# Unit STATISTICS

Course
Study-unit Code
20007009
Location
PERUGIA
Curriculum
In all curricula
CFU
9
Course Regulation
Coorte 2020
Offered
2021/22
Learning activities
Caratterizzante
Area
Statistico-matematico
SECS-S/01
Type of study-unit
Obbligatorio (Required)
Type of learning activities
Attività formativa monodisciplinare

### STATISTICS - Cognomi A-L

Code 20007009 PERUGIA 9 Elena Stanghellini Elena StanghelliniSilvia Pandolfi 63 ore - Elena Stanghellini12 ore - Silvia Pandolfi Caratterizzante Statistico-matematico SECS-S/01 Obbligatorio (Required) Italian The module gives the first notions to correctly perform a statistical analysis of economic data. Students who successfully complete the module will possess a good knowledge of descriptive and basic notions of inferential statistics. The course aims at enabling students to critically understand quantitative reports made by other researchers as well as to perform some simple analysis. Students who successfully complete the module will possess the knowledge not only on how to collect the data for a given study, but also on how to construct appropriate syntheses of them. They will know how to make meaningful comparisons among different datasets. From the inferential point of view, students who successfully complete the module are also able to provide answers to simple research questions on a population of interest from a sample randomly drawn from it. G. Cicchitelli, P. D’Urso, M. Minozzo. Statistica: Principi e metodi, Pearson, 2017. First notions of statistical data analysis with a particular view on economic problems. The course is divided into two parts of equal weight.Descriptive statisticsPreliminary concepts; Comparisons between statistical quantities; Statistical distributions; Graphical tools; Means; Variability and concentration; An overview of the characteristic constants; Dependence analysis; Regression analysis; Correlation. Inferential statisticsProbability; Random variables; Some specific probabilistic models; Sample distributions; Point estimation; Interval estimation; Hypothesis testing. Notions acquired in the first module of Principles of Mathematics. Six hours of lectures and two of practical exercises on a weekly basis. Students are given the possibility to attend sessions in the lab using the statistical software R. Compulsory written exam; oral exam on an elective basis. The course is divided into two parts of equal weight. The first part is called Descriptive statistics. The second part is called Inferential statistics.Descriptive statistics - Part I Preliminary concepts: historical notes about statistics; essential terminology; measurement of variables; genesis of statistical data; data collection; data matrix. Comparisons between quantities: statistical ratios; change rates.Statistical distributions: disaggregated statistical distributions; frequency distributions; relative frequencies; cumulative frequencies; frequency distributions with data grouped into classes with and without class totals; bivariate and multivariate distributions; time series; spatial series. Graphical tools: graphics for distributions of quantitative variables: bar chart; histogram; box-plot; graphical representation for nominal variables; pie charts; tri-dimensional graphics; graphical representation of time series and spatial series; proper axis scale choice. Means: arithmetic mean; geometric mean; square mean; case of frequency distributions; case of data grouped into classes; weighted mean; median; quartiles and quantiles; central value; mode. Average percentage indices; Laspeyres' formula to measure the average change of prices. Variability and concentration: variability; average deviations: mean deviation; standard deviation; alternative formula for the standard deviation; range; interquartile range; percentage variability indices; concentration; G and R concentration indices; geometric interpretation of concentration indices. Asymmetry indices: symmetry and asymmetry; asymmetry indices. An overview of the characteristic constants: graphics and characteristic constants; box plot. Index numbers: fixed-base and mobile-base index numbers. Mean percentage change. Index of Laspeyres.Dependence analysis: Disaggregate and frequency bivariate distributions; marginal and conditional distributions; graphical representations of bivariate distributions; chi-squared index of statistical association. Regression analysis: statistical relationships; simple linear regression; least square method for the regression parameters; fitting of data to regression line; index r-square and its properties. Time series case; mean error of prediction. Correlation: notion of correlation; Bravais correlation coefficient and its properties. Inferential statistics - Part II Probability: random experiments; sample space and events; basic set theory operations; probability; interpretation of probability; computing probabilities; conditional probability; independence; Bayes theorem. Random variables: discrete random variables; mean and standard deviation; continuous random variables; mean and standard deviation; quantiles; standardized random variables.Some specific probabilistic models: Bernoulli distribution; binomial distribution; Poisson distribution; normal distribution; standardized normal distribution; approximation of the binomial distribution through the normal distribution; chi-square distribution.Discrete and continuous bivariate random variables; joint probability distribution and marginal probability distribution; covariance; independent discrete random variables; continuous bivariate random variables; multivariate random variables and independence. Mean and Variance of a Linear combination of random variables (only introduction). Mean and variance of two particular combination of interest: the mean and the sum of independent random variables. Low of large numbers. Central limit Theorem (only introduction).Sample distributions: random sample; parameter; statistical inference: parameter estimation and hypothesis testing; sample statistics; sample distribution of the mean for normal populations and with large sample size (central limit theorem); sample distribution of the variance; sample distribution of the mean when the population variance is unknown; t-Student distribution and use of statistical tables. Point estimation: estimator; properties o estimators; unbiasedness; mean square error; asymptotic properties. Interval estimation: interval estimator and interval estimate; interval estimation of the mean of a normal population; size of confidence interval; the case of unknown variance; interval estimation of the mean with large sample sizes; confidence interval for the parameter p of a Bernoulli population; confidence interval of the variance of a normal population with unknown variance.Hypothesis testing: statistical hypotheses; errors of first and second type and their probabilities; power of a statistical test. Testing hypotheses on the mean of a normal population; Z-test; p-value; T-test; testing hypotheses on the mean in case of large sample size; testing hypotheses on the parameter p of a Bernoulli population; testing hypotheses on the variance of a normal population with unknown mean.Chi-square test of independence between two categorical random variables.

