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, mean squared error and consistency. 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

Module 2 lectures 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, flow controls and 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, see the recommended readings in the "Statistics: Module 2" website

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

For both Module 1+3 and Module 2 the assessment is via a written examination. The Module 1+3 full exam will comprise exercises and theoretical questions on Topics 1-3 of the "Course contents" section covered in class. Examples of past exam papers will be made available at the beginning of the Module. The Module 2 test can be taken on any of the available dates regardless on when the Module 1+3 exam is taken. The final mark for the whole Statistics course will be a weighted average of the marks obtained in the Module 1+3 exam and Module 2 exam. The mark obtained in either the Module 1+3 exam or the Module 2 exam will remain valid for at least one solar year.

 

Module 1+3 first midterm can only be taken by second-year students. Module 1+3 second midterm exam can only be taken by students that have passed the Module 1+3 first midterm exam. The Module 1+3 second midterm exam can be taken only once, either right at the end of the course or on the following call. If students fail the Module 1+3 second midterm exam, they will have to resit the Module 1+3 full exam and will lose the mark obtained in the Module 1+3 first midterm exam.

 

During the written examinations for both Module 1+3 and Module 2 the following are strictly prohibited:

• the use of mobile phones, smartwatches or any other electronic devices that have internet access;

• the use of any artificial intelligence (AI) tools;
  

• the use of calculators other than basic or scientific calculators, such as graphing, programmable or Computer Algebra System (CAS) calculators.

Failure to comply with these rules constitutes a violation of academic integrity and will result in the nullification of the exam.

 

Following the written examination, the lecturer may require students to take an oral examination as an additional means of assessing and verifying their knowledge and preparation. When required, the oral exam will take place shortly after the written examination and will consist of theoretical questions covering the course material.

 

Grade rejection

Students can reject the grade obtained at the written examination at most once. To this end, they must email a request to the instructor within the date that will be specified after the notification of the exam results.

If the grade of the Module 1+3 exam is rejected, the student must retake the full Module 1+3 exam, even if the second midterm exam was taken. The only grade that can be rejected without an explicit communication is the first midterm exam grade: in this case, the student can take the Module 1+3 full exam, thus losing the grade obtained in the first midterm exam.

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:

• The statistical software R can be freely downloaded from the web page https://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/
  
  
• Further details are provided in the "Statistics: Module 2" website.

Links to further information

https://virtuale.unibo.it/

Office hours

See the website of Paola Bortot

See the website of Filippo Piccinini