Statistical Methods

Fundamental notions of set algebra, differential and integral calculus.

Theoretical classes: Expository and inquisitive method; Concepts and techniques are exemplified using real data whenever possible.

Practical classes: students solve exercises, in groups or individually, using computer tools in the laboratory whenever the statistical analysis techniques justify it (EXCEL / R). 

Students are monitored, by clarifying theoretical doubts and solving exercises in class and during office hours.

Objectives: To provide the fundamentals of Probability and Statistics necessary for the study, analysis and data interpretation. Use of models with application in industrial engineering area.

Generic Skills: Application of acquired knowledge. Critical thinking and interpretation of results. Communication. Self-learning. Ability to work in groups, developing relationships interpersonal.

Specific Skills: Learn the main concepts of Probability and Statistics, for an understanding of the topics to be addressed in this curricular unit, namely, learning and know how to use the methods of data interpretation and analysis, correlation and linear regression, and the models probabilistic factors that form the basis of statistical inference. Learning to use and interpret basic tools of statistical inference. Use spreadsheet (Excel) on topics addressed.

1. Probabilities. Introduction. Random experience, space for results, events. Probability definition. Conditional probability. Independent events. Total probability theorem. Bayes’ theorem.

2. Random Variables and Discrete Probability Distributions. Introduction. Discrete random variables: Definition; Probability function; Distribution function; Location and dispersion parameters. Special discrete distributions: Bernoulli distribution; Binomial Distribution; Hypergeometric Distribution; Poisson distribution. Discrete bidimensional random variables: Definition; Joint probability and distribution functions; Marginal probability function; Conditioned probability function; Independence from random variables; Covariance and linear correlation coefficient.

3. Random Variables and Continuous Probability Distributions. Definition; Probability density function; Distribution function; Location and dispersion parameters. Special continuous distributions: Uniform and Exponential Distributions; Normal Distribution; Brief reference to Chisquare distribution, T-Student distribution, and F distribution.

4. Sampling and Sampling Distributions. Estimation. Introduction. Random sample. Statistics. Distribution of the Sample Average. Sampling Variance Distribution. Fundamental notions of Point and Interval Estimation. Confidence intervals for the mean value, for the proportion and for the population variance. Confidence intervals for the difference between two means, and for the ratio of two variances.

5. Parametric Hypothesis Tests. Fundamental notions. Tests for the mean value, for the proportion and for the variance of a population. Tests for the difference between two expected values, and for the ratio of variances of two normal populations.

6. Data analysis software. Use Excel / R to review some concepts. Descriptive statistics in one dimension: Frequency tables and graphical representation. Location measures and dispersion measures. Asymmetry measures. Descriptive statistics in two dimensions: Contingency tables and dispersion diagrams. Covariance and correlation coefficient. Simple linear regression. Determination coefficient.

NAO

Recommended:

Teacher notes and exercises list (available at Moodle and InforEstudante)

Guimarães, R., Cabral, J. (2007). Estatística, McGraw-Hill, Lisboa (available at ISEC library: 3-3-239)

Complementary:

Murteira, B., Ribeiro, C., Silva, J., Pimenta, C. (2002). Introdução à Estatística. McGraw Hill. (available at ISEC library: 3-3-148)

Montgomery, D., Runger, G. (2007). Applied Statistics and Probability for Engineers. 4th ed. Wiley, New York. (available at ISEC library: 3-3-192)

Ross, S. (2009). Introduction to probability and statistics for engineers and scientists. 4th ed. Amsterdam. Elsevier. (available at ISEC library: 3-3-191)