Statistics
A.Y. 2023/2024
Learning objectives
The main objective of the course is to ensure that students acquire an adequate knowledge and degree of understanding of the appropriate tools to synthetically describe one or more characters of interest that are found in the most various fields (political, administrative, sociological, historical, legal, economic, etc.). This description can be made by aggregating the data observed in tables, giving an adequate graphical representation, constructing appropriate position and variability indices, identifying the most appropriate measures that highlight the relationships. The statistical description must be accompanied by statistical induction, when the survey is not total but partial; in this case, the knowledge of the aforesaid characters is not in "certain" terms but only "probable" and has the purpose of providing indications on the entire population of reference. The basic topics of Probability and Statistical inference are therefore provided. Knowledge and understanding of these tools require a strong application capacity. Students will have to develop a marked independence of judgment, in order to be able to adequately choose the most suitable techniques for solving the proposed problems, and they will have to demonstrate that they also possess communication skills, essential to be able to explain the methodologies and logical paths used in solving the questions. Finally, they must acquire a more and more refined learning ability, which will allow them to face new situations with a high degree of autonomy.
Expected learning outcomes
At the end of this course, the student is expected to know and use the main statistical tools necessary for the analysis of phenomena in different fields (social, economic, etc) and in their various manifestations. The student will be able to organize the observed data of one or more phenomena of interest in a frequency or contingency table, to synthesize their main features and relationships through appropriate univariate or bivariate indices, and to infer more general results about the population from the observed sample data.
Lesson period: Second trimester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
A-K
Responsible
Lesson period
Second trimester
Course syllabus
Descriptive statistics
1) Classification of statistical phenomena (types of characters and scales of measurement) and frequency distributions (absolute, relative and cumulative frequencies).
2) Graphical representations: bar graph, stick graph, histogram.
3) Calculation of a mode, a median and a sample mean when the data are classified in a frequency table. Theorems and properties of the mean.
4) Some indices of variability and dispersion: range, interquartile difference, variance and standard deviation. The variation coefficient.
5) Contingency tables and bivariate analysis: definition of joint absolute and relative, marginal and conditioned frequency distributions; the Pearson index for independence; covariance and the linear correlation coefficient; the simple linear regression.
Probability and random variables
1) Introduction to probability theory: classical, frequentist, subjective and axiomatic probability definitions; elementary, compound and disjoint events; stochastic independence; types of sampling (extractions with and without replacement).
2) Definition of discrete and continuous random variables: probability distribution, probability density, distribution function; expected value (or mean), mode, median, variance of a random variable. Definition of independence between random variables.
3) The Normal random variable.
4) Central limit theorem and law of large numbers.
Inferential statistics
1) Point estimation: definition of unbiased estimator; the standard error as an accuracy measure of an estimator. The sample mean and variance; the sample proportion.
2) Confidence intervals for a mean (with Normal observations and known or unknown variance). Confidence intervals for a proportion.
3) General definition of statistical hypothesis testing: null and alternative hypotheses; type 1 and type 2 errors; rejection region; p-value. Hypothesis testing for a mean, with Normal observations and known or unknown variance. Hypothesis testing for a proportion.
4) The Chi-square test for checking the independence between two variables.
1) Classification of statistical phenomena (types of characters and scales of measurement) and frequency distributions (absolute, relative and cumulative frequencies).
2) Graphical representations: bar graph, stick graph, histogram.
3) Calculation of a mode, a median and a sample mean when the data are classified in a frequency table. Theorems and properties of the mean.
4) Some indices of variability and dispersion: range, interquartile difference, variance and standard deviation. The variation coefficient.
5) Contingency tables and bivariate analysis: definition of joint absolute and relative, marginal and conditioned frequency distributions; the Pearson index for independence; covariance and the linear correlation coefficient; the simple linear regression.
