Experimental methodologies in agriculture

A.Y. 2020/2021
Overall hours
Learning objectives
Acquisition of solid methodological and practical knowledge for the design of experimental tests and sample surveys in agriculture. Acquisition of software usage skills for statistical processing of biological data in agriculture. Acquisition of solid theoretical and practical bases for the presentation, reading and interpretation of the statistical results of experimental tests and sample surveys.
Expected learning outcomes
Students will acquire the ability to manage data and software to process results from experimental tests and sample surveys. They will also acquire the ability to present, read and interpret data from field and laboratory experiments and from sample surveys.
Course syllabus and organization

Single session

Lesson period
First semester
Teaching methods
The lessons will be held mainly on the Microsoft Teams platform in synchronization. Given the contents, it is recommended to follow the course step by step. The lessons will be recorded and available to students on the same platform. Two 'live', full-frontal lessons will take place in the middle and near the end of the course and will provide opportunities to work on exercises related to course topics. To participate in these 'live' lessons, a reservation with a special app will be required. For those who cannot attend, additional materials in the form of recorded classes will be made available. 'Live' participation in activities will be voluntary and will have no effect on the final grade.
All information about 'live' lessons, as well as all the didactic material of the course and notices about any updates in course organization will be published on the Ariel teaching site
The teaching will start on 2020, September 25th on teams. Please write an email to the teacher if you do not have the possibility to open the ariel site.
Program and reference material:
The program and reference material will not be changed.
Methods of learning verification and evaluation criteria
The exams will take place orally using the Microsoft Teams platform and will consist of theoretical questions, simple practical exercises on excel and a commentary on the results of an analysis carried out with statistical software in order to ascertain:
(a) your knowledge and ability to understand the topics of the course as well as mastery of the specific language related to the use of statistical techniques and the ability to present topics in a clear and orderly manner
(b) your ability to apply knowledge and understanding through the analysis of a dataset or the execution and discussion of a statistical problem using excel
(c) your ability to understand and interpret the results of statistical analysis by commenting on an analytical output of statistical software used during the course.
Each of the three above-mentioned criteria (a,b,c) will be scored from 1 to 10 points. The final evaluation is based on a total of 30 points.
Activities carried out by students during the course, such as commentaries on analyses, completion of exercises, a compilation of a dictionary of terms, etc. will also be taken into account when determining the final grade.
Course syllabus
Introduction: teaching organization and aims. Recommended texts and materials, examination methods.
Samples and populations. Estimates, estimators and parameters. Precision and accuracy. Characteristics of a good statistical sample: independence and randomization. Sampling plans. Type of variables and their graphical representations (histograms, box plot, stem and leaf, scatterplot). Frontal lesson: 5 hrs
Basic rules for setting up a good dataset. Absolute and relative references, use of simple formulas and matrices: syntax. Graphic representations with excel: histograms (matrix function); box plot; dispersion diagrams. Line diagrams and geo-referenced maps. Rules for graphs and tables. Practical exercises using PC: 6 hrs
Descriptive statistics: position and dispersion measurements. Asymmetry and kurtosis. Relationships between two quantitative variables: covariance, correlation and regression Frontal lesson: 4 hrs
Exercises about covariance, correlation and regression Expected values and residuals calculation and representation. Practical exercises, using PC: 5 hrs
Distributions: normal and standard normal. Central limit theorem. Sample distribution of averages. Standard error. Margin of error. Confidence intervals. Frontal lesson: 2hrs
Exercises about standardization; z scores; standard errors; confidence intervals. Practical exercises using PC: 4 hrs
Probability: basic rules. Permutations and combinations. Proof of hypotheses. Type I and II error. Power of statistical tests. Sample distribution of a proportion. Confidence intervals. Binomial distribution. Distribution of Poisson. Frontal lesson: 2 hrs
Exercises for the construction of a binomial distribution. Confidence intervals of a proportion. Hypothesis tests with Poisson distribution. Practical exercises using PC: 4 hrs
Testing of goodness of fit with probabilistic models. Chi squared distribution and his assumptions. Use of chi squared to test the goodness of fit to a proportion, binomial and Poisson distribution. The Chi squared test to verify the independence between two categorical variables. Tetrachoric tables and corrections of Yates. Fisher's exact test. Likelihood. Frontal lesson: 3 hrs
Exercises to verify the goodness of fit with different probabilistic models and independence between two categorical variables. Practical exercises using PC: 6 hrs
Confidence intervals, bilateral and unilateral alternative hypothesis on an average. t tests for repeated measurements or paired data. Critical values in two-tailed or one-tailed tests. Confidence interval. t Test for independent samples. Assumptions verification. Welch test. Frontal lesson: 3hrs
Exercises: confidence intervals of an average and definition of the P-values of the test statistic t o z. t tests with paired data and independent data. Construction of the test and hypotheses verification. P-values and interpretation of the results. Practical exercises using PC: 6 hrs
Analysis of variance: null and alternative hypothesis, sum of squares and degrees of freedom decomposition. Meaning of residual variability, F test. Assumptions: normality and homoschedasticity. Non parametric tests. Frontal lesson: 2hrs
Exercise of one-way ANOVA with three levels. Graphic method for normality: Q-Q plot, Shapiro Wilk test. Normalizing transformations. Homoschedasticity, Levene's test. Using JMP. Practical exercises using PC: 4 hrs
General linear model. Two-way Anova. Factorial and randomized block design. Mixed model: fixed and random factors. Interactions. Latin square. Covariate. Linear model and regression. Expected and residual
Hints about non-linear regressions and multivariate analysis. Frontal lesson: 2 hrs
Exercises with statistical software about design and analyses of models. Outputs and their interpretation Practical exercises using PC: 5 hrs
Prerequisites for admission
Basic knowledge of descriptive statistics.
Basic skill in using spreadsheet.
The prerequisites and the procedure of examination is the same for the students that will or will not attend the classes.
It is really recommended to attend the classes.
Teaching methods
The course is organized into frontal classes corresponding to 3 CFUs and practical training for 3 CFUs. The practical training will be carried out in informatic rooms .
Each class is organized in both theoretical and practical.
The aim of the lectures is to present the main statistical methodologies used in agriculture. The purpose of the PC exercises is to give the student the ability to apply the knowledge acquired by learning to build optimal datasets to carry out analysis by choosing with a critical spirit the most appropriate methodology and learning to comment on the results obtained.
Teaching Resources
The recommended book is The analysis of Biological data Whitlock M.C., Schluter D., Second edition Ed. W.H. Freeman Macmillan Learning. This text is useful to have a complete overview of the main methodologies presented in the course and for the solved exercises that can be used as in-depth material for students.Slides and materials (such as datasets, other book references, link and scientific papers) of the classes will be uploaded on Ariel website (https://pcrepaldimsa.ariel.ctu.unimi.it/)
Assessment methods and Criteria
The exam consists of a written and a practical examination followed by an optional interview. The written part consists of 6 questions (1 multiple choice question, 2 open theoretical questions; 2 practical problems; 1 statistical analysis to comment) and a computer session with 1 dataset to analyze with the software used in practical classes.
Criteria of evaluations: The exam will assess the ability to organize, summarize and represent the methodologies studied during the course choosing the appropriate experimental methodologies and statistical tests and the ability in using specific technical language and software.
The interview is optional and will focus on the results of the written and practical part to complete and clarify mistakes and to improve the final evaluation.
Computer room practicals: 40 hours
Lessons: 28 hours
Professor: Crepaldi Paola
keeping an appointment by e-mail
Sezione di Zootecnica Agraria, 1st floor, Via Celoria 2