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Facoltā di Scienze Agrarie e Alimentari Universitā degli Studi di Milano
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Statistical methodology for agricultural research
Code: G570N-
Teacher:  Marco Acutis
CFU subdivision: Lectures: 4
Practices in classroom: 2
Basic aims:  The course intends to complete and investigate 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.
Acquired skills:  The course allows students, through the use of the main statistical softwares, to deal with teoretical aspects and application of the principal techniques of mutivariate statistics and geostatistics.
Course contents:  Descriptive statistics. Contingency tables. Anova, one way and 2 or more way, with fixed and random factors. Randomized complete blocks, Latin square and split-plot designs. Linear regression, multiple regression, non linear regression. Definition of number of replication and sample size. How to manage experiment in field and in laboratory.
Program:  Descriptive statistics, sampling distribution and statistical test: Basic of descriptive statistics: central tendency and dispersion indices. Characteristics of samples and populations. Main probability distribution. Usage of the normal distribution and of the standardized normal distribution. Estimation of population parameters from a sample. Bias, consistency and efficiency of an estimator. The structure of a statistical test: two-tail and one tail-test, the null hypothesis, the significance level, power of a test, type I, II and III errors. Analysis of qualitative data: Analysis of data from enumeration. X2 test and condition of application. Relation between X2 and Z. Comparison among observed and theoretical proportion. Comparison among observed proportion. Contingency tables and related index for nominal or ordered data. Yates correction. G likelihood ratio test for small samples. Hint to log-linear models and more complex techniques for frequency data. Practical use of statistical software to do qualitative data analysis. t test and the analysis of variance Confidence bounds for a mean. Comparison of the mean of two samples; the Student t test. The t test for paired data. More than two samples: the ANOVA. Requirements needed to apply ANOVA: normality and homogeneity of variances tests. Data transformation. Factorial ANOVA and the concept of interaction. 2 way and 3 way ANOVA. Hierarchical ANOVA. Model at fixed effect and model with random effects. Techniques for multiple comparison among means: contrast and post-hoc tests. Hints to non-parametric ANOVA. Practical use of statistical software to do ANOVA. Correlation and regression analysis The correlation concept. Correlation coefficient and their statistical tests. Linear regression analysis. The squared minimum method. Requisites for the regression analysis and test for assumption. The regression coefficient and their standard error. Significance test for the regression coefficient and for intercept. Confidence bound of a regression line. The regression from the origin. The determination coefficient. Multiple regression analysis. The identification of the optimal model (backward, forward and stepwise regression). Hints of non parametric analysis of regression and correlation. Practical use of statistical software to do regression analysis. Experimental planning and field management of the experiments. Uncontrolled sources of error and the determination of the number of replication. Randomized blocks, Latin squares, split plot and strip plot experimental arrangement. Practical implementing in a field of experimental arrangement. Statistical analysis using specific software. Hints of geostatistics: semivariograms and spatial interpolation, with practical application. Introduction to multivariate analysis Basics of principal component analysis, discriminant analysis, multivariate analysis of variance and cluster analysis. First approach to the programs for multivariate analysis. Examples of interpretation of computer outputs and results reported in scientific papers
Prerequisites:  Basic knowledge of descriptive statistics. Basic level in usage of Excel spreadsheet.
Preparatory instructions:  Mahematics, Statistical analysis of data.
Learning materials:  Camussi A., Moller F.,Ottaviano E., SariGorla M., Metodi statistici per la sperimentazione biologica. Zanichelli. Snedecor G., Cochran W., Statistical methods, VIII ed., Iowa state University press. Freund R.J., Wilson W.J., Statistical methods. Academic press.1993 Lindman H. Analysis of variance in complex experimental design (reference book). W.H. Freeman, S. Francisco, 1974. 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 (2005 April Edition). Available on http://www.dsa.unipr.it/soliani/soliani.html
Other info:  Final test includes practical work at personal computer, open and multiple response tests and oral discussion.
Program of Statistical methodology for agricultural research (pdf version)
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