00914 - Statistics

Learning outcomes

At the end of the course students will have learnt the basic tools of calculus of probability and the main statistical tecniques for analysis of data, and for estimation and prediction of phenomena from sample data. In particular,  students will be able to summarize data through specific indicators and the linear regression model with and without specific softwares, to answer basic questions about calculus of probability and to estimate a parameter of interest employing inferential tecniques such as confindence intervals and hypothesis testing.

Course contents

To begin with, the statistical software R will be introduced and the presentation of the topics of the course will be supported by the usage of the R software.

 

PART 1 - DESCRIPTIVE STATISTICS

Steps and targets of a statistical survey, sources and collection of data. Definition of statistical unit, population, variable, parameter, statistic. Classification of variables. Possible graphic representations (in particular, boxplot). Distributions of non frequency data and frequency distributions of data. Absolute, relative and cumulative frequencies. Density and histogram for classified variables. Cumulative distribution functions. Descriptive analysis of data through measures of the center, the variability and the shape of data distributions. Mode, arithmetic, geometric, harmonic and power means. Median and quartiles. Standard deviation and variance. Skewness index. Bivariate descriptive analysis. Statistical association. Covariance and correlation coefficient. Linear dependence and independence. The simple linear regression model. A brief mention to the multiple linear regression model.

 

PART 2 - CALCULUS OF PROBABILITY

Random phenomena and uncertainty. Random experiment and space of events. Operations with events. Probabiity and axioms. Conditional probability and independence of events. Law of total probability. Bayes' Theorem. Random variables and probability distribution of discrete random variables and density function of absolutely continuous random variables. Expectation and variance. Linear combination of random variables. Some distributions of discrete random variables: discrete uniform, Bernoulli, binomial and Poisson. Some distributions for absolutely continuous random variables: uniform, Normal or Gaussian, Gamma, Chi-Squared, t-Student, Fisher. Zeta scores. Central limit theorem.

 

PART 3 - INFERENTIAL STATISTICS

Induction in the state of uncertainty. Random sampling and simple random samples. The population model and parameters. Inferential methods: point estimate, confidence intervals, hypothesis testing. Sample statistics, estimators and their probability distributions. Properties of estimators: unbiasedness, efficiency, mean squared error, consistency. The choice of an estimator. The sample mean. The sample variance. Estimate of a proportion. Point estimate and confidence intervals for the mean (in case of known and unknown variance) and the variance of a Gaussian population and for a proportion in case of one or two populations. Hypothesis tests. Type one and type two errors. Test power. Significance levels and probability value (p-value). Hypothesis test for the parameters of a normal population and of a proportion. Hypothesis test for comparing the means of two normal populations (in case of known variances or unknown but equal variances). Large samples hypothesis test for comparing two proportions.

 

 

Readings/Bibliography

Textbook:

Borra, S. e Di Ciaccio, A., Statistica, metodologie per le scienze sociali ed economiche, terza edizione, 2014, Mc Graw-Hill Education. link

Handouts will be provided about the R program during the course, but students can also refer to this book written in English which is freely available online: https://r4ds.had.co.nz/

Alternative books:

Cicchitelli, G. e D'Urso, P. e Minozzo, M., Statistica: principi e metodi, 2018, Pearson, link

Newbold, P., Carlson, W. e Thorne, B. Statistica, seconda edizione, 2010, Person, link

An English book is available here for free.

Iacus, S., Masarotto, G. Laboratorio di statistica con R, Mc Graw-Hill Education.

 

Teaching methods

Teacher's lectures.

Assessment methods

Written exam. Part of the exam will require usage of statistical softwares. Students can choose between a full exam of three partial exams.

Teaching tools

The statistical software R will be used as a pedagogical tool. That is, instead of viewing the computer merely as a convenient calculating device, computer calculation and simulation will be used as another way of explaining and helping students understand the underlying concepts.

Inside the Virtuale platform (virtuale.unibo.it), students will find plenty of material (in Italian): lecure slides, handouts and exercises useful to make practice before the exam.

Students with disability or specific learning disabilities (DSA) are required to make their condition known to find the best possibile accomodation to their needs.

Office hours

See the website of Pier Giovanni Bissiri