Statistical Methods in Biology

Objectives

Conceptual objectives (OC)

1. Master concepts related to exploratory data analysis

2. Master the fundamental concepts of sampling theory of and experimental design

3. Master the mechanics of hypothesis testing

4. Extend the concepts of correlation and regression to the generalized linear models

5. Understand the concept of maximum likelihood

6. Master fundamental concepts in Bayesian inference

7. Recognize methods of multivariate analysis

Skills General (CG)

1. Team work

2. Search literature and prepare synthesis

3. Report technical and scientific information

Specific (EC)

1. Develop statistical reasoning and thinking

2. Suggest appropriate methods for data analysis

3. Analyze experimental designs and calculate the number of required samples

4. Apply and interpret hypothesis tests

5. Calculate correlations and regression models

6. Calculate generalized linear models

7. Calculate Bayesian models

8. Use multivariate analysis techniques

Program

1. Exploratory data analysis
Tables and graphs
Measures of central tendency and of dispersion
Types of distribution
2. Sampling and experimental design
Calculating the minimum number of samples for a given precision
Margin of error and maximum error
Implications on the distribution of organisms
Types of experimental design
Controls of manipulations
Independence and pseudo-replication
3. Frequentist inference
Confidence intervals
Parametric and non-parametric tests
Comparison of two or k samples
4. Correlation and Regression
Correlation and linear regression
Estimation and validation of the regression model
Multiple regression
Nonlinear models
5. Generalized linear models
Maximum likelihood
Link function
Hierarchical models
6. Bayesian Inference
Bayes Theorem
Bayesian models
Using WinBUGS
7. Multivariate Analysis
Cluster analysis
Multivariate ANOVA
Principal component analysis
Discriminant analysis

Teaching Methodologies

There isn’t a clear separation between theoretical and practical lessons, but a sequence of presentation of concepts, examples and exploration of data manipulation and statistical applications, avoiding the teaching of recipes but valuing the practical application of tools. Classes run on a computer room for periods of 2.5 hours, for a maximum of 20 participants, divided into groups of up to two students.

Bibliography

AAfonso A & C Nunes (2011) Estatística e probabilidades: aplicações e soluções em SPSS. Escolar Editora, Lisboa, 554 pp.

Borcard D, F Gillet & P Legendre (2011) Numerical Ecology with R. Springer, New York

Gotelli NJ & AM Ellison (2012) A primer of Ecological Statistics. Second Edition. Sinauer Associates, Inc., Sunderland

Kéry M (2010) Introduction to WinBUGS for Ecologists. A Bayesian approach to regression, ANOVA, mixed models and related analyses. Academic Press, Elsevier, Burlington

McCarthy MA (2007) Bayesian Methods for Ecology. Cambridge University Press, Cambridge

Paulino CD, A Amaral Turkman & B Murteira (2003). Estatística Bayesiana. Fundação Calouste Gulbenkian, Lisboa, 446 pp.

Qian SS (2010) Environmental and ecological statistics with R. Chapman & Hall/CRC, Boca Raton

Stone JV (2013) Bayes’ Rule. A tutorial introduction to Bayesian analysis. Sebtel Press,

Zuur AF, EN Ieno & GM Smith (2007) Analysing ecological data. Springer, New York