Statistical Methods for the Environmental Research
A.Y. 2024/2025
Learning objectives
The course aims to complete and deepen the knowledge already acquired by students in the field of statistics during the three-year degree course, providing concepts and methodologies useful for environmental sciences, with particular attention to univariate statistics, and mentions of multivariate statistics and geostatistics.
The contents of the course will allow students to:
- improve the knowledge of univariate statistics applied to environmental analysis;
- understand which tools are available for the analysis of multivariate phenomena and for spatial analysis;
- understand the fundamental elements of statistical-probabilistic methodologies and their application in the field of spatial and environmental statistics;
- together with the Data Management course, acquire the techniques for surveying, acquiring and managing environmental data and information.
The contents of the course will allow students to:
- improve the knowledge of univariate statistics applied to environmental analysis;
- understand which tools are available for the analysis of multivariate phenomena and for spatial analysis;
- understand the fundamental elements of statistical-probabilistic methodologies and their application in the field of spatial and environmental statistics;
- together with the Data Management course, acquire the techniques for surveying, acquiring and managing environmental data and information.
Expected learning outcomes
Knowledge and understanding. At the end of the course the students should know:
o univariate statistics applied to spatial analysis: multiple way ANOVA, ANCOVA and regression, with particular attention to the variable selection methods;
o the fundamental elements of multivariate statistics and geostatistics;
o the basic principles of machine learning, with particular attention to neural networks and random forest.
Applying knowledge and understanding. At the end of the course the students should be able to:
o Apply ANOVA and regression to experimental and spatial data, using statistical software;
o correctly choose the most appropriate instruments for their own analysis, based on the possibility and limits of the various approaches available;
o carry out simple multivariate or geostatistical analyses.
o univariate statistics applied to spatial analysis: multiple way ANOVA, ANCOVA and regression, with particular attention to the variable selection methods;
o the fundamental elements of multivariate statistics and geostatistics;
o the basic principles of machine learning, with particular attention to neural networks and random forest.
Applying knowledge and understanding. At the end of the course the students should be able to:
o Apply ANOVA and regression to experimental and spatial data, using statistical software;
o correctly choose the most appropriate instruments for their own analysis, based on the possibility and limits of the various approaches available;
o carry out simple multivariate or geostatistical analyses.
Lesson period: Second semester
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
1) Statistical basis: CFU 0.5 lectures + CFU 0.25 practical
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.
2) statistical inference basis CFU 0.5 lectures CFU 0.25 practical
The statistical test: concepts of null hypothesis, bilateral and unilateral tests, level of significance, protection, power, errors of I, II and III species. Confidence limits of a mean.
3) Techniques for comparisons between sample means CFU 1.5 lectures + CFU 0.5 practical.
The 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).
Correlation and regression analysis CFU 1.5 lectures + CFU 0.5 practical.
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 determination coefficient. The analysis of multiple regression. The choice of the optimal model (backward, forward and stepwise regression).
5) Introduction to multivariate analysis and machine learning CFU 0.5 lectures
Basis of PCA, Cluster analysis and neural network.
There are not differences between the attending and non-attending students
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.
2) statistical inference basis CFU 0.5 lectures CFU 0.25 practical
The statistical test: concepts of null hypothesis, bilateral and unilateral tests, level of significance, protection, power, errors of I, II and III species. Confidence limits of a mean.
3) Techniques for comparisons between sample means CFU 1.5 lectures + CFU 0.5 practical.
The 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).
Correlation and regression analysis CFU 1.5 lectures + CFU 0.5 practical.
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 determination coefficient. The analysis of multiple regression. The choice of the optimal model (backward, forward and stepwise regression).
5) Introduction to multivariate analysis and machine learning CFU 0.5 lectures
Basis of PCA, Cluster analysis and neural network.
There are not differences between the attending and non-attending students
Prerequisites for admission
Maths, Basic Excel spreadsheet, basic knowledge of statistics
Teaching methods
The course consists of 40 hours of theoretical lessons and 24 hours of practical lessons, which will be held using dedicated statistics packages (IBM SPSS, Excel).
Teaching Resources
The slides used for the lectures will be available during the course, as well as examples of the practical activities. Recording of the lectures will be available. The books can be used as reference or to go more in depth.
The following books are recommended:
Experimental design and data analysis for biologists. Quinn G.P., Keough M.J., Cambridge University Press.
Contemporary statistical models for the plant and soils science.Schabenberger o., Pierce F.J. Taylor and Francis group
There are not differences between the attending and non-attending students; for not-attending students the recording of the lectures play a very important role
The following books are recommended:
Experimental design and data analysis for biologists. Quinn G.P., Keough M.J., Cambridge University Press.
Contemporary statistical models for the plant and soils science.Schabenberger o., Pierce F.J. Taylor and Francis group
There are not differences between the attending and non-attending students; for not-attending students the recording of the lectures play a very important role
Assessment methods and Criteria
Verification of learning is carried out by examination (on-line or in presence)
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; the student will perform the chosen test and briefly comment on the results.
Duration 1 hour.
2) Written exam: 2 open-ended questions and 5 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.
If the examination will be carried out on-line, writing part and short oral will be replaced by an oral examination of about 30'
There are not differences between the attending and non-attending students.
Students with SLD or disability certifications are kindly requested to contact the teacher at least 15 days before the date of the exam session to agree on individual exam requirements. In the email please make sure to add in cc the competent offices: [email protected] (for students with SLD) o [email protected] (for students with disability).
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; the student will perform the chosen test and briefly comment on the results.
Duration 1 hour.
2) Written exam: 2 open-ended questions and 5 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.
If the examination will be carried out on-line, writing part and short oral will be replaced by an oral examination of about 30'
There are not differences between the attending and non-attending students.
Students with SLD or disability certifications are kindly requested to contact the teacher at least 15 days before the date of the exam session to agree on individual exam requirements. In the email please make sure to add in cc the competent offices: [email protected] (for students with SLD) o [email protected] (for students with disability).
AGR/02 - AGRONOMY AND FIELD CROPS - University credits: 6
Practicals: 32 hours
Lessons: 32 hours
Lessons: 32 hours
Professor:
Acutis Marco
Shifts:
Turno
Professor:
Acutis MarcoProfessor(s)