Inglese

Il corso sviluppa i principi dell’inferenza statistica e della progettazione degli esperimenti in ottica “experimental statistics”. Si introducono test d’ipotesi, intervalli di confidenza, errori di I/II tipo e potenza; l’inferenza a due campioni; ANOVA e il modello lineare come quadro unificante per t-test e ANOVA; principi di DoE (randomisation, replication, blocking) e disegni fattoriali; cenni e applicazioni del modello lineare con errori di misura (measurement error) con focus su regressione.

Testi principali:

Montgomery, D. C. (2017). Design and analysis of experiments. John wiley & sons.

Taback, N. (2022). Design and analysis of experiments and observational studies using R. Chapman and Hall/CRC.

Testi consigliati:

Fuller, W. A. (2009). Measurement error models. John Wiley & Sons.

Box, G. E., Hunter, J. S., & Hunter, W. G. (2005). Statistics for experimenters: design, innovation, and discovery. John Wiley & Sons.

Al termine del corso lo studente sarà in grado di:

- impostare e interpretare intervalli di confidenza e test d’ipotesi nel caso one-sample e two-sample;
- comprendere errori di tipo I/II, potenza e criteri di scelta della numerosità campionaria;
- applicare test per differenze tra medie, confronto tra varianze e differenze tra proporzioni;
- utilizzare ANOVA e interpretare effetti principali e interazioni in disegni sperimentali;
- riconoscere t-test e ANOVA come casi particolari del modello lineare e utilizzare test t/F nel quadro del linear model;
- progettare esperimenti mediante randomisation, replication, blocking e disegni fattoriali (con cenni a frazioni e curvature);
- discutere l’impatto degli errori di misura (measurement error) e affrontare i concetti base della regressione con covariate misurate con errore.

È molto raccomandata una conoscenza di base della statistica e dell'inferenza statistica.

Lezioni teoriche ed esercitazioni (classiche e mediante software R).

Esame orale, con progetto in R e domande teoriche.

Slide, esercizi e materiale integrativo saranno resi disponibili attraverso i canali indicati dal docente. Per ulteriori informazioni o domande relative al corso, si prega di contattare il docente via e-mail e/o tramite MS Teams.

Richiami di inferenza: stima e intervalli; test d’ipotesi; p-value; ipotesi one-sided/two-sided; significatività statistica vs pratica.
Errori di tipo I/II e potenza: definizioni, funzione di potenza, scelta della numerosità campionaria; valutazione pratica della potenza.
Inferenza one-sample: test/intervalli per media (varianza nota/ignota), varianza (chi-quadro), proporzioni (approssimazione normale); metodi non parametrici (sign test, Wilcoxon signed-rank).
Inferenza two-sample: differenza tra medie (varianze note; varianze ignote con pooled/Welch), paired t-test; confronto tra varianze (F-test e intervalli sul rapporto); differenza tra proporzioni.
ANOVA: one-way; concetto di scomposizione della variabilità; contrasti e post-hoc (overview); introduzione a blocking/two-way.
Modello lineare; test t e F; modelli annidati; collegamenti tra t-test, ANOVA e regressione; diagnostica di base (residui, eteroschedasticità, outlier/influence in forma essenziale).
DoE: randomisation, replication, blocking; disegni fattoriali, effetti principali e interazioni; cenni a fractional factorial/aliasing e curvature/centre points; pure error vs lack-of-fit.
Linear regression with measurement error: modello classico; conseguenze su stima e inferenza (attenuation bias); ruolo di repliche e calibrazione; panoramica di strategie (a livello concettuale).

English

The course develops the foundations of statistical inference and design of experiments from an “experimental statistics” perspective. Topics include hypothesis testing and confidence intervals, Type I/II errors and power; two-sample inference; ANOVA and the linear model as a unifying framework for t-tests and ANOVA; DoE principles (randomisation, replication, blocking) and factorial designs; and an introduction to linear regression with measurement error, with an emphasis on practical implications.

Main texts:

Montgomery, D. C. (2017). Design and analysis of experiments. John wiley & sons.

Taback, N. (2022). Design and analysis of experiments and observational studies using R. Chapman and Hall/CRC.

Suggested readings:

Fuller, W. A. (2009). Measurement error models. John Wiley & Sons.

Box, G. E., Hunter, J. S., & Hunter, W. G. (2005). Statistics for experimenters: design, innovation, and discovery. John Wiley & Sons.

By the end of the module, students will be able to:

- formulate and interpret confidence intervals and hypothesis tests for one-sample and two-sample settings;
- understand Type I/II errors, power, and sample size planning principles;
- apply tests for differences in means, variance comparisons, and differences in proportions;
use ANOVA and interpret main effects and interactions in experimental designs;
- recognise t-tests and ANOVA as special cases of the linear model and use t/F tests within the linear-model framework;
- design experiments through randomisation, replication, blocking, and factorial designs (with brief notes on fractions and curvature);
- discuss the impact of measurement error and understand core ideas of regression with measurement error in covariates.

Basic knowledge of statistics and statistical inference is highly recommended.

Theoretical lectures and exercises (classical and with R software).

Oral exam, with R project and theory questions.

Slides, exercises, and additional materials will be shared through the channels indicated by the lecturer. For any further information or questions regarding the course, please contact the lecturer by email and/or via MS Teams.

Inference refresher: estimation and intervals; hypothesis testing; p-values; one-sided/two-sided hypotheses; statistical vs practical significance.
Type I/II errors and power: definitions, power function, sample size planning; practical power evaluation.
One-sample inference: tests/intervals for mean (known/unknown variance), variance (chi-square), proportions (normal approximation); nonparametric methods (sign test, Wilcoxon signed-rank).
Two-sample inference: difference in means (known variances; unknown variances via pooled/Welch), paired t-test; variance comparison (F-test and CI for variance ratio); difference in proportions.
ANOVA: one-way; variability decomposition; contrasts and post-hoc procedures (overview); introduction to blocking/two-way.
Linear model; t and F tests; nested models; links among t-tests, ANOVA and regression; basic diagnostics (residuals, heteroscedasticity, outliers/influence at an introductory level).
DoE: randomisation, replication, blocking; factorial designs, main effects and interactions; brief notes on fractional factorial/aliasing and curvature/centre points; pure error vs lack-of-fit.
Linear regression with measurement error: classical model; consequences for estimation and inference (attenuation bias); role of replicates and calibration; overview of strategies (conceptual level).