Business sciences

Il programma comprenderà i seguenti argomenti che vengono qui sottoelencati in ordine temporale. Le lezioni copriranno sia gli aspetti metodologici che quelli applicativi anche tramite l'uso di software statistici. Nozioni introduttive: collettivo statistico; unità statistica, caratteri e modalità; fonti dei dati; matrice dei dati; statistica descrittiva e inferenza statistica. Distribuzioni statistiche: frequenze assolute, relative e cumulate; distribuzioni di frequenze e raggruppamento in classi; distribuzioni doppie; serie storiche e territoriali. Rappresentazioni grafiche: caratteri quantitativi; caratteri qualitativi; grafici a barre; grafici per serie storiche e territoriali Posizione: media aritmetica, armonica, geometrica, quadratica, di potenza; medie analitiche per distribuzioni di frequenze; medie ponderate; quantili e altri indici di posizione. Variabilità: scostamenti medi; differenze medie; coefficiente di variazione; range e differenza interquantilica; misura della concentrazione per caratteri trasferibili (Lorenz e Gini); scomposizione della devianza. Forma: asimmetria e altri indici di forma basati su quantili. Numeri indici: definizione; variazioni relative e relative medie; numeri indici complessi. Analisi delle distribuzioni doppie: rappresentazioni grafiche; distribuzioni marginali, condizionate e indipendenza statistica; misura della dipendenza; dipendenza in media. Regressione: il modello di regressione lineare semplice; adattamento della retta di regressione ai dati; indipendenza lineare e misure del grado di associazione lineare. Probabilità: esperimenti casuali; spazio campionario ed eventi; definizioni di probabilità; assegnazione delle probabilità agli eventi; principali teoremi sulla probabilità; probabilità condizionata e indipendenza; formula di Bayes. Variabili casuali: variabili discrete e continue; funzione di ripartizione; valore atteso e varianza di variabili aleatorie; quantili. Alcuni modelli probabilistici: uniforme discreta; Bernoulli; binomiale; Poisson; esponenziale; normale e normale standard. Variabili casuali doppie: distribuzioni marginali e condizionate; covarianza e correlazione; indipendenza. La legge dei grandi numeri e teorema centrale del limite. Popolazione e campione: campione casuale; popolazione; spazio campionario; statistiche e loro distribuzioni campionarie. Stima puntuale: proprietà degli stimatori (distorsione ed errore quadratico medio); criteri di scelta. Stima per intervallo: intervalli di confidenza per la media di una popolazione normale con varianza nota o incognita, per la media di una popolazione qualsiasi nel caso di grandi campioni, per una proporzione nel caso di grandi campioni. Verifica delle ipotesi: ipotesi nulla e alternativa; tipologie di errore e livello di siginificatività; alcuni test sulla media.

Conoscenza degli strumenti principali di analisi matematica

Testo adottato Cicchitelli, D’Urso, Minozzo. Statistica: principi e metodi. Pearson, 3a o 4a edizione Testo di utile consultazione Piccolo. Statistica. Il Mulino Ulteriore materiale per la teoria e gli esercizi verrà fornito in forma di dispense su Google Classroom.

La frequenza è fortemente consigliata

Il voto finale si baserà su un esame scritto per valutare la conoscenza delle metodologie statistiche (60% del voto) e le competenze pratiche (40% del voto).

Le lezioni si svolgeranno in aula secondo calendario.

The program will include the following topics, which are listed below in chronological order. Introductory concepts: statistical collection; statistical units, characters and modes; data sources; data matrix; descriptive statistics and statistical inference. Statistical distributions: absolute, relative and cumulative frequencies; frequency distributions and grouping into classes; double distributions; time and spatial series. Graphical representations: quantitative characters; qualitative characters; bar graphs; time series and spatial graphs. Position: arithmetic, harmonic, geometric, quadratic, power mean; analytic averages for frequency distributions; weighted averages; quantiles and other indices of position. Variability : mean deviations; mean differences; coefficient of variation; range and interquartile difference; measure of concentration for transferable characters (Lorenz and Gini); deviance decomposition. Shape: skewness and other shape indices based on quantiles. Index numbers: definition; relative variances and relative averages; complex index numbers. Analysis of dual distributions: graphical representations; marginal, conditional and statistical independence distributions; measure of dependence; dependence on the mean. Regression: the simple linear regression model; fitting the regression line to the data; linear independence and measures of the degree of linear association. Probability: random experiments; sample space and events; definitions of probability; assignment of probabilities to events; main theorems on probability; conditional probability and independence; Bayes formula. Random variables: discrete and continuous variables; distribution function; expected value and variance of random variables; quantiles. Some probabilistic models: discrete uniform; Bernoulli; binomial; Poisson; exponential; normal and standard normal. Dual random variables: marginal and conditional distributions; covariance and correlation; independence. Law of large numbers and central limit theorem. Population and sample: random sample; population; sample space; statistics and their sample distributions. Point estimation: properties of estimators (bias and mean square error); selection criteria. Interval estimation: confidence intervals for the mean of a normal population with known or unknown variance, for the mean of any population in the case of large samples, for a proportion in the case of large samples. Hypothesis testing: null and alternative hypothesis; types of error and significance level; some tests on the mean.

