The course aims to discuss in more detail and complete the knowledge already acquired by the students during the three-year degree in the field of statistics, providing concepts and methodologies useful for agri-environmental sciences.
Expected learning outcomes
At the end of the course the student, also through the use of the main statistical software packages, will be able to deal with theoretical aspects and applications of the principal techniques of multivariate statistics and geostatistics.
Lesson period: First semester
(In case of multiple editions, please check the period, as it may vary)
Descriptive statistics and sample distributions, statistical tests: Overview of descriptive statistics: central tendency and dispersion indices. Characteristics of populations and samples (references to the most common probability distributions). The estimate of the unknown parameters of a population starting from samples. Distortion, efficiency and consistency of an estimator. The statistical test: concepts of null hypothesis, bilateral and unilateral tests, level of significance, protection, power, errors of I, II and III species. T test and analysis of variance. Confidence limits of an average. Techniques for comparisons between sample means: analysis of variance. Prerequisites and conditions of applicability of ANOVA (test of normality and homogeneity of variances). The transformation of data. The analysis of factorial experiments and the interaction: 2 and 3-way anova, and relative interpretation of the results. Multiple comparison techniques between averages (contrasts and post-hoc tests). Introduction to nonparametric analysis of variance techniques. Correlation and regression analysis: The concept of correlation. The correlation coefficient and related statistical tests. Linear regression analysis. The least squares method. Assumptions for regression and related tests. The regression coefficient and its standard error. Significance test for regression and intercept coefficient. Confidence intervals around the regression line. The regression through the origin. The determination coefficient. The analysis of multiple regression. The choice of the optimal model (backward, forward and stepwise regression). Introduction to nonparametric techniques for correlation analysis. Experimental schemes and management of experiments in the field. Experimental randomized block schemes: practical implementation in the field and on the computer, and related statistical analysis procedures. Elements of geostatistics: semivariograms and spatial interpolation techniques.
Prerequisites for admission
Knowledge of descriptive statistics and basic data analysis techniques. Use of the Excel spreadsheet.
The course consists of a part of lectures of 32 hours and 32 hours of computer practice using Excel and the statistical software SPSS.
Slides of the lectures and material to support the exercises. Freely downloadable from www.acutis.it Reference books:L. Soliani. Manuale di statistica per la ricerca e la professione -statistica univariata e bivariata parametrica e non-parametrica per le discipline ambientali e biologiche (edizione aprile 2005). Disponibile gratuitamente su internet all'indirizzo http://www.dsa.unipr.it/soliani/soliani.html. G.P. Quinn, M. J. Keough (2002) Experimental Design and Data Analysis for Biologists. ISBN: 978-0521009768
Assessment methods and Criteria
Verification of learning is carried out by examination. The exam will be carried out within a single day and will consist of three parts: 1) Test on the computer for statistical processing of assigned data. An Excel format data set containing data relating to fictitious experiments, briefly described, will be distributed to each student. The student will have to choose the appropriate statistical analysis based on the assigned data, perform it and briefly comment on the results (on Word document). Duration 1 hour. 2) Written exam: 1 open-ended question and 8 multiple choice questions. Duration 1 hour and 15 minutes. 3) Short oral test (maximum 10 minutes): discussion of statistical processing, verification of written answers and any questions.