The course aims at providing students with specific competences in sampling tecniques and statistical data analysis. Particular relevance is given to probability and inference, as the course means to provide students with the necessary tools for supporting decisional processes through the management of data bases and the use of statistical models.
Curriculum
Canali
teacher profile teaching materials
variables and their measurement
univariate distributions
describing data with tables and graphs
measures of position
variability
bivariate descriptive statistics
independence, association, correlation
probability distributions for discrete and continuous variables
sampling distributions
Inference:
estimation
hypothesis test
Statistical methods for the social sciences
Pearson International Edition - 4th edition 2009
Programme
descriptive statisticsvariables and their measurement
univariate distributions
describing data with tables and graphs
measures of position
variability
bivariate descriptive statistics
independence, association, correlation
probability distributions for discrete and continuous variables
sampling distributions
Inference:
estimation
hypothesis test
Prerequisiti
There are no formal prerequisites for this course. Nevertheless, a sound knowledge of the topics usually covered in a General Mathematics course is strongly recommended, including logarithms, function analysis, derivatives, and integrals.Core Documentation
A. Agresti, B. FinlayStatistical methods for the social sciences
Pearson International Edition - 4th edition 2009
Reference Bibliography
A. Agresti, B. Finlay Statistical methods for the social sciences Pearson International Edition - 4th edition 2009Type of delivery of the course
It is a traditional course with lectures in the classroom. There are also 2 hours a week dedicated to excersisesAttendance
Classes are held in person. Students authorized by the University may attend classes via live streaming.Type of evaluation
The examination consists of solving three or four exercises designed to assess the student's level of preparation. These are numerical exercises, not proofs and not theoretical questions. The examination lasts two hours. During the course, two midterm assessments are scheduled for attending students. These assessments will be administered through the online learning platform on dates set by the instructor and communicated well in advance. Students who successfully pass both midterm assessments will be eligible to take a final examination, to be completed within the summer examination session, covering only the topics related to statistical inference. teacher profile teaching materials
Frequency distributions, both simple and grouped, are discussed, as well as the main tabular and graphical representations of absolute, relative, and cumulative frequencies. Particular emphasis is placed on selecting the most appropriate graphical representations for qualitative, discrete, and continuous variables.
A substantial portion of the course concerns summary indices. Analytical means, measures of position, and distribution functions are introduced. The concept of variability is examined through mean deviations, standard deviation, variance, the coefficient of variation, and other indices of heterogeneity, with reference to their main theoretical properties.
Relationships between variables are analyzed through bivariate distributions, contingency tables, and measures of dependence and correlation. This is followed by an introduction to simple linear regression, the method of least squares, deviance decomposition, and measures of goodness of fit.
The probability section addresses random experiments, definitions of probability, independence, conditional probability, and Bayes’ theorem. Selected probability distributions are presented, including the Binomial and the Normal distributions, along with combinations of random variables. The course continues with sampling distributions, with particular reference to the sample mean and the use of tables for the Binomial, Normal, and Student’s t distributions.
The final part introduces the fundamentals of statistical inference: estimation theory, confidence intervals for proportions and means, hypothesis testing, and the analysis of Type I and Type II errors.
1. General aspects of Statistics: knowledge of collective phenomena through data collection, ordering, summarization, and analysis; national and international sources; data generation: statistical surveys (censuses and sample surveys), administrative and population registers, experiments; objectives and methods of descriptive and inferential statistics.
2. Nature of variables, data series, and frequency distributions (univariate and multivariate).
3. Graphical representations for statistical variables and attributes.
4. Measures of central tendency (analytical and positional means); arithmetic mean and its properties; weighted mean; mode; median, quartiles, and quantiles.
5. Measures of variability: mean absolute deviations; variance and its properties; standardization; coefficient of variation; interquartile range; heterogeneity indices.
6. Shape of frequency distributions: measures of skewness.
7. Dependence analysis in bivariate distributions; contingency tables and measures of dependence (chi-square indices, Cramér’s V); linear correlation.
8. Simple linear regression, estimation of regression coefficients via least squares, deviance decomposition, and goodness-of-fit measures.
9. Probability and introductory concepts: random experiments, sample space, events; probability and event definitions; union and intersection; conditional probability, independence of events, Bayes’ formula.
10. Random variables, probability distributions, distribution functions; discrete and continuous random variables (expectation and variance); linear combinations of random variables (expectation and variance).
11. Selected probability distributions: Bernoulli distribution, Binomial distribution, Normal distribution, Standard Normal distribution, Central Limit Theorem, approximation of the Binomial with the Normal.
12. Introduction to estimation theory; random samples, sample statistics, sampling distributions, estimator random variables, unbiasedness and efficiency, estimation of mean, variance, and proportion.
13. Interval estimation: confidence intervals for mean and proportion (known and unknown variance).
14. Hypothesis testing: tests for the mean and for the difference between means (known variance).
Cicchitelli G., D’Urso P., Minozzo M.
Ed. Pearson
Introduzione alla Statistica
Pelosi M. K., Sandifer T. M., Cerchiello P., Giudici P.
Ed. Mc Graw Hill
Programme
The course introduces the fundamental concepts of statistics, distinguishing from the outset between descriptive and inferential approaches. Methods of data collection and sources of data are examined, with attention to the nature of statistical variables and to the implications such characteristics have on the choice of analytical tools.Frequency distributions, both simple and grouped, are discussed, as well as the main tabular and graphical representations of absolute, relative, and cumulative frequencies. Particular emphasis is placed on selecting the most appropriate graphical representations for qualitative, discrete, and continuous variables.
A substantial portion of the course concerns summary indices. Analytical means, measures of position, and distribution functions are introduced. The concept of variability is examined through mean deviations, standard deviation, variance, the coefficient of variation, and other indices of heterogeneity, with reference to their main theoretical properties.
Relationships between variables are analyzed through bivariate distributions, contingency tables, and measures of dependence and correlation. This is followed by an introduction to simple linear regression, the method of least squares, deviance decomposition, and measures of goodness of fit.
The probability section addresses random experiments, definitions of probability, independence, conditional probability, and Bayes’ theorem. Selected probability distributions are presented, including the Binomial and the Normal distributions, along with combinations of random variables. The course continues with sampling distributions, with particular reference to the sample mean and the use of tables for the Binomial, Normal, and Student’s t distributions.
The final part introduces the fundamentals of statistical inference: estimation theory, confidence intervals for proportions and means, hypothesis testing, and the analysis of Type I and Type II errors.
1. General aspects of Statistics: knowledge of collective phenomena through data collection, ordering, summarization, and analysis; national and international sources; data generation: statistical surveys (censuses and sample surveys), administrative and population registers, experiments; objectives and methods of descriptive and inferential statistics.
