Quantitative Methods and Statistics for the Social Sciences

The course aims at illustrating the foundations of Statistics also through statistical learning based on data analysis.
In particular, the course is addressed to provide the basic tools of Statistics which can be used by students in order to reach the understanding and the solving of complex problems, with particular reference to the social sciences.

To this purpose, the main basic topics will be focused on:

1) descriptive statistics;
2) probability;
3) statistical inference.

With regard to point 1), we will proceed to:
a) provide a specific classification of the different types of variables under study based on their nature, differing between qualitative and quantitative variables which in turn are further classified into nominal or ordinal qualitative variables and discrete or continuous quantitative variables;
b) introduce the main central tendency measures (mean, mode, median, quartiles) and variability measures (variance, standard deviation, range, etc).

With regard point 2), we will proceed to:
a) introduce the notion of classical probability as well as the concepts concerning the probability of union and intersection events;
b) illustrate the main probability distributions, considering the cases of discrete and continuous probability distributions (Binomial, Uniform and Normal distributions).
With regard to point 3), we will proceed to:
a) define the concept of sampling distributions;
b) introduce the Central Limit Theorem;
c) specify the notion of confidence intervals for the unknown population mean in the different scenarios (known or unknown population variance) and for the unknown population proportion;
d) provide the construction of statistical tests for the unknown mean and proportion of the population
Finally, we will proceed to discuss the functional association existing between two variables and explained through the construction of the simple linear regression model in turn based on the correlation notion.

At the end of the course students should have achieved the required skills to: with reference to point 1), provide a descriptive summary of the data using synthetic indicators; with reference to point 2), proceed to the calculation of the probability of simple or compound events by evaluating which type of the probability distributions presented along the course is the most appropriate; with reference to pint 3), solve inferential problems with the aim of stating whether the conclusions related to the sample under study can be extended to the whole population.
Furthermore, students should be able to apply linear statistical models together with the related measures of fit and significance.
Finally, students must be able to express the obtained results through the proper statistical language. The lectures will be supplemented by practical tutorials using the sofware R