Probability and random variables
1) Introduction to probability theory: classical, frequentist, subjective and axiomatic probability definitions; elementary, compound and disjoint events; stochastic independence; types of sampling (extractions with and without replacement).
2) Definition of discrete and continuous random variables: probability distribution, probability density, distribution function; expected value (or mean), mode, median, variance of a random variable. Definition of independence between random variables.
3) The Normal random variable.
4) Central limit theorem and law of large numbers.
Inferential statistics
1) Point estimation: definition of unbiased estimator; the standard error as an accuracy measure of an estimator. The sample mean and variance; the sample proportion.
2) Confidence intervals for a mean (with Normal observations and known or unknown variance). Confidence intervals for a proportion.
3) General definition of statistical hypothesis testing: null and alternative hypotheses; type 1 and type 2 errors; rejection region; p-value. Hypothesis testing for a mean, with Normal observations and known or unknown variance. Hypothesis testing for a proportion.
4) The Chi-square test for checking the independence between two variables.
Prerequisites for admission
The standard knowledge of Math, adquired at the high school, is enough to attend this course.
Teaching methods
About the theoretical part, theprofessor explains on the blackboard basically without the use of slides, the lecture in this way is more interactive and is adapted to the needs of the classroom. Students who cannot attend can find everything in the reference material (textbook and lecture notes on ARIEL).
After the introduction of any new concept, various numerical examples are presented to fully understand its meaning and to practice the calculations.
In addition to the theoretical lessons, classroom exercises are also carried out. The exercises carried out during the classes are available on the course web page (ARIEL) to facilitate non-attending students.
Comments and requests for clarification during the lessons / exercises by the students are always welcome, because they make the lessons more lively and certainly more useful for everyone.
After the introduction of any new concept, various numerical examples are presented to fully understand its meaning and to practice the calculations.
In addition to the theoretical lessons, classroom exercises are also carried out. The exercises carried out during the classes are available on the course web page (ARIEL) to facilitate non-attending students.
Comments and requests for clarification during the lessons / exercises by the students are always welcome, because they make the lessons more lively and certainly more useful for everyone.
Teaching Resources
I) Descriptive statistics: two lecture notes will be available on the ARIEL page of the course.
II) Probability and random variables: Introduzione all'inferenza statistca. Authors: Ferrari, Nicolini and Tommasi, Giappichelli Editore - Turin (2009) - CHAPTERS: 1-2.
III) Inferential statistics: Introduzione all'inferenza statistica. Authors: Ferrari, Nicolini and Tommasi, Giappichelli Editore - Turin (2009) - CHAPTERS: 3-4-5
and the supplementary notes "la stima puntuale", that will be available on the ARIEL page of the course.
II) Probability and random variables: Introduzione all'inferenza statistca. Authors: Ferrari, Nicolini and Tommasi, Giappichelli Editore - Turin (2009) - CHAPTERS: 1-2.
III) Inferential statistics: Introduzione all'inferenza statistica. Authors: Ferrari, Nicolini and Tommasi, Giappichelli Editore - Turin (2009) - CHAPTERS: 3-4-5
and the supplementary notes "la stima puntuale", that will be available on the ARIEL page of the course.
Assessment methods and Criteria
The exam consists of a written test lasting 45 minutes, consisting of 10 exercises and/or theoretical questions (either multiple choice or open questions), concerning the topics listed in the program. The exam is rated from 0 to 33 and is considered sufficient if a score of at least 18 is obtained.
The structure of the exam allows the student to check the theoretical and practical skills learned during the lessons and exercises.
Remark: to carry out the written test you need to bring a calculator with you.
The structure of the exam allows the student to check the theoretical and practical skills learned during the lessons and exercises.
Remark: to carry out the written test you need to bring a calculator with you.
L-Z
Responsible
Lesson period
Second trimester
Educational website(s)
Professor(s)
Reception:
Wednesday from 9:00 to 12:00
Via Conservatorio, III floor, Room n. 35