Quantitative Methods

Code:

MT117

Acronym:

M_QUAN

Keywords
Classification	Keyword
OFICIAL	Medicine

Instance: 2005/2006 - 1S

Active?	Yes
Responsible unit:	Population Studies
Course/CS Responsible:	Medicine

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MED	192	Plano oficial a partir de 2003	1	4		-

Objectives

The aim of this course is to familiarise first year students with basic mathematical/statistical concepts and techniques essential for formulating and understanding models in biology.

Program

I - Differential/Integral Calculus:
- A review of functions: algebraic, logarithmic, exponential. Limits and continuity. Differentiation: rules of differentiation, implicit differentiation. Applications of differentiation. Curve sketching.
- Functions of several variables: Introduction. Partial derivatives: definition and the geometric interpretation. Optimising functions of several variables.
- Introduction to Integral Calculus: Integration - the definitive integral and areas under a curve: The definitive integral. Standard integrals and methods of integration: by partial fractions. Impropers integrals. Applications in Biology.
- Differential Equations: Introduction. First order differential equations: variables separable differential equations. Applications: Deterministic model: exponential growth and decline in continuous time; Logistic and Gompertz model for limited population growth.
II - Descriptive statistics
Biological data and its graphical display; Descriptive statistics; Probability and probability distributions.
III - Statistical Inference
- Basic concepts of statistical inference: Sampling and sampling distributions; The Central Limit Theorem; Estimation and hypothesis testing; Confidence Intervals.
- Inferences concerning means: Hypothesis testing and Confidence Intervals - Inference for a mean of a population; Comparing two means (paired and independent samples); The F test for comparing two standard deviations .
- Inferences concerning proportions: Hypothesis testing and Confidence Intervals - Inference for a population proportion; Comparing two proportions (paired and independent samples); Comparing more than two proportions. Measuring associations with odds ratios and relative risk. Case-control and Cohort studies.
- Correlation and Linear regression: The regression model. The method of least squares. Hypothesis testing and Confidence Interval for the regression slope. Correlation coeficient. Residual analysis. Stochastic models and curve fitting: linear relationships, power and exponential laws.
IV - Computer sections: use of packages for mathematical and statistical analysis.

Main Bibliography

- Lectures notes.
- Eason, G, CW Coles e G Gettinby, “Mathematics and Statistics for the Bio-Sciences”, Ellis Horwood Ltd, 1989.
- Brown D, P Rothery, “Models in Biology - Mathematics, Statistics and Computing”, John Wiley & Sons Ltd, 1993.
- Dawson-Saunders e Trapp, “Basic and Clinical Biostatistics”. McGraw-Hill, 2000.
- Polking J, A Boggess e D Arnold, “Differential Equations”, Prentice Hall, 2001.
- Petrie, A e C Sabin, “Medical Statistics at a Glance”, Blackwell Science Ltd., 2000.
- Siegel S e Castellan NJ Jr, “Non-parametric statistics for Behavioral Sciences”, McGraw-Hill, Inc ,1988.
- Altman DG. “Pratical Statistics for Medical Research”, Chapman and Hall, 1991.
- David S Moore, “The Basic Practice of Statistics”. WH Freeman and Company, 1996
- Riffenburgh, RH “Statistics in Medicine”, Academic Press, 1999.

Complementary Bibliography

- A.C. Mennel & M.J. Bazin. “Mathematics for the Biosciences”. Ellis Horwood Ltd, 1988.
- A Ostrowski. “Lições de Cálculo Diferencial e Integral”, Vol I. Fundação Calouste Gulbenkian, 1969.
- J Benny, A Noprcliffe & S Mumble. “Introductory Mathematics through Science Applications”. Cambridge University Press, 1992.
- J Callahan, David Cox, K Hoffman, Donald O’Shea, H Pollatsek and L Senechal. “Calculs in Context – The Five College Calculus Course”. Freeman, 1995.
- James L Cornette, Ralph A Ackerman, Brian A Keller and Gail B Johnston. “Calculus for Biology – Preliminary Edition”. Prentice Hall, 1998.
- Christensen, R. “Analysis of variance, design and regression”. Chapman and Hall, 1996.
- Fisher, L e G Belle. “Biostatistics - A Methodology for the Health Sciences”. John Wiley and Sons, 1998.
- Guimarães, RG e JA Sarsfield Cabral. “Estatística”. McGraw-Hill, 1997.
- Joseph Fleiss. “Statistical Methods for Rates and Proportion”. John Wiley & Sons, 1981.
- Kleinbaum, D, L Kupper, K Muller e A Nizam. “Applied regression analysis and other multivariate methods”. Duxbury Press, 1998.
- Pestana, D, Veloso, S. "Introdução à Probabilidade e à Estatística" Vol I. Fund. Calouste Gulbenkian. 2002.

Teaching methods and learning activities

The topics covered are introduced in the theoretical lectures, through an example of application in the biological sciences. During these lectures the mathematical/statistical concepts and techniques needed to solve the problems are taught. In practical lessons students use SPSS software to solve complex exercises. Emphasis is given to teaching the need of understanding and using methods of formulating models, rather than the mechanical use of the techniques.

Software

SPSS 12.0

Evaluation Type

Distributed evaluation with final exam

Calculation formula of final grade

0.25xP + 0.75xT