2. Nature of variables, data series, and frequency distributions (univariate and multivariate).
3. Graphical representations for statistical variables and attributes.
4. Measures of central tendency (analytical and positional means); arithmetic mean and its properties; weighted mean; mode; median, quartiles, and quantiles.
5. Measures of variability: mean absolute deviations; variance and its properties; standardization; coefficient of variation; interquartile range; heterogeneity indices.
6. Shape of frequency distributions: measures of skewness.
7. Dependence analysis in bivariate distributions; contingency tables and measures of dependence (chi-square indices, Cramér’s V); linear correlation.
8. Simple linear regression, estimation of regression coefficients via least squares, deviance decomposition, and goodness-of-fit measures.
9. Probability and introductory concepts: random experiments, sample space, events; probability and event definitions; union and intersection; conditional probability, independence of events, Bayes’ formula.
10. Random variables, probability distributions, distribution functions; discrete and continuous random variables (expectation and variance); linear combinations of random variables (expectation and variance).
11. Selected probability distributions: Bernoulli distribution, Binomial distribution, Normal distribution, Standard Normal distribution, Central Limit Theorem, approximation of the Binomial with the Normal.
12. Introduction to estimation theory; random samples, sample statistics, sampling distributions, estimator random variables, unbiasedness and efficiency, estimation of mean, variance, and proportion.
13. Interval estimation: confidence intervals for mean and proportion (known and unknown variance).
14. Hypothesis testing: tests for the mean and for the difference between means (known variance).
Prerequisiti
There are no formal prerequisites, but it is strongly recommended that students have passed the General Mathematics exam.Core Documentation
Statistica – Principi e MetodiCicchitelli G., D’Urso P., Minozzo M.
Ed. Pearson
Introduzione alla Statistica
Pelosi M. K., Sandifer T. M., Cerchiello P., Giudici P.
Ed. Mc Graw Hill
Attendance
Attendance is not mandatory, but is strongly recommended.Type of evaluation
The exam consists exclusively of a written test comprising exercises and theoretical questions. During the exam, students are not allowed to bring any formula sheets or books into the examination room. Only calculators are permitted. Probability distribution tables will be provided by the instructor during the exam. In exceptional cases, the instructor may require an oral examination. Two midterm tests are scheduled during the course (the first approximately halfway through the course and the second near the end of the teaching period). Only students who achieve a passing grade on the first midterm test are eligible to take the second one. The midterm tests are open to all students enrolled in the course, regardless of whether they attend classes. Registration for the midterm tests must be completed exclusively through GOMP, following the same procedure used for regular exam sessions.Canali
teacher profile teaching materials
variables and their measurement
univariate distributions
describing data with tables and graphs
measures of position
variability
bivariate descriptive statistics
independence, association, correlation
probability distributions for discrete and continuous variables
sampling distributions
Inference:
estimation
hypothesis test
Statistical methods for the social sciences
Pearson International Edition - 4th edition 2009
Programme
descriptive statisticsvariables and their measurement
univariate distributions
describing data with tables and graphs
measures of position
variability
bivariate descriptive statistics
independence, association, correlation
probability distributions for discrete and continuous variables
sampling distributions
Inference:
estimation
hypothesis test
Prerequisiti
There are no formal prerequisites for this course. Nevertheless, a sound knowledge of the topics usually covered in a General Mathematics course is strongly recommended, including logarithms, function analysis, derivatives, and integrals.Core Documentation
A. Agresti, B. FinlayStatistical methods for the social sciences
Pearson International Edition - 4th edition 2009
Reference Bibliography
A. Agresti, B. Finlay Statistical methods for the social sciences Pearson International Edition - 4th edition 2009Type of delivery of the course
It is a traditional course with lectures in the classroom. There are also 2 hours a week dedicated to excersisesAttendance
Classes are held in person. Students authorized by the University may attend classes via live streaming.Type of evaluation
The examination consists of solving three or four exercises designed to assess the student's level of preparation. These are numerical exercises, not proofs and not theoretical questions. The examination lasts two hours. During the course, two midterm assessments are scheduled for attending students. These assessments will be administered through the online learning platform on dates set by the instructor and communicated well in advance. Students who successfully pass both midterm assessments will be eligible to take a final examination, to be completed within the summer examination session, covering only the topics related to statistical inference. teacher profile teaching materials
Frequency distributions, both simple and grouped, are discussed, as well as the main tabular and graphical representations of absolute, relative, and cumulative frequencies. Particular emphasis is placed on selecting the most appropriate graphical representations for qualitative, discrete, and continuous variables.
A substantial portion of the course concerns summary indices. Analytical means, measures of position, and distribution functions are introduced. The concept of variability is examined through mean deviations, standard deviation, variance, the coefficient of variation, and other indices of heterogeneity, with reference to their main theoretical properties.
Relationships between variables are analyzed through bivariate distributions, contingency tables, and measures of dependence and correlation. This is followed by an introduction to simple linear regression, the method of least squares, deviance decomposition, and measures of goodness of fit.
The probability section addresses random experiments, definitions of probability, independence, conditional probability, and Bayes’ theorem. Selected probability distributions are presented, including the Binomial and the Normal distributions, along with combinations of random variables. The course continues with sampling distributions, with particular reference to the sample mean and the use of tables for the Binomial, Normal, and Student’s t distributions.
The final part introduces the fundamentals of statistical inference: estimation theory, confidence intervals for proportions and means, hypothesis testing, and the analysis of Type I and Type II errors.
1. General aspects of Statistics: knowledge of collective phenomena through data collection, ordering, summarization, and analysis; national and international sources; data generation: statistical surveys (censuses and sample surveys), administrative and population registers, experiments; objectives and methods of descriptive and inferential statistics.
2. Nature of variables, data series, and frequency distributions (univariate and multivariate).
3. Graphical representations for statistical variables and attributes.
4. Measures of central tendency (analytical and positional means); arithmetic mean and its properties; weighted mean; mode; median, quartiles, and quantiles.
5. Measures of variability: mean absolute deviations; variance and its properties; standardization; coefficient of variation; interquartile range; heterogeneity indices.
6. Shape of frequency distributions: measures of skewness.
7. Dependence analysis in bivariate distributions; contingency tables and measures of dependence (chi-square indices, Cramér’s V); linear correlation.
8. Simple linear regression, estimation of regression coefficients via least squares, deviance decomposition, and goodness-of-fit measures.
9. Probability and introductory concepts: random experiments, sample space, events; probability and event definitions; union and intersection; conditional probability, independence of events, Bayes’ formula.
10. Random variables, probability distributions, distribution functions; discrete and continuous random variables (expectation and variance); linear combinations of random variables (expectation and variance).
11. Selected probability distributions: Bernoulli distribution, Binomial distribution, Normal distribution, Standard Normal distribution, Central Limit Theorem, approximation of the Binomial with the Normal.
