Statistics (2020/2021)

Learning outcomes

The course aims at providing the basic techniques of descriptive statistics, probability and statistical inference to undergraduate students in economic and business sciences. Prerequisite to the course is the mastering of a few basic mathematical concepts such as limit, derivative and integration at the level of an undergraduate introductory course in calculus. Overall, these techniques provide the necessary toolkit for quantitative analysis in processes related to the observation and understanding of collective phenomena. From a practical point of view, they are necessary for descriptive, interpretative and decision-making purposes when carrying out statistical studies related to economic and social phenomena. In addition to providing the necessary mathematical apparatus, the course aims at providing conceptual tools for a critical evaluation of the methodologies considered.

a) Descriptive statistics

• Data collection and classification; data types.
• Frequency distributions; histograms and charts.
• Measures of central tendency; arithmetic mean, geometric mean and harmonic mean; median; quartiles and percentiles.
• Fixed-base indices and chain indices; Laspayres and Paasche indices.
• Variability and measures of dispersion; variance and standard deviation; coefficient of variation.
• Moments; indices of skewness and kurtosis.
• Multivariate distributions; scatterplots; covariance; variance of the sum of more variables.
• Multivariate frequency distributions; conditional distributions; chi-squared index of dependence; index of association C; Simpson’s paradox.
• Method of least squares; least-squares regression line; Pearson’s coefficient of linear correlation r; Cauchy-Schwarz inequality; R-square coefficient; explained deviance and residual deviance.

b) Probability

• Random events; algebras and sigma-algebras; probability spaces and event trees; combinatorics.
• Conditional probability; independence; Bayes theorem.
• Discrete and continuous random variables; distribution function; expectation and variance; Markov and Chebyshev inequalities.
• Discrete uniform distributions; Bernoulli distribution; binomial distribution; Poisson distribution; geometric distribution.
• Continuous uniform distributions; normal distribution; exponential distribution.
• Multivariate discrete random variables; joint probability distribution; marginal and conditional probability distributions; independence; covariance; correlation coefficient.
• Linear combinations of random variables; average of independent random variables; sum of independent and Gaussian random variables.
• Weak law of large numbers; Bernoulli’s law of large numbers for relative frequencies; central limit theorem.

c) Inferential statistics

• Sample statistics and sampling distributions; chi-square distribution; Student-t distribution; Snedecors-F distribution.
• Point estimates and estimators; unbiasedness; efficiency; consistency; estimate of the mean, of a proportion and of a variance.
• Confidence intervals for a mean, for a proportion (large samples) and for a variance.
• Hypothesis testing; power and observed significance level; one and two tails tests for a mean, for a proportion (large samples) and for a variance; hypothesis testing for differences in two means, two proportions (large samples) and two variances.

SUPPORTING MATERIAL

Detailed indications, regarding the use of the textbook, will be given during the course. Supporting material (written records of the lessons, exercises with solutions, past exam papers with solutions, etc.) is available on the E-learning platform of the University (Moodle).

TEACHING METHODS

Students are supposed to have acquired mathematical knowledge of basic concepts such as limit, derivative and integral.

Course load is equal to 84 hours. Exercise sessions are an integral part of the course and, together with the classes, they are essential to a proper understanding of the topics of the course. The working language is Italian. In addition to lessons and exercise hours, there will also be tutoring hours devoted to revision. More detailed information will be available during the course.

Due to the COVID-19 health emergency, the way lessons will be delivered might change during the course of the semester. In any case, distance learning will always be guaranteed so that all face-to-face lessons, in addition to telematic ones (pre-recorded or online), will be recorded and made available for later viewing.

Due to the COVID-19 health emergency, at the moment it is not possible to predict whether the final examination will be face-to-face or remotely. If the examination will be held face-to-face, it will consist of a written test (lasting about 2 hours and 30 minutes) made up of a selection of exercises and multiple choice questions. For the written test, only a calculator can be used and no other material (books, notes, etc.) will be allowed. The written test will be followed by an oral test (optional), which can only be accessed by students who have obtained a mark greater than or equal to 15/30 both in the exercises and in the multiple choice questions. To take the tests, students must present themselves with a university card or a suitable identification document.

In the event that the examination will be held remotely, it will consist of a written test through Moodle's QUIZ tool (lasting about 1 hour and 15 minutes) made up of a selection of numerical exercises and multiple choice questions. The written test will be followed by a compulsory oral test, which can only be accessed by students who have obtained a sufficiently adequate mark in the written test. The oral exam will also take place remotely through Zoom.

For the 2020/2021 academic year, remote examination is always guaranteed for all students who request it. Regardless of the modality (face-to-face or remotely), the exams will be calibrated to guarantee the same level of difficulty. Finally, we remind that the examination methods are the same for all students and there are no differences according to the number of lessons attended.