Being able to produce, interpret and communicate data in a social science framework. Being able to able appropriately with data variability and uncertainty.

Curriculum

Canali

teacher profile teaching materials

Least-squares and regression. Goodness of fit of a regression line.

Discrete random variables. Expectation and variance. Continuous random variables and probability density. Normal distribution, chi square, Student’s t, Fisher’s F.

Estimators and parameters. Sampling distribution of an estimator. Bias and efficiency. Punctual estimation of parameters: the mean and the variance. Confidence intervals. Confidence intervals of a single mean. Optimal sample size. Hypothesis test for a mean.

Programme

The data matrix. Types of statistical variables: factor, ordered factor, discrete. Frequency distributions. Barplots. Continuous variables: classes, frequency distributions and histograms. Cumulative distribution function. Quantiles. Bivariate distributions. Marginal and conditional distributions. Chi square: independence and dependence. Mean and variance. Deviance decomposition. Linear transformations. Scatterplots. Covariance and linear correlation.Least-squares and regression. Goodness of fit of a regression line.

Discrete random variables. Expectation and variance. Continuous random variables and probability density. Normal distribution, chi square, Student’s t, Fisher’s F.

Estimators and parameters. Sampling distribution of an estimator. Bias and efficiency. Punctual estimation of parameters: the mean and the variance. Confidence intervals. Confidence intervals of a single mean. Optimal sample size. Hypothesis test for a mean.

Core Documentation

Alan Agresti, Christine A. Franklin and Bernhard Klingenberg (2017) Statistics: The Art and Science of Learning from Data (4th Edition) ISBN 978-0321997838Reference Bibliography

Freedman, Pisani, Purves, Statistics. Norton and Company: New York Sally Caldwell, Statistics. Wadsworth: Belmont CA Tom Baguley, Serious Stats, MacMillan InternationalType of delivery of the course

The course includes lectures and labs. Attendance is not mandatory, but highly encouragedType of evaluation

The exam is written and must be completed within two hours. It requires the solution of numerical exercises and the answers to theoretical questions, related to the topics of the syllabus. During the exam, students are not allowed to read textbooks, use PCs, tablets and mobile phones; they are only allowed to use a basic electronic calculator and the usual statistical tables. Students who pass this exam are eligible for an additional oral exam. More details on the moodle platform of the course. teacher profile teaching materials

Least-squares and regression. Goodness of fit of a regression line.

Axioms of elementary probability. Elementary theorems of probability. Mutually exclusive events. Conditional probability. Independence. Bayes theorem. Discrete random variables. Expectation. Bernoulli distribution. Binomial distribution and random walk. Hypergeometric distribution. Poisson distribution.

Continuous random variables. Probability density. Normal distribution. Normal tables. Normal approximation to the binomial distribution. Student's t.

Estimators and parameters. Sampling distribution of an estimator. Bias and efficiency. Punctual estimation of parameters: the mean, the variance and the proportion. Confidence intervals. Confidence intervals of a single mean and of the difference between two means. Confidence interval of a proportion and of the difference between two proportions. Optimal sample size.

Programme

The data matrix. Types of statistical variables: factor, ordered factor, discrete. Frequency distributions. Barplots. Continuous variables: classes, frequency distributions and histograms. Entropy. Cumulative distribution function. Quantiles. Bivariate distributions. Marginal and conditional distributions. Chi square: independence and dependence. Mean and variance. Benjamin-Cebicev inequality. Variance decomposition. Linear transformations. Scatterplots. Covariance and linear correlation.Least-squares and regression. Goodness of fit of a regression line.

Axioms of elementary probability. Elementary theorems of probability. Mutually exclusive events. Conditional probability. Independence. Bayes theorem. Discrete random variables. Expectation. Bernoulli distribution. Binomial distribution and random walk. Hypergeometric distribution. Poisson distribution.

Continuous random variables. Probability density. Normal distribution. Normal tables. Normal approximation to the binomial distribution. Student's t.

Estimators and parameters. Sampling distribution of an estimator. Bias and efficiency. Punctual estimation of parameters: the mean, the variance and the proportion. Confidence intervals. Confidence intervals of a single mean and of the difference between two means. Confidence interval of a proportion and of the difference between two proportions. Optimal sample size.

