# Quantitative Methods in Environment and Safety

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### Objectives

Learning goals (LG)
1. Understand concepts relative to exploratory data analysis
2. Understand the basis of sampling theory
3. Understand hypothesis testing procedures
4. Widen the concepts of correlation and regression to generalized linear models (GLM)
5. Recognize classification and ordination methods
6. Understand the use of questionnaires
7. Develop a framework for concepts related to reliability
8. Distinguish constant and variable failure modes
9. Identify typical survival curves
Skills
General (GS)
1. Team work
2. Search literature and write synthesis
3. Write a technical report
Specific (CSS)
1. Develop statistical reasoning
2. Suggest procedures for data treatment
3. Calculate sample size
4. Apply hypothesis testing
5. Calculate correlations, regressions and GLM
6. Apply classification and ordination methods
7. Analyze reliability of questionnaire scales
8. Simulate random variables used in reliability
9. Calculate and discuss reliability and maintenance

### Program

1. Exploratory Data Analysis: Data analysis. Frequency distributions. Data summary. Data display
2. Point Estimation and Confidence Estimation: Point estimation. Confidence interval on the mean of a normal distribution. Confidence interval on the difference of the means of two independent normal populations.
3. Hypothesis Testing (parametric and non-parametric): Basic concepts. Tests on the mean of a normal population. Tests on a proportion. Tests on two or more means of independent normal populations (one-way ANOVA). Tests on two proportions. Wilcoxon-Mann-Whitney test and Kruskall-Wallis test. Goodness-of-fit tests.
4. Simple and Multiple Linear Regression: Model interpretation. Estimation of the model’s parameters. Inference on the model’s parameters. Measure of fit.
5. Principal Components Analysis: Principal components computation. Total variance decomposition. Rotation and interpretation of principal components.
6. Cluster Analysis: Proximity, similarity and dissimilarity measures. Hierarchical classification analysis of individuals and variables: Agglomeration criteria, dendrogram and cut point. Non-hierarchical classification analysis: k-means method. Validation of the classification structures.
7. Linear Discriminant Analysis: Objectives and criteria. Discriminant axes and their properties. Classification of new observations.
8. Sampling: Introduction to sampling theory and investigation through surveys. Survey designs. Empirical and non-probabilistic sampling techniques. Probabilistic sampling techniques. Choice of sample size.
9. Surveys: General rules for designing surveys. Psychometric characteristics for measuring instruments (validation and reliability analysis).
10. Reliability: Fundamental concepts in Reliability. Quality control. Statistical process control and Impresso em 17-01-2024 15:03 por: Maria de Fátima Almeida Brilhante 6 de 8 quality improvment: control charts for variables and attributes. Important theoretical distributions in Reliability. Modeling methods: block diagram and repairable systems. Reliability of systems. Analysis and prevention of failures. Reliability and maintenance. Human reliability analysis methodologies.

### Teaching Methodologies

This curricular unit is organized into two modules, one on Statistics and the other on Reliability. The topics covered in each module are presented and explored in a more applied manner. Examples and exercises from the master's degree main scientific areas are presented, which are solved with the help of SPSS (whenever justified).

### Bibliography

Everitt, Brian S., Dunn, Graham (2001). Applied Multivariate Data Analysis. Edward Arnold: London, UK. ISBN:0340741228 (BibUAç 519.23 E94a).
Gotelli, N. J., A. M. Ellison (2004). A primer of Ecological Statistics. Sinauer Associates, Inc., Sunderland, 510 pp.
Heeringa, S. G., B. T. West, P. A. Berglund (2010). Applied survey data analysis. Chapman & Hall/CRC, Boca Raton,
Hill, M. M., A. Hill (2009). Investigação por questionário, 2ª ed. Edições Sílabo, Lisboa, 377 pp.
Johnson, Richard A., Wichern, Dean W. (2002). Applied Multivariate Statistical Analysis. Prentice Hall: Upper Saddle River. ISBN: 0-13-092553-5 (BibUAç EG 519.23 J65ap - 102963).
Lohr, S.L. (2009). Sampling: design and analysis, 2ª edição. Duxbury Press.
Marôco, João (2018). Análise Estatística com o SPSS Statistics, 7ª ed. ReportNumber.
Montgomery, D. C., Runger, G. C. (2003). Applied statistics and probability for engineers, 3ª ed. John Wiley.
Reis, Elizabeth (2001). Estatística Multivariada Aplicada. Sílabo: Lisboa, Portugal. ISBN: 972-618-247- 6 (BibUAç SD 519.23 R299e 102967E2).
Smith, David J. (2011). Reliability, maintainability and risk: practical methods for engineers, 8th ed. Elsevier, Amsterdam, 440 p.
Zuur A.F., E.N. Ieno, G.M. Smith (2007). Analysing ecological data. Springer, New York, 672 pp.

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5

### Classes

• Teóricas - 35 hours

### Evaluation Methodology

• 1st Test (Statistics): 40%
• 2nd Test (Reliability): 60%