12. Introduction to estimation theory; random samples, sample statistics, sampling distributions, estimator random variables, unbiasedness and efficiency, estimation of mean, variance, and proportion.
13. Interval estimation: confidence intervals for mean and proportion (known and unknown variance).
14. Hypothesis testing: tests for the mean and for the difference between means (known variance).
Cicchitelli G., D’Urso P., Minozzo M.
Ed. Pearson
Introduzione alla Statistica
Pelosi M. K., Sandifer T. M., Cerchiello P., Giudici P.
Ed. Mc Graw Hill
Programme
The course introduces the fundamental concepts of statistics, distinguishing from the outset between descriptive and inferential approaches. Methods of data collection and sources of data are examined, with attention to the nature of statistical variables and to the implications such characteristics have on the choice of analytical tools.Frequency distributions, both simple and grouped, are discussed, as well as the main tabular and graphical representations of absolute, relative, and cumulative frequencies. Particular emphasis is placed on selecting the most appropriate graphical representations for qualitative, discrete, and continuous variables.
A substantial portion of the course concerns summary indices. Analytical means, measures of position, and distribution functions are introduced. The concept of variability is examined through mean deviations, standard deviation, variance, the coefficient of variation, and other indices of heterogeneity, with reference to their main theoretical properties.
Relationships between variables are analyzed through bivariate distributions, contingency tables, and measures of dependence and correlation. This is followed by an introduction to simple linear regression, the method of least squares, deviance decomposition, and measures of goodness of fit.
The probability section addresses random experiments, definitions of probability, independence, conditional probability, and Bayes’ theorem. Selected probability distributions are presented, including the Binomial and the Normal distributions, along with combinations of random variables. The course continues with sampling distributions, with particular reference to the sample mean and the use of tables for the Binomial, Normal, and Student’s t distributions.
The final part introduces the fundamentals of statistical inference: estimation theory, confidence intervals for proportions and means, hypothesis testing, and the analysis of Type I and Type II errors.
1. General aspects of Statistics: knowledge of collective phenomena through data collection, ordering, summarization, and analysis; national and international sources; data generation: statistical surveys (censuses and sample surveys), administrative and population registers, experiments; objectives and methods of descriptive and inferential statistics.
2. Nature of variables, data series, and frequency distributions (univariate and multivariate).
3. Graphical representations for statistical variables and attributes.
4. Measures of central tendency (analytical and positional means); arithmetic mean and its properties; weighted mean; mode; median, quartiles, and quantiles.
5. Measures of variability: mean absolute deviations; variance and its properties; standardization; coefficient of variation; interquartile range; heterogeneity indices.
6. Shape of frequency distributions: measures of skewness.
7. Dependence analysis in bivariate distributions; contingency tables and measures of dependence (chi-square indices, Cramér’s V); linear correlation.
8. Simple linear regression, estimation of regression coefficients via least squares, deviance decomposition, and goodness-of-fit measures.
9. Probability and introductory concepts: random experiments, sample space, events; probability and event definitions; union and intersection; conditional probability, independence of events, Bayes’ formula.
10. Random variables, probability distributions, distribution functions; discrete and continuous random variables (expectation and variance); linear combinations of random variables (expectation and variance).
11. Selected probability distributions: Bernoulli distribution, Binomial distribution, Normal distribution, Standard Normal distribution, Central Limit Theorem, approximation of the Binomial with the Normal.
12. Introduction to estimation theory; random samples, sample statistics, sampling distributions, estimator random variables, unbiasedness and efficiency, estimation of mean, variance, and proportion.
13. Interval estimation: confidence intervals for mean and proportion (known and unknown variance).
14. Hypothesis testing: tests for the mean and for the difference between means (known variance).
Prerequisiti
There are no formal prerequisites, but it is strongly recommended that students have passed the General Mathematics exam.Core Documentation
Statistica – Principi e MetodiCicchitelli G., D’Urso P., Minozzo M.
Ed. Pearson
Introduzione alla Statistica
Pelosi M. K., Sandifer T. M., Cerchiello P., Giudici P.
Ed. Mc Graw Hill
Attendance
Attendance is not mandatory, but is strongly recommended.Type of evaluation
The exam consists exclusively of a written test comprising exercises and theoretical questions. During the exam, students are not allowed to bring any formula sheets or books into the examination room. Only calculators are permitted. Probability distribution tables will be provided by the instructor during the exam. In exceptional cases, the instructor may require an oral examination. Two midterm tests are scheduled during the course (the first approximately halfway through the course and the second near the end of the teaching period). Only students who achieve a passing grade on the first midterm test are eligible to take the second one. The midterm tests are open to all students enrolled in the course, regardless of whether they attend classes. Registration for the midterm tests must be completed exclusively through GOMP, following the same procedure used for regular exam sessions.Canali
teacher profile teaching materials
variables and their measurement
univariate distributions
describing data with tables and graphs
measures of position
variability
bivariate descriptive statistics
independence, association, correlation
probability distributions for discrete and continuous variables
sampling distributions
Inference:
estimation
hypothesis test
Statistical methods for the social sciences
Pearson International Edition - 4th edition 2009
Programme
descriptive statisticsvariables and their measurement
univariate distributions
describing data with tables and graphs
measures of position
variability
bivariate descriptive statistics
independence, association, correlation
probability distributions for discrete and continuous variables
sampling distributions
Inference:
estimation
hypothesis test
Prerequisiti
There are no formal prerequisites for this course. Nevertheless, a sound knowledge of the topics usually covered in a General Mathematics course is strongly recommended, including logarithms, function analysis, derivatives, and integrals.Core Documentation
A. Agresti, B. FinlayStatistical methods for the social sciences
Pearson International Edition - 4th edition 2009
Reference Bibliography
A. Agresti, B. Finlay Statistical methods for the social sciences Pearson International Edition - 4th edition 2009Type of delivery of the course
It is a traditional course with lectures in the classroom. There are also 2 hours a week dedicated to excersisesAttendance
Classes are held in person. Students authorized by the University may attend classes via live streaming.Type of evaluation
The examination consists of solving three or four exercises designed to assess the student's level of preparation. These are numerical exercises, not proofs and not theoretical questions. The examination lasts two hours. During the course, two midterm assessments are scheduled for attending students. These assessments will be administered through the online learning platform on dates set by the instructor and communicated well in advance. Students who successfully pass both midterm assessments will be eligible to take a final examination, to be completed within the summer examination session, covering only the topics related to statistical inference. teacher profile teaching materials
Frequency distributions, both simple and grouped, are discussed, as well as the main tabular and graphical representations of absolute, relative, and cumulative frequencies. Particular emphasis is placed on selecting the most appropriate graphical representations for qualitative, discrete, and continuous variables.
A substantial portion of the course concerns summary indices. Analytical means, measures of position, and distribution functions are introduced. The concept of variability is examined through mean deviations, standard deviation, variance, the coefficient of variation, and other indices of heterogeneity, with reference to their main theoretical properties.