Core Documentation

Freedman, Pisani, Purves, Statistics. Norton and Company: New YorkReference Bibliography

Sally Caldwell, Statistics. Wadsworth: Belmont CA Tom Baguley, Serious Stats, MacMillan InternationalType of delivery of the course

The course includes lectures and exercises.Attendance

Attendance is not necessary but strongly recommended.Type of evaluation

The exam includes a written test of length approximately equal to 120 minutes. the written test requires 1) the solution of numerical exercises related to the main topics covered during the course 2) answering to theoretical questions on the topics included in the course programme. During the written test students are not allowed to read textbooks, use pcs, tablets and mobile phones; they are only allowed to use a basic electronic calculator and the usual statistical tables. Attention:In the period January-February 2023 ,in case of covid-19 pandemic crisis, a 1-hour exam will be administered through the Moodle platform of the course. Those who pass this exam can participate in a supplementary oral examination.Canali

Programme

The data matrix. Types of statistical variables: factor, ordered factor, discrete. Frequency distributions. Barplots. Continuous variables: classes, frequency distributions and histograms. Cumulative distribution function. Quantiles. Bivariate distributions. Marginal and conditional distributions. Chi square: independence and dependence. Mean and variance. Deviance decomposition. Linear transformations. Scatterplots. Covariance and linear correlation.Least-squares and regression. Goodness of fit of a regression line.

Discrete random variables. Expectation and variance. Continuous random variables and probability density. Normal distribution, chi square, Student’s t, Fisher’s F.

Estimators and parameters. Sampling distribution of an estimator. Bias and efficiency. Punctual estimation of parameters: the mean and the variance. Confidence intervals. Confidence intervals of a single mean. Optimal sample size. Hypothesis test for a mean.

Core Documentation

Alan Agresti, Christine A. Franklin and Bernhard Klingenberg (2017) Statistics: The Art and Science of Learning from Data (4th Edition) ISBN 978-0321997838Reference Bibliography

Freedman, Pisani, Purves, Statistics. Norton and Company: New York Sally Caldwell, Statistics. Wadsworth: Belmont CA Tom Baguley, Serious Stats, MacMillan InternationalType of delivery of the course

The course includes lectures and labs. Attendance is not mandatory, but highly encouragedType of evaluation

The exam is written and must be completed within two hours. It requires the solution of numerical exercises and the answers to theoretical questions, related to the topics of the syllabus. During the exam, students are not allowed to read textbooks, use PCs, tablets and mobile phones; they are only allowed to use a basic electronic calculator and the usual statistical tables. Students who pass this exam are eligible for an additional oral exam. More details on the moodle platform of the course.Programme

The data matrix. Types of statistical variables: factor, ordered factor, discrete. Frequency distributions. Barplots. Continuous variables: classes, frequency distributions and histograms. Entropy. Cumulative distribution function. Quantiles. Bivariate distributions. Marginal and conditional distributions. Chi square: independence and dependence. Mean and variance. Benjamin-Cebicev inequality. Variance decomposition. Linear transformations. Scatterplots. Covariance and linear correlation.Least-squares and regression. Goodness of fit of a regression line.

Axioms of elementary probability. Elementary theorems of probability. Mutually exclusive events. Conditional probability. Independence. Bayes theorem. Discrete random variables. Expectation. Bernoulli distribution. Binomial distribution and random walk. Hypergeometric distribution. Poisson distribution.

Continuous random variables. Probability density. Normal distribution. Normal tables. Normal approximation to the binomial distribution. Student's t.

Estimators and parameters. Sampling distribution of an estimator. Bias and efficiency. Punctual estimation of parameters: the mean, the variance and the proportion. Confidence intervals. Confidence intervals of a single mean and of the difference between two means. Confidence interval of a proportion and of the difference between two proportions. Optimal sample size.

