Statistics

Recommended Prerequisites

Mathematics.  

Teaching Methods

The teaching is provided in both theoretical and theoretical-practical sessions. The theoretical lectures are expository and include the presentation of examples. In order to apply the acquired knowledge, the theoretical-practical sessions are focused on solving a complete set of practical exercises.
Small  projects  involving  the  development  of  simple  statistical   models  and  computational  tools   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 this course is to introduce basic mathematical knowledge to prepare the student to model the behavior of random phenomena arising in the context of health sciences. It contributes to prepare students to describe, analyze and interpret real situations using non-deterministic mathematical models. The correct use of statistical methods in specific cases and the strict interpretation of the results require a theoretical base in Statistics, for which this course contributes.
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 getting explanation to interpret, predict and decide on the phenomena under study.

This unit allows developing the following skills: analysis and synthesis, problem solving, critical thinking, work in interdisciplinary teams, autonomous learning, adaptability to new situations and application of theoretical knowledge.

Work Placement(s)

No

Syllabus

Probability
Kolmogorov’s definition and its consequences. Conditional probability and Bayes theorem. Independence  of  events.   Random  variables  and  distributions.  Moments  and  order  parameters.  Common probabilistic models. Central limit theorem and applications.
Descriptive Statistics
Numerical and graphical methods for describing and summarizing data sets.
Inferential statistics
Population and sample. Sampling distributions.  Point and interval parametric estimation. Parametric hypothesis testing. Inferences concerning means and proportions: one and two populations. Inferences concerning variances: one and two gaussian populations. Chi-Square tests: goodness of fit, independence and homogeneity.
Simple linear regression
Presentation of the model and underlying hypothesis. Least squares estimates, confidence intervals and hypothesis testing for the parameters. Inference for the mean response and prediction of new observations. Model checking.

Head Lecturer(s)

Maria da Graça Santos Temido Neves Mendes

Assessment Methods

Continuous Assessment
Frequency: 100.0%

Final Assessment
Exam: 100.0%

Bibliography

Gonçalves, E., Nogueira, E. e Rosa, A. C, Noções de Probabilidades e Estatística, Departamento de Matemática, FCTUC, 2014.
Murteira, B., Ribeiro, J., Silva, C. e Pimenta, C., Introdução à Estatística (3ª Ed.), Escolar Editora, 2010.  
Daniel, W., Biostatistics: A foundation for analysis in the health sciences (9ª Ed.), John Wiley & Sons, 2009.
Devore, J., Probability and Statistics for Engineering and the Sciences (8ª Ed.), Brooks/Cole, 2011.
Marôco, J., Análise Estatística com o SPSS Statistics, 5ª Ed, ReportNumber, Pêro Pinheiro, 2011.
Moore, D. e Mccabe, G., Introduction to the practice of statistics (7ª Ed.), Freeman, 2011.
Rosner, B., Fundamentals of Biostatistics (7ª Ed.), Brooks/Cole, 2011.