Statistical Methods

Recommended Prerequisites

Mathematics and Modelling.

Teaching Methods

The teaching is provided in T and TP sessions. The lectures are expository and include the presentation of examples that motivate and enable to understand the notions exposed. In order to apply the acquired knowledge, exercises are systematically proposed and  students must participate in solving them.

Small projects involving fieldwork, development of simple statistical models and computational resources may be suggested to develop critical skills and interpretation of results.

Weekly, tutorial time is offered to help students to overcome their learning difficulties.

Learning Outcomes

The aim of the course is to introduce basic mathematical knowledge to prepare the student to model  random phenomena that arise in areas of science. It contributes to prepare students to describe, analyze and interpret real situations using non-deterministic mathematical models. The correct use of statistical methods and the strict interpretation of the results requires a theoretical base in Probability and Statistics, present in this course.

It is also intended to prepare students for applying statistical  methods and concepts to real situations involving the estimation of parameters of a model, testing its fitness and  interpret, predict and deciding on the characteristic under study.

Work Placement(s)

No

Syllabus

1. Probability.

Definition of probability. Conditional probability and Independence.

2. Random Variables and Distributions

Discrete and continuous real random variables. Moments and order parameters. Principal discrete and continuous probabilistic models used in Statistics.

3. Inferential Statistics

Population and sample. Descriptive statistics: review of numerical methods for describing and summarizing data sets.

Parametric Estimation: Point and intervalar estimation for the mean and variance of populations and for a proportion

Hypothesis Tests: Tests for the mean and  variance of populations and for a proportion).  Chi-square tests: goodness of fit, independence and homogeneity. The p-value and its use in statistical software.

4. Simple Linear Regression

 The model. Confidence intervals and tests for the parameters. Model checking. Inference for the mean response and prediction of new observations.

Head Lecturer(s)

Maria da Graça Santos Temido Neves Mendes

Assessment Methods

Continous Assessment
Frequency: 100.0%

Final Assessment
Exam: 100.0%

Bibliography

E. Gonçalves,  E. Nogueira, A.C. Rosa (2015) Noções de Probabilidades e Estatística, 241 pp., Departamento de Matemática, FCTUC.

B. Murteira,  C. S. Ribeiro, J. A. Silva, C. Pimenta, F. Pimenta (2015) Introdução à Estatística, 3ª ed., Escolar Editora, Lisboa.

L.C. Andrews,  R.L. Phillips (2003) Mathematical Techniques for engineers and scientists, Spie Press, Washington.

 J.L. Devore,  (2011) Probability and statistics for engineering and the sciences, 8ª ed., Brooks/Cole.

R. Guimarães, J. Sarsfield Cabral (2007) Estatística, 2ª ed., McGraw-Hill, Lisboa.

J. Maroco (2007) - Estatística com utilização do SPSS, 3ª ed., Edições Sílabo.

D.C. Montgomery, G.C. Runger (2007)  Applied Statistics and Probability for Engineers, 4ª ed., 2007, Wiley.

D. Moore, G.  McCabe (2011) -  Introduction to the practice of statistics,  7ª ed., Freeman, New York.