Statistical analysis of data

Recommended Prerequisites

Mathematical Analysis I, Mathematical Analysis II.

Teaching Methods

The teaching is provided in theoretical and practical 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 means 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 the behavior of random phenomena that arise in the context of engineering. 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 of Engineering involving the estimation of parameters of a model, testing its fitness and  interpret, predict and decide on the phenomena under study.

Instrumental skills: analysis and synthesis, problem solving and decision-making capacity.

Personal skills: development of critical thinking, work in interdisciplinary teams, autonomous learning, adaptability to new situations and application of theoretical knowledge.

Work Placement(s)

No

Syllabus

Probability

Random experience, the space of outcomes, events.  Kolmogorov’ definition of probability. Conditional probability. Independence of events.

Random Variables and Distributions

Discrete and continuous real random variables. Moments. Order parameters. Principal discrete and continuous probabilistic models. Central limit theorem.

Parametric Estimation

Introduction to inferential statistics. Review of descriptive statistics. Point estimation: estimators, empirical mean and variance, point estimation methods. Interval estimation: confidence intervals, the method of the pivotal variable, applications (confidence intervals for the mean of a population, for the variance of a Gaussian population and for a proportion).

Hypothesis Tests

Parametric tests. Applications (test for the mean of a population, for the variance of a Gaussian population and for a proportion).  The use of p-value.

Head Lecturer(s)

Maria Esmeralda Elvas Gonçalves

Assessment Methods

Assessment
There are 2 types of grading: during the semester or by final examination. Grading during the semester may involve problem solving or the development of a project (weighting from 0 to 40%), taking tests (with 0-30% total weight) or midterm exams (with 50-100% weight). Grading by final examination includes taking a written exam (weighting 50 to 100%): 100.0%

Bibliography

• Gonçalves, E., E. Nogueira, A.C. Rosa (2014) - Noções de Probabilidades e Estatística, 241 p. Departamento de Matemática, FCTUC.

• Murteira, B., C. S. Ribeiro, J. A. Silva, C. Pimenta (2010) - Introdução à Estatística, 3ª ed., Escolar Editora, Lisboa.

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

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

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

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

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

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