Course program
PART A: Introduction to Statistics - Elements of Probability.
1. Basics of Statistics and Data Science.
2. Probability.
(a) Test, Sample Space, Events, Operations, and Relationships between Events.
(b) Definitions and Properties of Probability.
(c) Conditional Probability and Independence. Marginal Probability.
(d) Bayes' Theorem.
(e) Discrete and Continuous Random Variables.
(f) Probability Function, Probability Density Function, and Distribution Function.
(g) Discrete Distributions: Uniform, Bernoulli, Binomial, and Poisson.
(h) Continuous Distributions: Uniform, Normal, and Exponential.
(i) Mean and Variance Operators and Their Properties.
PART B: Univariate Statistics
1. Types of Statistical variables and Measurement Scales.
2. Measures of Location: Mean, Median, Mode, Quantiles.
3. Measures of Variability: Variance, Simple/Standard Deviations from the Mean/Median, Range, Interquartile Range, Coefficient of Variation.
4. Measures of Skewness.
5. Statistical Plots.
6. Index Numbers.
PART C: Bivariate Statistics
1. Contingency Tables.
2. Joint, Conditional, and Marginal Distributions and Their Relationships.
3. Independence of Random Variables and Bayes' Theorem.
4. Independence Table and Measure of the Relationship between Two Variables.
5. Properties of the Mean and Variance Operators for Multiple Variables.
6. Dependence on Mean.
7. Variance Decomposition.
8. Scatterplot, Covariance, and Correlation.
PART D: Simple Linear Regression (Descriptive Statistics Part)
1. The Simple Linear Regression Model: Assumptions.
2. Least-squares Estimates of the Intercept and Slope.
3. Index of Determination.
4. Prediction.
PART E: Point Estimation.
1. Sampling Distribution, Estimators, and Estimates.
2. Estimates of Means and Proportions and the Central Limit Theorem.
3. Consistency, Bias, and Efficiency of an Estimator.
4. Mean Squared Error.
PART F: Confidence Intervals and Hypothesis Testing
1. Confidence Intervals for the Mean and the Proportion.
2. General Hypothesis Testing: Type I and Type II Errors.
3. Tests on the Population Mean and the Student's t-Distribution.
4. Composite Hypotheses and One-Way Tests.
5. Significance and p-value.
6. Chi-square Test of Independence.
7. Simple Linear Regression (Inferential Part).
8. Tests on the Intercept and Regression Coefficients.
Prerequisites
The course is introductory and requires no particular prerequisites other than a minimal knowledge of basic mathematical concepts, including limits, integrals, derivatives, and matrix algebra.
Books
Main textbook: Cicchitelli, D’Urso, Minozzo: ”Statistica: principi e metodi”. Pearson.
Alternative/Optional Readings:
F. Mecatti: "Statistica di base: come, quando e perché", McGraw-Hill.
D. Piccolo: "Statistica", Il Mulino.
Exercise Textbooks:
F. Pauli, N. Torelli, M. Trevisani: "Statistica: esercizi ed esempi", Pearson.
V. Cicogna, D. Olivieri: "Temi svolti di statistica (anni 2005-2012)", Cedam.
Frequency
Class attendance is not mandatory, but we strongly recommend attending classes, at least those covering more difficult topics.
Exam mode
The exam consists of a written test both with exercises to be solved and with multiple choice questions. During the course, non-mandatory tasks will be assigned which can contribute to the final evaluation.
Lesson mode
Lectures tend to engage students. For example, the provision of additional points for completing small tasks during the course increases student participation. The R/RStudio software tool is also used, especially for completing exercises: this tool also encourages students to consider the potential future use of data analysis for their thesis and, more generally, in the workplace. A good mix of theory and practice (theory, including the formulation of basic theorems in mathematical statistics, and practice, including the presentation of solutions to exercises based on real data) should enhance students' well-rounded preparation.
