47732 - STATISTICS

Conoscenze e abilità da conseguire

At the end of the course students have the basic tools for analysing and describing a set of data through numerical indexes, graphical representations and dependence models for both univariate and bivariate data. The students are able to deal with basic tools of probability theory and its applications. The students will be also able to estimate population parameters from sample data by using standard inferential techniques (point estimation, confidence interval and hypothesis testing).

Contenuti

This course offers a comprehensive introduction to statistical methods for data analysis. In the first weeks, students learn how to describe and interpret univariate and bivariate data using numerical measures, graphical tools, and basic dependence models. Then, the course focuses on fundamental concepts of probability theory and their practical applications. The course concludes with an overview of inferential techniques, enabling students to make inferences on population parameters through point estimation, confidence intervals, and hypothesis testing, equipping them with essential tools for quantitative analysis in various contexts.

Structure of the course:

1. Introduction to the course. Case study.
2. Data basics. Data collection principles.
3. Examining numerical data: mean, frequency distributions. Frequency distributions. Histograms. Shape of a distribution: modality, skewness, outliers.
4. Variability:population variance, sample variance, unbiased sample variance, standard deviation.
5. Exercise on computation of variances. Median, percentiles, interquartile range.
6. Boxplot. Robustness of summary measures based on rankings. Transfomations.
7. Defining probability: frequentisti and Bayesian intepretation. Law of large numbers. Sample space. Addition rule for the union of events. Complementary events.
8. Marginal, joint, conditional probability.
9. Independence.Bayes theorem. Examples.
10. Example: infectious diseases. Random variables. Discrete random variables, probability mass function, cumulative distribution function.
11. Expected value and variance of a discrete random variable. Continuous random variables.
12. Linear transformation of random variables. Linear combinations of independent random variables. Properties.
13. The family of normal random variables. The standard normal random variable. Normal probability tables, computation of quantiles and percentiles.
14. Geometric distribution. Binomial distribution.
15. The choose function. Normal approximation to the binomial.
16. Variability in estimates: introduction
17. Sampling distribution of the mean. Introduction to confidence intervals.
18. Confidence intervals. Margin of error. Interpretation.
19. Test of hypothesis as a court trial. Test statitics. P-values.
20. More on P-values. Type I and type II errors.
21. Nominal significance level. Choice of Type I error.
22. Example: inference on two means. The t distribution.
23. Inference on the mean with the t distribution.
24. Paired data.
25. Inference for a single proportion.
26. Covariance and correlation.
27. Simple linear regression model.
28. Fitting a line through least squares. Prediction, extrapolation. Residuals analysis.
29. Residual analysis. Regression with a dummy variable. A worked example. Types of outliers.
30. Exercises. Discussion. Closing of the course.

Testi/Bibliografia

Required Readings:

David M Diez, Christopher D Barr, Mine C ̧etinkaya-Rundel OpenIntro Statistics (Fourth Edition), 2015.

This textbook is available under a Creative Commons license. Visit openintro.org for a free PDF

Metodi didattici

The main instructional approaches used in the course are:

- Lectures

Modalità di verifica e valutazione dell'apprendimento

Though not compulsory, class attendance and weekly homework is strongly encouraged.
Course evaluation will be different depending on the non-compulsory homework, as detailed in the following:
Students submitting homework:
Component Weight (%)
Midterm Exam 40
Final Exam 40
Homework 20

Students who do not do their homework:
Component Weight (%)
Midterm Exam 50
Final Exam 50

Exam structure:
One hour online test (1/2 hour for each midterm) via Moodle platform. In what follows, the chapters refer to the required reading book.
- First midterm: One cloze question on Chapter 1, one cloze question on Chapter 3 of the book, One cloze question on Chapter 4, 4/5 rapid fire questions on the topics of the first 15 lectures
- Second midterm: One cloze question on Chapter 6, one cloze question on Chapter 7, one cloze question on Chapter 8, 2/3 rapid fire questions on the topics of the second 15 lectures.
- Full: two separate online tests having the structure of first and second midterm

When grading, technically correct solutions are valued along with clearly stated explanations and neat reasoning. Numerically correct answers, alone, are not sufficient.

Exam policy:
Students can attend a mid-term exam (not compulsory) during the break at the end of the first sub-cycle, and then the second mid-term exam at the end of the course. The grades of the two mid-term exams will be summed up to compute the “final written exam” grade.
• Candidates who have not yet passed Mathematics, are allowed to submit homework. However, they can sign up for the exam only after having passed Mathematics.
• There is not a minimum passing grade for the I-midterm: candidates can sit the II-midterm irrespective of the grade they got in the I-midterm. A minimum passing grade exists only for the final mark. This minimum passing grade is standard and equivalent to 18/30.
• It is not necessary to formally reject the mark of the I-midterm if candidates intend to do so. Registration for the I-full will be automatically interpreted as the rejection of the mark of the I-midterm.
• Candidates sitting the exam (partial or full) can withdraw without any consequence within 10 minutes from the beginning of each exam session. Beyond this limit, whatever you provide is considered to be a submission.
• Grades are posted on Almaesami. The mark displayed is the final mark, which includes both parts of the exam (I-mid and II-mid) and any bonus points from homework (for eligible candidates).
• Only one rejection of the full mark is admitted per academic year. Candidates who are eligible for rejection and intend to reject the mark are invited to send an email, communicating their intention, to the main instructor by the date communicated through Almaesami.
• Candidates who reject the mark of the full, as well as candidates who failed the full, will resit the whole assessment (part I + part II).
• Candidates who rejected and resit the exam:
• won’t benefit again from the homework bonus, if available;
• will have the resit’s mark verbalized, even in the case that this is lower than the rejected mark.

Grading scale:
< 18: failed
18-23: sufficient
24-27: good
28-30: very good
30 e lode: outstanding

Students with disability or specific learning disabilities (DSA) are required to make their condition known to find the best possibile accommodation to their needs.

Strumenti a supporto della didattica

Tools, platforms, or resources used during the course:
- Learning platform: Virtuale (virtuale.unibo.it) contains the slides and the Homework assignments
- Presentation software: PDF
- Communication tools: Email; Teams; Forum on Virtuale
- Facilitating tools:
• Answering multiple-choice questions
Rapid-fire questions are made available via Virtuale. All questions are taken from past papers to provide examples of what candidates may be asked. Five attempts are available for each quiz.
• Warm-up
One crucial skill to be learned is time management. Exam papers are calibrated to be solved -if well prepared- in less time than granted. However, conscious time management is key to success and helps control exam pressure (not just for this specific exam). Exams hacks are made available via Virtuale to help candidates find their time management strategy.

Link ad altre eventuali informazioni

https://www.unibo.it/sitoweb/monica.chiogna2/

Orario di ricevimento

Consulta il sito web di Monica Chiogna