89990 - Physics Experimentation 1 (6 CFU)

Learning outcomes

The aim of the course is to provide an introduction to the statistical interpretation of experimental data and to the analysis of the uncertainties. The student will be able to use the main statistical techniques to calculate the parameters of a polynomial relation, to verify or reject statistical hypotheses and to perform simple laboratory experiments.

Course contents

•Historical background of statistics.

•The experimental method; experimental uncertainties,  resolution, systematic and random uncertainties; precision and accuracy; statistical description of the data; histograms and distributions.

• Introduction to probability and statistics; axiomatic definition of probability; probability distributions (Gauss, uniform, binomial, Poisson); moments of a distribution

• Central limit theorems.

• Statistical evaluation of astronomical data (signal-to-noise ratio).

• Propagation of uncertainties and examples in astronomy.

• Maximum likelihood; method of the least mean squares. Applications of these methods in astronomy.

• Statistical tests: chi-square, Student, Z-test, Fisher, K-S and correlation tests.

• Laboratory experiences: Geiger counter.

• Computer lab: statistical analysis with Python; statistical analysis of astronomical data.

Readings/Bibliography

Suggested readings for further study

P. Fornasini, “The uncertainty in physical measurements”, Springer.

P. R. Bevington & D. K. Robinson, "Data reduction and error analysis for the physical sciences", McGraw Hill

R. J. Barlow, “Statistics”, Wiley

Teaching methods

Teaching includes powerpoint presentations and blackboard lessons.

The course includes the mandatory participation to (1) a laboratory experience related to general physics and (2) an experience related to the statistical analysis of astronomical data. Students will be divided into working groups of 3 students each. Also, the course includes lessons in the computer lab aimed at applying the main statistical techniques.

Assessment methods

The exam includes:

• a final report for each group including a description of the experiments and obtained results. The reports will not receive an explicit grade, but they are required in order to take the oral exam.
• an oral exam consisting in questions related to statistics and probability; during the exam will be discussed the reports of the laboratory experiences

Teaching tools

Powerpoint presentations and blackboard. All the slides used during the lectures will be available.

Office hours

See the website of Alessio Mucciarelli