Relationships between variables are analyzed through bivariate distributions, contingency tables, and measures of dependence and correlation. This is followed by an introduction to simple linear regression, the method of least squares, deviance decomposition, and measures of goodness of fit.
The probability section addresses random experiments, definitions of probability, independence, conditional probability, and Bayes’ theorem. Selected probability distributions are presented, including the Binomial and the Normal distributions, along with combinations of random variables. The course continues with sampling distributions, with particular reference to the sample mean and the use of tables for the Binomial, Normal, and Student’s t distributions.
The final part introduces the fundamentals of statistical inference: estimation theory, confidence intervals for proportions and means, hypothesis testing, and the analysis of Type I and Type II errors.
1. General aspects of Statistics: knowledge of collective phenomena through data collection, ordering, summarization, and analysis; national and international sources; data generation: statistical surveys (censuses and sample surveys), administrative and population registers, experiments; objectives and methods of descriptive and inferential statistics.
2. Nature of variables, data series, and frequency distributions (univariate and multivariate).
3. Graphical representations for statistical variables and attributes.
4. Measures of central tendency (analytical and positional means); arithmetic mean and its properties; weighted mean; mode; median, quartiles, and quantiles.
5. Measures of variability: mean absolute deviations; variance and its properties; standardization; coefficient of variation; interquartile range; heterogeneity indices.
6. Shape of frequency distributions: measures of skewness.
7. Dependence analysis in bivariate distributions; contingency tables and measures of dependence (chi-square indices, Cramér’s V); linear correlation.
8. Simple linear regression, estimation of regression coefficients via least squares, deviance decomposition, and goodness-of-fit measures.
9. Probability and introductory concepts: random experiments, sample space, events; probability and event definitions; union and intersection; conditional probability, independence of events, Bayes’ formula.
10. Random variables, probability distributions, distribution functions; discrete and continuous random variables (expectation and variance); linear combinations of random variables (expectation and variance).
11. Selected probability distributions: Bernoulli distribution, Binomial distribution, Normal distribution, Standard Normal distribution, Central Limit Theorem, approximation of the Binomial with the Normal.
12. Introduction to estimation theory; random samples, sample statistics, sampling distributions, estimator random variables, unbiasedness and efficiency, estimation of mean, variance, and proportion.
13. Interval estimation: confidence intervals for mean and proportion (known and unknown variance).
14. Hypothesis testing: tests for the mean and for the difference between means (known variance).
Cicchitelli G., D’Urso P., Minozzo M.
Ed. Pearson
Introduzione alla Statistica
Pelosi M. K., Sandifer T. M., Cerchiello P., Giudici P.
Ed. Mc Graw Hill
Programme
The course introduces the fundamental concepts of statistics, distinguishing from the outset between descriptive and inferential approaches. Methods of data collection and sources of data are examined, with attention to the nature of statistical variables and to the implications such characteristics have on the choice of analytical tools.Frequency distributions, both simple and grouped, are discussed, as well as the main tabular and graphical representations of absolute, relative, and cumulative frequencies. Particular emphasis is placed on selecting the most appropriate graphical representations for qualitative, discrete, and continuous variables.
A substantial portion of the course concerns summary indices. Analytical means, measures of position, and distribution functions are introduced. The concept of variability is examined through mean deviations, standard deviation, variance, the coefficient of variation, and other indices of heterogeneity, with reference to their main theoretical properties.
Relationships between variables are analyzed through bivariate distributions, contingency tables, and measures of dependence and correlation. This is followed by an introduction to simple linear regression, the method of least squares, deviance decomposition, and measures of goodness of fit.
The probability section addresses random experiments, definitions of probability, independence, conditional probability, and Bayes’ theorem. Selected probability distributions are presented, including the Binomial and the Normal distributions, along with combinations of random variables. The course continues with sampling distributions, with particular reference to the sample mean and the use of tables for the Binomial, Normal, and Student’s t distributions.
The final part introduces the fundamentals of statistical inference: estimation theory, confidence intervals for proportions and means, hypothesis testing, and the analysis of Type I and Type II errors.
1. General aspects of Statistics: knowledge of collective phenomena through data collection, ordering, summarization, and analysis; national and international sources; data generation: statistical surveys (censuses and sample surveys), administrative and population registers, experiments; objectives and methods of descriptive and inferential statistics.
2. Nature of variables, data series, and frequency distributions (univariate and multivariate).
3. Graphical representations for statistical variables and attributes.
4. Measures of central tendency (analytical and positional means); arithmetic mean and its properties; weighted mean; mode; median, quartiles, and quantiles.
5. Measures of variability: mean absolute deviations; variance and its properties; standardization; coefficient of variation; interquartile range; heterogeneity indices.
6. Shape of frequency distributions: measures of skewness.
7. Dependence analysis in bivariate distributions; contingency tables and measures of dependence (chi-square indices, Cramér’s V); linear correlation.
8. Simple linear regression, estimation of regression coefficients via least squares, deviance decomposition, and goodness-of-fit measures.
9. Probability and introductory concepts: random experiments, sample space, events; probability and event definitions; union and intersection; conditional probability, independence of events, Bayes’ formula.
10. Random variables, probability distributions, distribution functions; discrete and continuous random variables (expectation and variance); linear combinations of random variables (expectation and variance).
11. Selected probability distributions: Bernoulli distribution, Binomial distribution, Normal distribution, Standard Normal distribution, Central Limit Theorem, approximation of the Binomial with the Normal.
12. Introduction to estimation theory; random samples, sample statistics, sampling distributions, estimator random variables, unbiasedness and efficiency, estimation of mean, variance, and proportion.
13. Interval estimation: confidence intervals for mean and proportion (known and unknown variance).
14. Hypothesis testing: tests for the mean and for the difference between means (known variance).
Prerequisiti
There are no formal prerequisites, but it is strongly recommended that students have passed the General Mathematics exam.Core Documentation
Statistica – Principi e MetodiCicchitelli G., D’Urso P., Minozzo M.
Ed. Pearson
Introduzione alla Statistica
Pelosi M. K., Sandifer T. M., Cerchiello P., Giudici P.
