTS |
Contact hours |
Total Time |
MIEGI |
82 |
Syllabus since 2006/2007 |
2 |
- |
6 |
56 |
162 |
Teaching language
Suitable for English-speaking students
Objectives
This course unit aims to allow students to consolidate knowledge on Descriptive Statistics, Probability Theory and Probability Distributions. To develop new knoeledge on the important field of Statistic Inference, including Random Sampling and Sampling Distributions, Point and Interval Estimation, Hypothesis Testing and Non-Parametric Tests. The course unit also includes an introduction to Analysis of Variance and Regression Analysis.
Later, on course unit Multivariate Statistics, students will be asked to recall this knowledge in order to learn advanced statistics techniques, which will have an important application in their future career.
Learning outcomes and competences
At the end of the semester, students should be capable of:
- identifying the concepts of this course unit in a structured way;
- using descriptive statistics tools in the analysis of data samples;
- solving common problems, which involve elementary probability theory, random variables, probability distributions, point and interval estimation, statistical hypothesis testing (parametric and nonparametric), analysis of variance with one factor and simple linear regression;
- using spreadsheets to solve the above mentioned problems.
Working method
Presencial
Pre-requirements (prior knowledge) and co-requirements (common knowledge)
Basic spreadsheets skills.
Program
- INTRODUCTION TO STATISTICS: Data and Observations. Populations and Samples. Statistical Method.
- DESCRIBING, ORGANIZING AND VISUALIZING DATA: Types of Data and Measure Scales. Summarizing Categorical, Quantitative and Bivariate Data. Spreadsheet Engineering. Information Visualization.
- PROBABILITIES: Experiments. Sampling Spaces and Events. Probability, Conditional Probability and Independence. Total Probability and Bayes Theorems.
- RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS: Random Variables. Discrete and Continous Random Variables. Mass, Density and Cumulative Probability Functions. Population Parameters. Joint Probability Distributions. Covariance and Correlation. Transformed Variables.
- MAIN DISCRETE AND CONTINUOS DISTRIBUTIONS: Binomial, Negative Binomial, Hypergeometric and Poisson Distributions. Uniform, Exponential and Normal Distributions. Chi-square, t and F Distributions.
- STATISTICAL INFERENCE: Statistical Inference Methodology. Significance Level and Ststistical Power (Type I and Type II Errors). Sampling and Random Sampling. Sampling Distributions. Central Limit Theorem. Generation of Random Samples and Sampling Distributions with Spreadsheets. Introduction to Monte Carlo Simulation.
- ESTIMATION AND CONFIDENCE INTERVALS: Estimators and Estimates. Desirable Properties os Estimators. Estimation Methods. Confidence Interval. Confidence Intervals for Expected Values, Variances and Proportions. Sample Size Determination. Bootstrapping Confidence Intervals.
- STATISTICAL HYPOTHESIS TESTING: Hypothesis Testing Methodology. Relationship between Hypothesis Testing and Confidence Intervals. Hypothesis Testing concerning Expected Values, Variances and Proportions.
- NON-PARAMETRIC TESTS AND RANDOMIZATION TESTS: Goodness of Fit Tests. Median Localization Tests. Other Non-Parametric Tests. Randomizations Tests.
- INTRODUCTION TO ANALYSIS OF VARIANCE: One-Way ANOVA. Fixed and Random Effects Models. Multiple Comparisons and Post-Hoc Analysis. ANOVA Assumptions. Non-Parametric ANOVA.
- INTRODUCTION TO REGRESSION ANALYSIS: Simple Linear Regression Model. Regressin Parameters Estimation (OLS). Inferences about regression Parameters. Predictions based on the Simple Linear Regression Model. Regression Assumptions.
Mandatory literature
A. Miguel Gomes e José F. Oliveira; Estatística - Apontamentos de Apoio às Aulas, 2016
Guimarães, R. M. C. e J. A. Sarsfield Cabral;
Estatística, Verlag Dashöfer Portugal, 2010. ISBN: 978-989-642-108-3
Complementary Bibliography
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
Jay L. Devore, Kenneth N. Berk;
Modern mathematical statistics with applications. ISBN: 978-1-4614-0390-6
Thomas Wonnacott, Ronald J. Wonnacott;
Introdução à estatística. ISBN: 85-216-0039-9
Teaching methods and learning activities
Methods and techniques are introduced using systematically practical examples. The learning process is complemented with problem solving sessions supported by computer software and two teamwork assignments.
Software
Folhas de Cálculo
keywords
Physical sciences > Mathematics > Statistics
Physical sciences > Mathematics > Probability theory
Evaluation Type
Distributed evaluation with final exam
Assessment Components
Designation |
Weight (%) |
Exame |
60,00 |
Teste |
15,00 |
Trabalho prático ou de projeto |
25,00 |
Total: |
100,00 |
Amount of time allocated to each course unit
Designation |
Time (hours) |
Elaboração de projeto |
50,00 |
Elaboração de relatório/dissertação/tese |
16,00 |
Estudo autónomo |
40,00 |
Frequência das aulas |
56,00 |
Total: |
162,00 |
Eligibility for exams
Admission criteria set according to Article 4 of General Evaluation Rules of FEUP.
Calculation formula of final grade
The final mark (CF) will be obtained by the following formula:
CF = 0.15 FA + 0.25 TG + 0.60 EF
FA - Quizzes:
- 7 quizzes (pratical classes);
- the quizzes mark (FA) is obtained by the average of the best 5 marks achieved by each student.
TG - Teamwork assignments:
- 2 small size teamwork assignments (TG1 e TG2).
- the teamwork assignments mark (TG) is obtained by the average of the two teamwork assignments.
EF - Final Exam
- written exam.
To pass this course, apart from a final grade no less than 10, is required a minimum grade of 6 in the final exam.
Special assessment (TE, DA, ...)
Special evaluations will be made by a written exam.
Classification improvement
Students may choose between:
- improving simultaneously components Quizzes (FA) and Final Exam (EF);
- improving only component Final Exam (FE).
Component teamwork assignments (TG) is not possible to improve.