Core Documentation

Freedman, Pisani, Purves, Statistics. Norton and Company: New YorkReference Bibliography

Sally Caldwell, Statistics. Wadsworth: Belmont CA Tom Baguley, Serious Stats, MacMillan InternationalType of delivery of the course

The course includes lectures and exercises.Attendance

Attendance is not necessary but strongly recommended.Type of evaluation

The exam includes a written test of length approximately equal to 120 minutes. the written test requires 1) the solution of numerical exercises related to the main topics covered during the course 2) answering to theoretical questions on the topics included in the course programme. During the written test students are not allowed to read textbooks, use pcs, tablets and mobile phones; they are only allowed to use a basic electronic calculator and the usual statistical tables. Attention:In the period January-February 2023 ,in case of covid-19 pandemic crisis, a 1-hour exam will be administered through the Moodle platform of the course. Those who pass this exam can participate in a supplementary oral examination.Canali

Programme

The data matrix. Types of statistical variables: factor, ordered factor, discrete. Frequency distributions. Barplots. Continuous variables: classes, frequency distributions and histograms. Cumulative distribution function. Quantiles. Bivariate distributions. Marginal and conditional distributions. Chi square: independence and dependence. Mean and variance. Deviance decomposition. Linear transformations. Scatterplots. Covariance and linear correlation.Least-squares and regression. Goodness of fit of a regression line.

Discrete random variables. Expectation and variance. Continuous random variables and probability density. Normal distribution, chi square, Student’s t, Fisher’s F.

Estimators and parameters. Sampling distribution of an estimator. Bias and efficiency. Punctual estimation of parameters: the mean and the variance. Confidence intervals. Confidence intervals of a single mean. Optimal sample size. Hypothesis test for a mean.

Core Documentation

Alan Agresti, Christine A. Franklin and Bernhard Klingenberg (2017) Statistics: The Art and Science of Learning from Data (4th Edition) ISBN 978-0321997838Reference Bibliography

Freedman, Pisani, Purves, Statistics. Norton and Company: New York Sally Caldwell, Statistics. Wadsworth: Belmont CA Tom Baguley, Serious Stats, MacMillan InternationalType of delivery of the course

The course includes lectures and labs. Attendance is not mandatory, but highly encouragedType of evaluation

The exam is written and must be completed within two hours. It requires the solution of numerical exercises and the answers to theoretical questions, related to the topics of the syllabus. During the exam, students are not allowed to read textbooks, use PCs, tablets and mobile phones; they are only allowed to use a basic electronic calculator and the usual statistical tables. Students who pass this exam are eligible for an additional oral exam. More details on the moodle platform of the course.Programme

The data matrix. Types of statistical variables: factor, ordered factor, discrete. Frequency distributions. Barplots. Continuous variables: classes, frequency distributions and histograms. Entropy. Cumulative distribution function. Quantiles. Bivariate distributions. Marginal and conditional distributions. Chi square: independence and dependence. Mean and variance. Benjamin-Cebicev inequality. Variance decomposition. Linear transformations. Scatterplots. Covariance and linear correlation.Least-squares and regression. Goodness of fit of a regression line.

Axioms of elementary probability. Elementary theorems of probability. Mutually exclusive events. Conditional probability. Independence. Bayes theorem. Discrete random variables. Expectation. Bernoulli distribution. Binomial distribution and random walk. Hypergeometric distribution. Poisson distribution.

Continuous random variables. Probability density. Normal distribution. Normal tables. Normal approximation to the binomial distribution. Student's t.

Estimators and parameters. Sampling distribution of an estimator. Bias and efficiency. Punctual estimation of parameters: the mean, the variance and the proportion. Confidence intervals. Confidence intervals of a single mean and of the difference between two means. Confidence interval of a proportion and of the difference between two proportions. Optimal sample size.

Core Documentation

Freedman, Pisani, Purves, Statistics. Norton and Company: New YorkReference Bibliography

Sally Caldwell, Statistics. Wadsworth: Belmont CA Tom Baguley, Serious Stats, MacMillan InternationalType of delivery of the course

The course includes lectures and exercises.Attendance

Attendance is not necessary but strongly recommended.Type of evaluation

The exam includes a written test of length approximately equal to 120 minutes. the written test requires 1) the solution of numerical exercises related to the main topics covered during the course 2) answering to theoretical questions on the topics included in the course programme. During the written test students are not allowed to read textbooks, use pcs, tablets and mobile phones; they are only allowed to use a basic electronic calculator and the usual statistical tables. Attention:In the period January-February 2023 ,in case of covid-19 pandemic crisis, a 1-hour exam will be administered through the Moodle platform of the course. Those who pass this exam can participate in a supplementary oral examination.