Ed. Mc Graw Hill
Attendance
Attendance is not mandatory, but is strongly recommended.Type of evaluation
The exam consists exclusively of a written test comprising exercises and theoretical questions. During the exam, students are not allowed to bring any formula sheets or books into the examination room. Only calculators are permitted. Probability distribution tables will be provided by the instructor during the exam. In exceptional cases, the instructor may require an oral examination. Two midterm tests are scheduled during the course (the first approximately halfway through the course and the second near the end of the teaching period). Only students who achieve a passing grade on the first midterm test are eligible to take the second one. The midterm tests are open to all students enrolled in the course, regardless of whether they attend classes. Registration for the midterm tests must be completed exclusively through GOMP, following the same procedure used for regular exam sessions.Canali
teacher profile teaching materials
variables and their measurement
univariate distributions
describing data with tables and graphs
measures of position
variability
bivariate descriptive statistics
independence, association, correlation
probability distributions for discrete and continuous variables
sampling distributions
Inference:
estimation
hypothesis test
Statistical methods for the social sciences
Pearson International Edition - 4th edition 2009
Programme
descriptive statisticsvariables and their measurement
univariate distributions
describing data with tables and graphs
measures of position
variability
bivariate descriptive statistics
independence, association, correlation
probability distributions for discrete and continuous variables
sampling distributions
Inference:
estimation
hypothesis test
Prerequisiti
There are no formal prerequisites for this course. Nevertheless, a sound knowledge of the topics usually covered in a General Mathematics course is strongly recommended, including logarithms, function analysis, derivatives, and integrals.Core Documentation
A. Agresti, B. FinlayStatistical methods for the social sciences
Pearson International Edition - 4th edition 2009
Reference Bibliography
A. Agresti, B. Finlay Statistical methods for the social sciences Pearson International Edition - 4th edition 2009Type of delivery of the course
It is a traditional course with lectures in the classroom. There are also 2 hours a week dedicated to excersisesAttendance
Classes are held in person. Students authorized by the University may attend classes via live streaming.Type of evaluation
The examination consists of solving three or four exercises designed to assess the student's level of preparation. These are numerical exercises, not proofs and not theoretical questions. The examination lasts two hours. During the course, two midterm assessments are scheduled for attending students. These assessments will be administered through the online learning platform on dates set by the instructor and communicated well in advance. Students who successfully pass both midterm assessments will be eligible to take a final examination, to be completed within the summer examination session, covering only the topics related to statistical inference. teacher profile teaching materials
Frequency distributions, both simple and grouped, are discussed, as well as the main tabular and graphical representations of absolute, relative, and cumulative frequencies. Particular emphasis is placed on selecting the most appropriate graphical representations for qualitative, discrete, and continuous variables.
A substantial portion of the course concerns summary indices. Analytical means, measures of position, and distribution functions are introduced. The concept of variability is examined through mean deviations, standard deviation, variance, the coefficient of variation, and other indices of heterogeneity, with reference to their main theoretical properties.
Relationships between variables are analyzed through bivariate distributions, contingency tables, and measures of dependence and correlation. This is followed by an introduction to simple linear regression, the method of least squares, deviance decomposition, and measures of goodness of fit.
The probability section addresses random experiments, definitions of probability, independence, conditional probability, and Bayes’ theorem. Selected probability distributions are presented, including the Binomial and the Normal distributions, along with combinations of random variables. The course continues with sampling distributions, with particular reference to the sample mean and the use of tables for the Binomial, Normal, and Student’s t distributions.
The final part introduces the fundamentals of statistical inference: estimation theory, confidence intervals for proportions and means, hypothesis testing, and the analysis of Type I and Type II errors.
1. General aspects of Statistics: knowledge of collective phenomena through data collection, ordering, summarization, and analysis; national and international sources; data generation: statistical surveys (censuses and sample surveys), administrative and population registers, experiments; objectives and methods of descriptive and inferential statistics.
2. Nature of variables, data series, and frequency distributions (univariate and multivariate).
3. Graphical representations for statistical variables and attributes.
4. Measures of central tendency (analytical and positional means); arithmetic mean and its properties; weighted mean; mode; median, quartiles, and quantiles.
5. Measures of variability: mean absolute deviations; variance and its properties; standardization; coefficient of variation; interquartile range; heterogeneity indices.
6. Shape of frequency distributions: measures of skewness.
7. Dependence analysis in bivariate distributions; contingency tables and measures of dependence (chi-square indices, Cramér’s V); linear correlation.
8. Simple linear regression, estimation of regression coefficients via least squares, deviance decomposition, and goodness-of-fit measures.
9. Probability and introductory concepts: random experiments, sample space, events; probability and event definitions; union and intersection; conditional probability, independence of events, Bayes’ formula.
10. Random variables, probability distributions, distribution functions; discrete and continuous random variables (expectation and variance); linear combinations of random variables (expectation and variance).
11. Selected probability distributions: Bernoulli distribution, Binomial distribution, Normal distribution, Standard Normal distribution, Central Limit Theorem, approximation of the Binomial with the Normal.
12. Introduction to estimation theory; random samples, sample statistics, sampling distributions, estimator random variables, unbiasedness and efficiency, estimation of mean, variance, and proportion.
13. Interval estimation: confidence intervals for mean and proportion (known and unknown variance).
14. Hypothesis testing: tests for the mean and for the difference between means (known variance).
Cicchitelli G., D’Urso P., Minozzo M.
Ed. Pearson
Introduzione alla Statistica
Pelosi M. K., Sandifer T. M., Cerchiello P., Giudici P.
Ed. Mc Graw Hill
Programme
The course introduces the fundamental concepts of statistics, distinguishing from the outset between descriptive and inferential approaches. Methods of data collection and sources of data are examined, with attention to the nature of statistical variables and to the implications such characteristics have on the choice of analytical tools.Frequency distributions, both simple and grouped, are discussed, as well as the main tabular and graphical representations of absolute, relative, and cumulative frequencies. Particular emphasis is placed on selecting the most appropriate graphical representations for qualitative, discrete, and continuous variables.
A substantial portion of the course concerns summary indices. Analytical means, measures of position, and distribution functions are introduced. The concept of variability is examined through mean deviations, standard deviation, variance, the coefficient of variation, and other indices of heterogeneity, with reference to their main theoretical properties.
Relationships between variables are analyzed through bivariate distributions, contingency tables, and measures of dependence and correlation. This is followed by an introduction to simple linear regression, the method of least squares, deviance decomposition, and measures of goodness of fit.
The probability section addresses random experiments, definitions of probability, independence, conditional probability, and Bayes’ theorem. Selected probability distributions are presented, including the Binomial and the Normal distributions, along with combinations of random variables. The course continues with sampling distributions, with particular reference to the sample mean and the use of tables for the Binomial, Normal, and Student’s t distributions.
The final part introduces the fundamentals of statistical inference: estimation theory, confidence intervals for proportions and means, hypothesis testing, and the analysis of Type I and Type II errors.
1. General aspects of Statistics: knowledge of collective phenomena through data collection, ordering, summarization, and analysis; national and international sources; data generation: statistical surveys (censuses and sample surveys), administrative and population registers, experiments; objectives and methods of descriptive and inferential statistics.
2. Nature of variables, data series, and frequency distributions (univariate and multivariate).
3. Graphical representations for statistical variables and attributes.
4. Measures of central tendency (analytical and positional means); arithmetic mean and its properties; weighted mean; mode; median, quartiles, and quantiles.
