STATISTICS

The course is one of the basic quantitative training activities of the Bachelor's Degree Programme in Environmental Sciences. The aim is to get the student familiar with the main statistical tools for use in environmental and biological sciences, and their application for prediction and decision making under conditions of uncertainty.
The course provides knowledge of descriptive statistics, probability and inference, as well as skills in the use of specific programs for analysing data and reporting.
At the end of the course, the student will be able to identify suitable models and methodologies in the context of interest; moreover he will learn to interpret and communicate the obtained results, with the aim of driving appropriate decisions.

1. Knowledge and understanding:
    - to know the main tools for graphical representation and summary of a dataset
    - to know the basic concepts of probability calculus and distributions for inference
    - to know the basic methodologies of statistical inference

2. Ability to apply knowledge and understanding:
    - to use specific programs for data analysis and reporting
    - to use the appropriate terminology in all the processes of application and communication of the acquired knowledge

3. Ability to judge:
    - to apply the acquired knowledge in a specific context, identifying the most appropriate statistical models and inferential methods for the analysis

4. Communication skills:
    - to produce a report that presents in a clear and exhaustive way the results obtained from a statistical analysis
    - to know how to interact with the other students and with the instructor during the classes and on the virtual forum
  
5. Learning skills:
    - to use and integrate information from notes, books, slides and practical lab sessions
    - to assess the achieved knowledge through quizzes, exercises and assignments during the course

Knowledge of mathematics at the level of the course Mathematics and exercises.

Descriptive statistics: population and samples; types of variables; basic graphical representations and summaries; relationship between two factors and the Chi-squared statistics; relationship between two numerical variables, correlation and regression.
Probability: sample space, events and probability; discrete and continuous random variables; the binomial and the normal distributions.
Inference: sample distributions; confidence intervals; hypotheses testing and p-values; goodness of fit.

The course provides a practical introduction to statistics. The aim of the first part of the course is to get the students familiar with the most useful statistical techniques for summarising and representing data. Then some basic concepts about elementary probability and distributions are presented. The last part is devoted to statistical inference methods for estimation, testing and prediction. Theoretical presentations are always motivated by practical examples and applications to environmental and biological problems. The use of the statistical package R (http://cran.r-project.org/ ) is also introduced for data analysis, simulation and inference.

Robinson, R. and White, H. (2016) Elementary Statistics with R. Available at http://homerhanumat.github.io/elemStats .
Moore, D.S. (2005) Statistica di Base, Apogeo ISBN: 9788850322534
Iacus, S.M. and Masarotto, G. (2007) Laboratorio di Statistica con R (II ed.), McGraw-Hill ISBN: 9788838663697

The achievement of the course objectives is assessed through participation in activities and assignments during the course (30%) and a short final exam (70%). For those students that do not take part on the assignments during the course, the whole evaluation is based on the full final exam (100%).
Activities and assignments consist of discussions about different topics on the Moodle forum and solution of quizzes and exercises in Moodle. The solution to some exercises is in the form of short reports.
The final exam takes place in the computer lab and is composed of quizzes and exercises to be solved with R. The exercises are similar to those assigned in Moodle during the course and are thought to assess the expected learning results.
The use of the software R is part of the program of the course and the main tool for solving the assignments and for the exam.

Interactive approach based on lectures, practical lab sessions using R and real dataset analyses. Use of the e-learning platform Moodle for discussions and learning assessment. Open-source programs for data analysis and reporting.

Italian

written