93064 - Statistics

Learning outcomes

The course aims at providing students with the main concepts of Statistical Theory and tools of Data Analysis. These include - exploratory techniques for describing and summarizing data by graphical devices and summary measures, in both univariate and bivariate problem; - inferential methods of point and interval estimation and hypothesis testing in the context of random sampling from Gaussian and Binomial populations. To be able to understand the probabilistic aspects involved in statistical inference, students will also acquire knowledge of basic results of Probability Theory. In addition, during lab sessions students will be introduced to the use of the statistical software R for the application of some of the methods covered in the conventional lectures.

Course contents

The course program is organized in four parts as described below.

1. Exploratory data analyis
Graphical tools for data analysis and presentation. Frequency tables. Frequency distributions. Summary measures of position and dispersion. Two-way contingency tables. Joint, marginal and conditional distributions. Independence and Association. Covariance and correlation.

2. Probability Theory
Approaches to Probability Theory. Axiomatic approach to probability. Sets and Events. Conditional probability. Independent events. Total probability theorem. Random variables. Mean, quantiles and variance. Discrete and Continuous Uniform distribution. Binomial distribution. Gaussian distribution. Independent variables. Sums of random variables. Central limit theorem and related corollaries. The Student's t distribution.

3. Inferential Statistics
Random sampling. Parametric statistical models. Sampling distributions. Point estimation. Bias and mean squared error. Confidence intervals for the mean of a Gaussian population. Approximate confidence interval for a probability. Approximate confidence interval for the mean of non-Gaussian population. Confidence interval for the difference between the means of two Gaussian populations. Hypothesis testing on the mean of a Gaussian population. The p-value. Large-sample test on a probability. Large-sample test on the mean of non-Gaussian population Test on the difference between the means of two Gaussian populations.

4. Laboratory of Computer Programming

Some lectures will aim at providing a basic knowledge of Programming. No computer pre-requisites are required. A description of the R language is provided, including variables, expressions and statements; flow controls; functions, with particular attention to functions for importing data files and performing basic data analyses.

Readings/Bibliography

For topics 1-3 of the "Course contents" section the recommended readings are:

• Cicchitelli, G., D'Urso, P., Minozzo, M. (2021). Statistics: Principles and Methods, Pearson.

• Lecture notes that will be made available online at the beginning of the course on the platform Virtuale

• For further reading: Anderson, D.R., Sweeney, D.J., Williams, T.A., Camm. J.D., Cochran, J.J., Freeman, J., Shoesmith, E. (2020), Statistics for Business and Economics, Cengage Learning EMEA, Andover, UK. 5th Edition.

   

For topic 4 of the "Course contents" section the recommended readings are:

• E-Book: "R Programming", tutorialspoint. Website: https://www.tutorialspoint.com/r/index.htm

• E-Book: "Get started in R: a complete beginners workbook", R Statistics.Net. Website: http://rstatistics.net/r-tutorial-exercise-for-beginners/

Teaching methods

For topics 1-3 of the "Course contents" section: Traditional classroom lectures

For topic 4 of the "Course contents" section: Classroom lessons and practice using the student's notebook. It is therefore important that the students bring their personal notebooks during the lab lessons. In the absence of a personal notebook, the student can work with a partner.

Assessment methods

Format

Written examination. The full exam will comprise exercises and theoretical questions on all the topics covered in class. Examples of past exam papers will be made available at the beginning of the course.

Students taking the first mid-term exam can sit the second mid-term exam only if they obtained a sufficient mark. The second-mid-term can be taken only once either right at the end of the course or on the following call. If the student fails the second mid-term, he/she will have to resit the full exam and will lose the grade obtained in the first mid-term.

In some cases, after the full or second mid-term exam, the lecturer may require an oral exam as a further tool of assessment of the student's preparation.

NOTE:  The examination format might be subject to changes due to the evolution of the COVID-19 epidemic situation.

 

Grade rejection

Students can reject the grade obtained at the exam once. To this end, he/she must email a request to the instructor within the date set for registration. The instructor will confirm reception of the request.

Rejection is intended with respect to the whole exam, whose grade is the average of the grades obtained in the two mid-terms. If the grade is rejected, the student must retake the full exam (consisting of both parts). The only grade that can be rejected without any communication from the student is the one of the first mid-term: in this case the student can either take the second mid-term or sit the full exam (thus losing the grade obtained in the first mid-term).

 

Teaching tools

For topics 1-3 of the "Course contents" section: Teaching material (lecture notes, exercises, past exam papers, etc) and further information about the course will be available at the beginning of the course on the platform Virtuale.

For topic 4 of the "Course contents" section:

• under the "Teaching" section of  Filippo Piccinini's personal website all the slides used during the lessons are available for download as well as software tools for practice.

• The statistical software R can be freely downloaded from the web page http://http//www.r-project.org/

• The software RStudio can be used as an interface for R and can be freely downloaded from the site https://rstudio.com/products/rstudio/

Links to further information

https://virtuale.unibo.it/

Office hours

See the website of Paola Bortot

See the website of Filippo Piccinini