5. Measures of variability: mean absolute deviations; variance and its properties; standardization; coefficient of variation; interquartile range; heterogeneity indices.
6. Shape of frequency distributions: measures of skewness.
7. Dependence analysis in bivariate distributions; contingency tables and measures of dependence (chi-square indices, Cramér’s V); linear correlation.
8. Simple linear regression, estimation of regression coefficients via least squares, deviance decomposition, and goodness-of-fit measures.
9. Probability and introductory concepts: random experiments, sample space, events; probability and event definitions; union and intersection; conditional probability, independence of events, Bayes’ formula.
10. Random variables, probability distributions, distribution functions; discrete and continuous random variables (expectation and variance); linear combinations of random variables (expectation and variance).
11. Selected probability distributions: Bernoulli distribution, Binomial distribution, Normal distribution, Standard Normal distribution, Central Limit Theorem, approximation of the Binomial with the Normal.
12. Introduction to estimation theory; random samples, sample statistics, sampling distributions, estimator random variables, unbiasedness and efficiency, estimation of mean, variance, and proportion.
13. Interval estimation: confidence intervals for mean and proportion (known and unknown variance).
14. Hypothesis testing: tests for the mean and for the difference between means (known variance).
Prerequisiti
There are no formal prerequisites, but it is strongly recommended that students have passed the General Mathematics exam.Core Documentation
Statistica – Principi e MetodiCicchitelli G., D’Urso P., Minozzo M.
Ed. Pearson
Introduzione alla Statistica
Pelosi M. K., Sandifer T. M., Cerchiello P., Giudici P.
Ed. Mc Graw Hill
Attendance
Attendance is not mandatory, but is strongly recommended.Type of evaluation
The exam consists exclusively of a written test comprising exercises and theoretical questions. During the exam, students are not allowed to bring any formula sheets or books into the examination room. Only calculators are permitted. Probability distribution tables will be provided by the instructor during the exam. In exceptional cases, the instructor may require an oral examination. Two midterm tests are scheduled during the course (the first approximately halfway through the course and the second near the end of the teaching period). Only students who achieve a passing grade on the first midterm test are eligible to take the second one. The midterm tests are open to all students enrolled in the course, regardless of whether they attend classes. Registration for the midterm tests must be completed exclusively through GOMP, following the same procedure used for regular exam sessions.Canali
teacher profile teaching materials
variables and their measurement
univariate distributions
describing data with tables and graphs
measures of position
variability
bivariate descriptive statistics
independence, association, correlation
probability distributions for discrete and continuous variables
sampling distributions
Inference:
estimation
hypothesis test
Statistical methods for the social sciences
Pearson International Edition - 4th edition 2009
Programme
descriptive statisticsvariables and their measurement
univariate distributions
describing data with tables and graphs
measures of position
variability
bivariate descriptive statistics
independence, association, correlation
probability distributions for discrete and continuous variables
sampling distributions
Inference:
estimation
hypothesis test
Prerequisiti
There are no formal prerequisites for this course. Nevertheless, a sound knowledge of the topics usually covered in a General Mathematics course is strongly recommended, including logarithms, function analysis, derivatives, and integrals.Core Documentation
A. Agresti, B. FinlayStatistical methods for the social sciences
Pearson International Edition - 4th edition 2009
Reference Bibliography
A. Agresti, B. Finlay Statistical methods for the social sciences Pearson International Edition - 4th edition 2009Type of delivery of the course
It is a traditional course with lectures in the classroom. There are also 2 hours a week dedicated to excersisesAttendance
Classes are held in person. Students authorized by the University may attend classes via live streaming.Type of evaluation
The examination consists of solving three or four exercises designed to assess the student's level of preparation. These are numerical exercises, not proofs and not theoretical questions. The examination lasts two hours. During the course, two midterm assessments are scheduled for attending students. These assessments will be administered through the online learning platform on dates set by the instructor and communicated well in advance. Students who successfully pass both midterm assessments will be eligible to take a final examination, to be completed within the summer examination session, covering only the topics related to statistical inference. teacher profile teaching materials
Frequency distributions, both simple and grouped, are discussed, as well as the main tabular and graphical representations of absolute, relative, and cumulative frequencies. Particular emphasis is placed on selecting the most appropriate graphical representations for qualitative, discrete, and continuous variables.
A substantial portion of the course concerns summary indices. Analytical means, measures of position, and distribution functions are introduced. The concept of variability is examined through mean deviations, standard deviation, variance, the coefficient of variation, and other indices of heterogeneity, with reference to their main theoretical properties.
Relationships between variables are analyzed through bivariate distributions, contingency tables, and measures of dependence and correlation. This is followed by an introduction to simple linear regression, the method of least squares, deviance decomposition, and measures of goodness of fit.
The probability section addresses random experiments, definitions of probability, independence, conditional probability, and Bayes’ theorem. Selected probability distributions are presented, including the Binomial and the Normal distributions, along with combinations of random variables. The course continues with sampling distributions, with particular reference to the sample mean and the use of tables for the Binomial, Normal, and Student’s t distributions.
The final part introduces the fundamentals of statistical inference: estimation theory, confidence intervals for proportions and means, hypothesis testing, and the analysis of Type I and Type II errors.
1. General aspects of Statistics: knowledge of collective phenomena through data collection, ordering, summarization, and analysis; national and international sources; data generation: statistical surveys (censuses and sample surveys), administrative and population registers, experiments; objectives and methods of descriptive and inferential statistics.
2. Nature of variables, data series, and frequency distributions (univariate and multivariate).
3. Graphical representations for statistical variables and attributes.
4. Measures of central tendency (analytical and positional means); arithmetic mean and its properties; weighted mean; mode; median, quartiles, and quantiles.
5. Measures of variability: mean absolute deviations; variance and its properties; standardization; coefficient of variation; interquartile range; heterogeneity indices.
6. Shape of frequency distributions: measures of skewness.
7. Dependence analysis in bivariate distributions; contingency tables and measures of dependence (chi-square indices, Cramér’s V); linear correlation.
8. Simple linear regression, estimation of regression coefficients via least squares, deviance decomposition, and goodness-of-fit measures.
9. Probability and introductory concepts: random experiments, sample space, events; probability and event definitions; union and intersection; conditional probability, independence of events, Bayes’ formula.
10. Random variables, probability distributions, distribution functions; discrete and continuous random variables (expectation and variance); linear combinations of random variables (expectation and variance).
11. Selected probability distributions: Bernoulli distribution, Binomial distribution, Normal distribution, Standard Normal distribution, Central Limit Theorem, approximation of the Binomial with the Normal.
12. Introduction to estimation theory; random samples, sample statistics, sampling distributions, estimator random variables, unbiasedness and efficiency, estimation of mean, variance, and proportion.