Knowledge of the main tools of mathematical analysis.

Cicchitelli, D'Urso, Minozzo. Statistica: principi e metodi. Pearson, 3a o 4a edizione

Attendance is strongly recommended.

The final evaluation will be based on a written exam to assess knowledge of statistical methodologies (60 percent of the grade) and practical skills (40 percent of the grade).

Lessons will be held in the classroom according to schedule.

Introduction to statistical terminology: population, statistical unit, variable. Statistical disaggregate distribution and frequency distribution. Cumulative frequencies. Frequency distribution by classes. Graphs. Empirical distribution function and its graphical representation. Introduction to means: analytical means and location indices. Arithmetic mean and its properties. Arithmetic mean for a frequency distribution and for a frequency distribution by classes. Mode, median and quantiles. Calculation of mode, median and quantiles for a frequency distribution and for a frequency distribution by classes. Variability indices: simple average deviations, standard deviation and variance. Deviance decomposition formula. Mean absolute difference. Range. Interquartile range. Coefficient of variation. Concentration and its measures: Lorenz curve and the Gini coefficient for a statistical disaggregate distribution. Heterogeneity and its measures. Symmetry and measures of skewness. Index numbers: simple and complex. Bivariate distribution. Absolute independence, perfect dependency and measures of dependency. Independence in average and measures of the dependency in average degree. Linear independence and measures of the linear association degree. Introduction to the simple linear regression. Calculation of the parameters values of the regression line. Goodness of fit of the regression line to the observed data and the coefficient of determination. Introduction to the probability theory. Random events and space of events. Probability definitions. Assignment of probabilities to events. The most important theorems of probability. Conditional probability and stochastic independence. The Bayes theorem. Introduction to the random variables theory. Discrete random variable, continue random variable and distribution function. Expected value and variance of a random variable. Some discrete probabilistic models: Bernoulli, binomial and Poisson. Normal distribution and the use of its tables. The law of large numbers and the central limit theorem. Population and sample: introduction to the sampling distributions. The sampling distribution of the sample mean. References to the point estimation theory and to the properties of estimators. Introduction to the confidence intervals theory. Confidence intervals for the mean of a normal population with known variance and with unknown variance. Confidence intervals for the mean of a population for a large sample. Confidence intervals for the proportion for a large sample. Introduction to the statistical hypothesis testing theory and types of error. Hypothesis testing for the mean of a normal population with known variance and with unknown variance. Hypothesis testing for the mean of a population for a large sample. Hypothesis testing for the proportion for a large sample. Chi-square test of independence. Statistical inference for the simple linear regression model. The time devoted to each part of the program may vary from time to time depending on the students' feedback

Knowledge of the basic notions and instruments of calculus

G. Cicchitelli, P. D’Urso, M. Minozzo, Statistica: principi e metodi, Pearson, 2022, except for the following sections and sub-sections: 4.3, 4.4, 4.6, 4.14, 5.3, 6.3, 14.7, 21, 24-26. As an alternative: S. Borra e A. Di Ciaccio, Statistica, McGraw-Hill, IV ed. or former, except for the following sections, sub-sections and chapters: 3.3, 3.4, 6.7, 10.7, 11.9, 13.7.1, 13.8, 14.5-14.7, 16, 18-21; chapters 7 and 17 are not needed for the exam, but they can be useful for exercise. Being an institutional course, students can actually refer to any basic statistic text at university level containing all the topics present in the program. Further didactic materials will eventually be made available online at https://web.uniroma1.it/memotef/users/guagnano-giuseppina

Attendance is not mandatory and is expected to be in presence

The evaluation aims to assess the knowledge that students acquired, as well as their skills in explaining theoretical concepts using the appropriate terminology, in quantitative analysis of real data (applying the most appropriate statistical tools) and in the critical interpretation of the results obtained in the statistical analysis. The evaluation is based on a written test of two hours, containing numerical exercises and multiple-choice or open questions. In particular, the multiple-choice and open questions are designed to test the candidate's knowledge of the theoretical aspects of the subjects covered by the programme and the ability to interpret and critically evaluate the results of the use of statistical tools; the numerical exercises are designed to test the candidate's ability to use statistical tools in a quantitative analysis. Each question is given a specific mark and the overall score of the written test is expressed in thirtieths. In certain cases - e.g. if a student scores just under 18/30 ,or if the origin of the answers given is doubtful - the teacher reserves the right to supplement the written test with an oral examination. In all other cases, the oral test is optional. However, for those who obtain a score higher than 23/30 in the written test, the oral exam will be required to confirm this mark; in the absence of this further confirmation, the score of 23/30 will be recorded, regardless of the previous score. In all cases, the final mark will be the average of the marks obtained in the two tests (written and oral).

The teaching activity is mainly carried out through lectures, but may also include group works and the draft of short paper dealing with real data analysis.