Corso di studio in Economia

The course aims at providing the main concepts and methods of statistical reasoning. In particular, it consists of an introduction to data analysis and a presentation of elementary notions of probability theory and statistical inference. The importance of statistics in various disciplines will also be emphasized.

At the end of the course, the student is expected to:

• Understand the main statistical concepts;
• Appropriately formalize a statistical problem in order to apply the methods taught during the course;
• Face a simple statistical problem and interpret the results of the statistical analysis;
• Present in written form the knowledge gained during the course;
• Being able to successfully attend intermediate level classes in statistics and econometrics.
  

The course is articulated in 96 hours of formal in‐class lecture time, plus around 10 tutorials. The teaching is foreseen to be in presence. Teaching material will be made available through the course Moodle page.

Written test with muplie choice questions, possibly requiring resolving an excercise. Duration: 1h30mins. No oral examination is foreseen for this course. The test will take place in presence (if allowed by the current University regulations) and online for those entitled to take the test remotely.

The topics of the course are as follows:

1. Descriptive statistics

   • descriptive and inferential statistics (1.1-1.3)

   • statistical variables and their classifications (1.2)

   • graphical representations for categorical variables (1.3)

   • graphical representations for time series (1.4)

   • graphical representations for numerical variables (1.5)

   • measures of central tendency and other position indices: mode, means, median, quartiles, percentiles (2.1)

   • measures of variability: range of variation, interquartile difference, variance, mean square deviation, coefficient of variation, box plots, Chebyshev's inequality and the Empirical Rule (2.2)

   • summary measures for pooled data (2.3)

   • measures of relationships between two variables (2.4)

2. Probability calculus

   • random experiments and sample spaces (3.1)

   • conceptions of probability and axiomatic setting (3.2)

   • rules of probability calculus and conditional probability (3.3)

   • joint probabilities, marginal probabilities, independence between events (3.4)

   • Bayes' theorem (3.5)

3. Discrete random variables

   • definition, probability function and distribution function (4.1, 4.2)

   • expected value, variance, moments of a discrete r.v., linear transformations of a discrete r.v. (4.3)

   • Bernoulli distribution, binomial distribution (4.4)

   • Poisson distribution (4.5)

   • Hypergeometric distribution (4.6)

   • Joint distributions of two discrete r.v., independence, covariance and correlation, linear combinations of r.v. (4.7)

4. Continuous random variables.

   • definition, density function, uniform distribution (5.1)

   • expected value, variance (5.2)

   • normal distribution (5.3)

   • approximation of binomial distribution with normal distribution (5.4)

   • exponential distribution (5.5)

5. Sampling and sample distributions

   • random sample (6.1)

   • sample mean distribution, Central Limit Theorem (6.2)

   • sample proportion distribution (6.3)

   • sample variance distribution, chi-square distribution (6.4)

6. Estimation problems on a single population

   • point estimation: properties of non-bias, asymptotic non-bias, and efficiency (7.1)

   • confidence intervals for the mean when variance is known (7.2)

   • confidence intervals for the mean when variance is unknown, Student's t distribution (7.3)

   • confidence intervals for the proportion (large samples) (7.4)

   • confidence intervals on the variance of a normal population (7.5)

7. Hypothesis testing on a single population

   • basic concepts of hypothesis testing (9.1)

   • hypothesis testing on the mean when the variance is known (9.2)

   • testing of hypotheses about the mean when the variance is not known (9.3)

   • hypothesis testing on the proportion (large samples) (9.4)

   • hypothesis testing on the variance of a normal population (9.6)

8. Additional topics

   • chi-square test for contingency tables (14.3)

   • other topics to be confirmed at the end of the course