13. Interval estimation: confidence intervals for mean and proportion (known and unknown variance).
14. Hypothesis testing: tests for the mean and for the difference between means (known variance).
Cicchitelli G., D’Urso P., Minozzo M.
Ed. Pearson
Introduzione alla Statistica
Pelosi M. K., Sandifer T. M., Cerchiello P., Giudici P.
Ed. Mc Graw Hill
Programme
The course introduces the fundamental concepts of statistics, distinguishing from the outset between descriptive and inferential approaches. Methods of data collection and sources of data are examined, with attention to the nature of statistical variables and to the implications such characteristics have on the choice of analytical tools.Frequency distributions, both simple and grouped, are discussed, as well as the main tabular and graphical representations of absolute, relative, and cumulative frequencies. Particular emphasis is placed on selecting the most appropriate graphical representations for qualitative, discrete, and continuous variables.
A substantial portion of the course concerns summary indices. Analytical means, measures of position, and distribution functions are introduced. The concept of variability is examined through mean deviations, standard deviation, variance, the coefficient of variation, and other indices of heterogeneity, with reference to their main theoretical properties.
Relationships between variables are analyzed through bivariate distributions, contingency tables, and measures of dependence and correlation. This is followed by an introduction to simple linear regression, the method of least squares, deviance decomposition, and measures of goodness of fit.
The probability section addresses random experiments, definitions of probability, independence, conditional probability, and Bayes’ theorem. Selected probability distributions are presented, including the Binomial and the Normal distributions, along with combinations of random variables. The course continues with sampling distributions, with particular reference to the sample mean and the use of tables for the Binomial, Normal, and Student’s t distributions.
The final part introduces the fundamentals of statistical inference: estimation theory, confidence intervals for proportions and means, hypothesis testing, and the analysis of Type I and Type II errors.
1. General aspects of Statistics: knowledge of collective phenomena through data collection, ordering, summarization, and analysis; national and international sources; data generation: statistical surveys (censuses and sample surveys), administrative and population registers, experiments; objectives and methods of descriptive and inferential statistics.
2. Nature of variables, data series, and frequency distributions (univariate and multivariate).
3. Graphical representations for statistical variables and attributes.
4. Measures of central tendency (analytical and positional means); arithmetic mean and its properties; weighted mean; mode; median, quartiles, and quantiles.
5. Measures of variability: mean absolute deviations; variance and its properties; standardization; coefficient of variation; interquartile range; heterogeneity indices.
6. Shape of frequency distributions: measures of skewness.
7. Dependence analysis in bivariate distributions; contingency tables and measures of dependence (chi-square indices, Cramér’s V); linear correlation.
8. Simple linear regression, estimation of regression coefficients via least squares, deviance decomposition, and goodness-of-fit measures.
9. Probability and introductory concepts: random experiments, sample space, events; probability and event definitions; union and intersection; conditional probability, independence of events, Bayes’ formula.
10. Random variables, probability distributions, distribution functions; discrete and continuous random variables (expectation and variance); linear combinations of random variables (expectation and variance).
11. Selected probability distributions: Bernoulli distribution, Binomial distribution, Normal distribution, Standard Normal distribution, Central Limit Theorem, approximation of the Binomial with the Normal.
12. Introduction to estimation theory; random samples, sample statistics, sampling distributions, estimator random variables, unbiasedness and efficiency, estimation of mean, variance, and proportion.
13. Interval estimation: confidence intervals for mean and proportion (known and unknown variance).
14. Hypothesis testing: tests for the mean and for the difference between means (known variance).
Prerequisiti
There are no formal prerequisites, but it is strongly recommended that students have passed the General Mathematics exam.Core Documentation
Statistica – Principi e MetodiCicchitelli G., D’Urso P., Minozzo M.
Ed. Pearson
Introduzione alla Statistica
Pelosi M. K., Sandifer T. M., Cerchiello P., Giudici P.
Ed. Mc Graw Hill
Attendance
Attendance is not mandatory, but is strongly recommended.Type of evaluation
The exam consists exclusively of a written test comprising exercises and theoretical questions. During the exam, students are not allowed to bring any formula sheets or books into the examination room. Only calculators are permitted. Probability distribution tables will be provided by the instructor during the exam. In exceptional cases, the instructor may require an oral examination. Two midterm tests are scheduled during the course (the first approximately halfway through the course and the second near the end of the teaching period). Only students who achieve a passing grade on the first midterm test are eligible to take the second one. The midterm tests are open to all students enrolled in the course, regardless of whether they attend classes. Registration for the midterm tests must be completed exclusively through GOMP, following the same procedure used for regular exam sessions.Canali
teacher profile teaching materials
variables and their measurement
univariate distributions
describing data with tables and graphs
measures of position
variability
bivariate descriptive statistics
independence, association, correlation
probability distributions for discrete and continuous variables
sampling distributions
Inference:
estimation
hypothesis test
Statistical methods for the social sciences
Pearson International Edition - 4th edition 2009
Programme
descriptive statisticsvariables and their measurement
univariate distributions
describing data with tables and graphs
measures of position
variability
bivariate descriptive statistics
independence, association, correlation
probability distributions for discrete and continuous variables
sampling distributions
Inference:
estimation
hypothesis test
Prerequisiti
There are no formal prerequisites for this course. Nevertheless, a sound knowledge of the topics usually covered in a General Mathematics course is strongly recommended, including logarithms, function analysis, derivatives, and integrals.Core Documentation
A. Agresti, B. FinlayStatistical methods for the social sciences
Pearson International Edition - 4th edition 2009
Reference Bibliography
A. Agresti, B. Finlay Statistical methods for the social sciences Pearson International Edition - 4th edition 2009Type of delivery of the course
It is a traditional course with lectures in the classroom. There are also 2 hours a week dedicated to excersisesAttendance
Classes are held in person. Students authorized by the University may attend classes via live streaming.Type of evaluation
The examination consists of solving three or four exercises designed to assess the student's level of preparation. These are numerical exercises, not proofs and not theoretical questions. The examination lasts two hours. During the course, two midterm assessments are scheduled for attending students. These assessments will be administered through the online learning platform on dates set by the instructor and communicated well in advance. Students who successfully pass both midterm assessments will be eligible to take a final examination, to be completed within the summer examination session, covering only the topics related to statistical inference. teacher profile teaching materials
Frequency distributions, both simple and grouped, are discussed, as well as the main tabular and graphical representations of absolute, relative, and cumulative frequencies. Particular emphasis is placed on selecting the most appropriate graphical representations for qualitative, discrete, and continuous variables.
A substantial portion of the course concerns summary indices. Analytical means, measures of position, and distribution functions are introduced. The concept of variability is examined through mean deviations, standard deviation, variance, the coefficient of variation, and other indices of heterogeneity, with reference to their main theoretical properties.