### STATISTICS - Cognomi M-Z

Code 20007009 PERUGIA 9 Francesco Bartolucci Francesco BartolucciSilvia Pandolfi 63 ore - Francesco Bartolucci12 ore - Silvia Pandolfi Caratterizzante Statistico-matematico SECS-S/01 Obbligatorio (Required) Italian The module gives the first notions to correctly perform a statistical analysis of economic data. Students who successfully complete the module will possess a good knowledge of descriptive and basic notions of inferential statistics. The course aims at enabling students to critically understand quantitative reports made by other researchers as well as to perform some simple analysis. Students who successfully complete the module will possess the knowledge not only on how to collect the data for a given study, but also on how to construct appropriate syntheses of them. They will know how to make meaningful comparisons among different datasets. From the inferential point of view, students who successfully complete the module are also able to provide answers to simple research questions on a population of interest from a sample randomly drawn from it. G. Cicchitelli, P. D’Urso, M. Minozzo. Statistica: Principi e metodi, Pearson, 2017. First notions of statistical data analysis with a particular view on economic problems. The course is divided into two parts of equal weight.Descriptive statisticsPreliminary concepts; Comparisons between statistical quantities; Statistical distributions; Graphical tools; Means; Variability and concentration; An overview of the characteristic constants; Dependence analysis; Regression analysis; Correlation. Inferential statisticsProbability; Random variables; Some specific probabilistic models; Sample distributions; Point estimation; Interval estimation; Hypothesis testing. Notions acquired in the first module of Principles of Mathematics. Six hours of lectures and two of practical exercises on a weekly basis. Students are given the possibility to attend sessions in the lab using the statistical software R. Compulsory written exam; oral exam on an elective basis. The course is divided into two parts of equal weight. The first part is called Descriptive statistics. The second part is called Inferential statistics.Descriptive statistics - Part I Preliminary concepts: historical notes about statistics; essential terminology; measurement of variables; genesis of statistical data; data collection; data matrix. Comparisons between quantities: statistical ratios; change rates.Statistical distributions: disaggregated statistical distributions; frequency distributions; relative frequencies; cumulative frequencies; frequency distributions with data grouped into classes with and without class totals; bivariate and multivariate distributions; time series; spatial series. Graphical tools: graphics for distributions of quantitative variables: bar chart; histogram; box-plot; graphical representation for nominal variables; pie charts; tri-dimensional graphics; graphical representation of time series and spatial series; proper axis scale choice. Means: arithmetic mean; geometric mean; square mean; case of frequency distributions; case of data grouped into classes; weighted mean; median; quartiles and quantiles; central value; mode. Average percentage indices; Laspeyres' formula to measure the average change of prices. Variability and concentration: variability; average deviations: mean deviation; standard deviation; alternative formula for the standard deviation; range; interquartile range; percentage variability indices; concentration; G and R concentration indices; geometric interpretation of concentration indices. Asymmetry indices: symmetry and asymmetry; asymmetry indices. An overview of the characteristic constants: graphics and characteristic constants; box plot. Index numbers: fixed-base and mobile-base index numbers. Mean percentage change. Index of Laspeyres.Dependence analysis: Disaggregate and frequency bivariate distributions; marginal and conditional distributions; graphical representations of bivariate distributions; chi-squared index of statistical dependence. Regression analysis: statistical relationships; simple linear regression; least square method for the regression parameters; fitting of data to regression line; index r-square and its properties. Time series case; mean error of prediction. Correlation: notion of correlation; Bravais correlation coefficient and its properties. Inferential statistics - Part II Probability: random experiments; sample space and events; basic set theory operations; probability; interpretation of probability; computing probabilities; conditional probability; independence; Bayes theorem. Random variables: discrete random variables; mean and standard deviation; continuous random variables; mean and standard deviation; quantiles; standardized random variables.Some specific probabilistic models: Bernoulli distribution; binomial distribution; Poisson distribution; normal distribution; standardized normal distribution; approximation of the binomial distribution through the normal distribution; chi-square distribution.Discrete and continuous bivariate random variables; joint probability distribution and marginal probability distribution; covariance; independent discrete random variables; continuous bivariate random variables; multivariate random variables and independence. Mean and Variance of a Linear combination of random variables (only introduction). Mean and variance of two particular combination of interest: the mean and the sum of independent random variables. Low of large numbers. Central limit Theorem (only introduction).Sample distributions: random sample; parameter; statistical inference: parameter estimation and hypothesis testing; sample statistics; sample distribution of the mean for normal populations and with large sample size (central limit theorem); sample distribution of the variance; sample distribution of the mean when the population variance is unknown; t-Student distribution and use of statistical tables. Point estimation: estimator; properties o estimators; unbiasedness; mean square error; asymptotic properties. Interval estimation: interval estimator and interval estimate; interval estimation of the mean of a normal population; size of confidence interval; the case of unknown variance; interval estimation of the mean with large sample sizes; confidence interval for the parameter p of a Bernoulli population; confidence interval of the variance of a normal population with unknown variance. Hypothesis testing: statistical hypotheses; errors of first and second type and their probabilities; power of a statistical test. Testing hypotheses on the mean of a normal population; Z-test; p-value; T-test; testing hypotheses on the mean in case of large sample size; testing hypotheses on the parameter p of a Bernoulli population; testing hypotheses on the variance of a normal population with unknown mean.Chi-square test of independence between two categorical random variables.
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