Learning objectives
Students will acquire skills enabling them to design and analyse, in statistical terms, quantitative datasets deriving from experiments conducted in natural environments, as well as the ability to analyse ecological/environmental datasets using multivariate statistical models.
Prerequisites
Knowledge of basic univariate statistics is required.
Course unit content
1. Review of matrix algebra: definitions, addition, subtraction between matrices; multiplication and inversion of matrices, etc. <br />
2. Multiple regression: general remarks on the method, examples of calculation, verification of the degree of fit of the model, etc. <br />
Examples of calculation applied to the environmental field. <br />
3. Multiple covariance analysis via multiple regression. Methodology with examples of calculation. <br />
Examples of application to the environmental sciences. <br />
4. Principal component analysis: theory with examples of calculation of components. <br />
Characterisation and interpretation of components. <br />
Examples of application to the environmental sciences. <br />
5. Multivariate normal distribution: main statistical/sampling characteristics. <br />
Multivariate significance testing: general remarks and in relation to the univariate case; <br />
Tests on 1 multivariate sample; <br />
Tests on 2 multivariate samples; <br />
Tests on K multivariate samples (K>2); <br />
6. Discriminant analysis: theory and calculation of discriminant functions and their characterisation. <br />
7. Canonical correlation analysis: theory with examples of calculation of canonical correlations. Characterisation and interpretation of correlations. <br />
Examples of application in the environmental field. <br />
8. Multivariate analysis of variance: general remarks and in relation to the univariate case. <br />
The case of 1 classification criterion. Examples of calculation applied to environmental research. <br />
9. Multivariate analysis of variance. <br />
The case of 2 classification criteria. Interaction: calculation and interpretation. <br />
Examples of application to the environmental field. <br />
10. Multivariate classification techniques: general remarks. <br />
Hierarchical clustering methods. Other methods. <br />
Examples of hierarchical clustering in territorial analysis. <br />
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Full programme
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Bibliography
Course textbook: <br />
O. Rossi, 2009. Metodi statistici multivariati per l'analisi di dati ecologici ed ambientali. Uni. Nova Ed. <br />
Teaching methods
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Assessment methods and criteria
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Other information
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