Relationships between variables are analyzed through bivariate distributions, contingency tables, and measures of dependence and correlation. This is followed by an introduction to simple linear regression, the method of least squares, deviance decomposition, and measures of goodness of fit.
The probability section addresses random experiments, definitions of probability, independence, conditional probability, and Bayes’ theorem. Selected probability distributions are presented, including the Binomial and the Normal distributions, along with combinations of random variables. The course continues with sampling distributions, with particular reference to the sample mean and the use of tables for the Binomial, Normal, and Student’s t distributions.
The final part introduces the fundamentals of statistical inference: estimation theory, confidence intervals for proportions and means, hypothesis testing, and the analysis of Type I and Type II errors.
1. General aspects of Statistics: knowledge of collective phenomena through data collection, ordering, summarization, and analysis; national and international sources; data generation: statistical surveys (censuses and sample surveys), administrative and population registers, experiments; objectives and methods of descriptive and inferential statistics.
2. Nature of variables, data series, and frequency distributions (univariate and multivariate).
3. Graphical representations for statistical variables and attributes.
4. Measures of central tendency (analytical and positional means); arithmetic mean and its properties; weighted mean; mode; median, quartiles, and quantiles.
5. Measures of variability: mean absolute deviations; variance and its properties; standardization; coefficient of variation; interquartile range; heterogeneity indices.
6. Shape of frequency distributions: measures of skewness.
7. Dependence analysis in bivariate distributions; contingency tables and measures of dependence (chi-square indices, Cramér’s V); linear correlation.
8. Simple linear regression, estimation of regression coefficients via least squares, deviance decomposition, and goodness-of-fit measures.
9. Probability and introductory concepts: random experiments, sample space, events; probability and event definitions; union and intersection; conditional probability, independence of events, Bayes’ formula.
10. Random variables, probability distributions, distribution functions; discrete and continuous random variables (expectation and variance); linear combinations of random variables (expectation and variance).
11. Selected probability distributions: Bernoulli distribution, Binomial distribution, Normal distribution, Standard Normal distribution, Central Limit Theorem, approximation of the Binomial with the Normal.
12. Introduction to estimation theory; random samples, sample statistics, sampling distributions, estimator random variables, unbiasedness and efficiency, estimation of mean, variance, and proportion.
13. Interval estimation: confidence intervals for mean and proportion (known and unknown variance).
14. Hypothesis testing: tests for the mean and for the difference between means (known variance).
Cicchitelli G., D’Urso P., Minozzo M.
Ed. Pearson
Introduzione alla Statistica
Pelosi M. K., Sandifer T. M., Cerchiello P., Giudici P.
Ed. Mc Graw Hill
Programme
The course introduces the fundamental concepts of statistics, distinguishing from the outset between descriptive and inferential approaches. Methods of data collection and sources of data are examined, with attention to the nature of statistical variables and to the implications such characteristics have on the choice of analytical tools.Frequency distributions, both simple and grouped, are discussed, as well as the main tabular and graphical representations of absolute, relative, and cumulative frequencies. Particular emphasis is placed on selecting the most appropriate graphical representations for qualitative, discrete, and continuous variables.
A substantial portion of the course concerns summary indices. Analytical means, measures of position, and distribution functions are introduced. The concept of variability is examined through mean deviations, standard deviation, variance, the coefficient of variation, and other indices of heterogeneity, with reference to their main theoretical properties.
Relationships between variables are analyzed through bivariate distributions, contingency tables, and measures of dependence and correlation. This is followed by an introduction to simple linear regression, the method of least squares, deviance decomposition, and measures of goodness of fit.
The probability section addresses random experiments, definitions of probability, independence, conditional probability, and Bayes’ theorem. Selected probability distributions are presented, including the Binomial and the Normal distributions, along with combinations of random variables. The course continues with sampling distributions, with particular reference to the sample mean and the use of tables for the Binomial, Normal, and Student’s t distributions.
The final part introduces the fundamentals of statistical inference: estimation theory, confidence intervals for proportions and means, hypothesis testing, and the analysis of Type I and Type II errors.
1. General aspects of Statistics: knowledge of collective phenomena through data collection, ordering, summarization, and analysis; national and international sources; data generation: statistical surveys (censuses and sample surveys), administrative and population registers, experiments; objectives and methods of descriptive and inferential statistics.
2. Nature of variables, data series, and frequency distributions (univariate and multivariate).
3. Graphical representations for statistical variables and attributes.
4. Measures of central tendency (analytical and positional means); arithmetic mean and its properties; weighted mean; mode; median, quartiles, and quantiles.
5. Measures of variability: mean absolute deviations; variance and its properties; standardization; coefficient of variation; interquartile range; heterogeneity indices.
6. Shape of frequency distributions: measures of skewness.
7. Dependence analysis in bivariate distributions; contingency tables and measures of dependence (chi-square indices, Cramér’s V); linear correlation.
8. Simple linear regression, estimation of regression coefficients via least squares, deviance decomposition, and goodness-of-fit measures.
9. Probability and introductory concepts: random experiments, sample space, events; probability and event definitions; union and intersection; conditional probability, independence of events, Bayes’ formula.
10. Random variables, probability distributions, distribution functions; discrete and continuous random variables (expectation and variance); linear combinations of random variables (expectation and variance).
11. Selected probability distributions: Bernoulli distribution, Binomial distribution, Normal distribution, Standard Normal distribution, Central Limit Theorem, approximation of the Binomial with the Normal.
12. Introduction to estimation theory; random samples, sample statistics, sampling distributions, estimator random variables, unbiasedness and efficiency, estimation of mean, variance, and proportion.
13. Interval estimation: confidence intervals for mean and proportion (known and unknown variance).
14. Hypothesis testing: tests for the mean and for the difference between means (known variance).
Prerequisiti
There are no formal prerequisites, but it is strongly recommended that students have passed the General Mathematics exam.Core Documentation
Statistica – Principi e MetodiCicchitelli G., D’Urso P., Minozzo M.
Ed. Pearson
Introduzione alla Statistica
Pelosi M. K., Sandifer T. M., Cerchiello P., Giudici P.
Ed. Mc Graw Hill
Attendance
Attendance is not mandatory, but is strongly recommended.Type of evaluation
The exam consists exclusively of a written test comprising exercises and theoretical questions. During the exam, students are not allowed to bring any formula sheets or books into the examination room. Only calculators are permitted. Probability distribution tables will be provided by the instructor during the exam. In exceptional cases, the instructor may require an oral examination. Two midterm tests are scheduled during the course (the first approximately halfway through the course and the second near the end of the teaching period). Only students who achieve a passing grade on the first midterm test are eligible to take the second one. The midterm tests are open to all students enrolled in the course, regardless of whether they attend classes. Registration for the midterm tests must be completed exclusively through GOMP, following the same procedure used for regular exam sessions.