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

The course consists of lectures and laboratory activities.
The topics covered in the course are organized into the following main areas:

(1) Basic Concepts of Statistics
The measurement process; measurement errors, resolution errors, systematic and random errors; precision and accuracy; statistical and graphical description of data samples. Basic elements of probability and statistics; axiomatic definition of probability; Bayes’ theorem.

(2) Probability Distributions
General overview of the characteristics of discrete and continuous probability distributions. Moments of a distribution. Detailed discussion of some commonly used probability distributions: normal, uniform, binomial, and Poisson. Central limit theorems.

(3) Statistical Tools for the Analysis of Experimental Data
Error propagation for indirect measurements (theoretical treatment). Practical examples of error propagation in astrophysics. Calculation of the signal-to-noise ratio in astronomy.
Parameter estimation based on experimental data: the maximum likelihood principle (general and Gaussian case); least squares method. Practical examples of the application of these methods in astrophysics.

(4) Statistical Tests
General introduction to the use of statistical tests. Detailed discussion of some statistical tests commonly used in astrophysics: Student’s t-test, Z-test, chi-square test, Fisher test, K-S test, correlation tests.

Lectures and computer lab sessions will be held every week. The computer lab sessions are an integral part of the course and will provide a practical approach to the concepts and topics discussed during the lectures, using the Python programming language. All course topics will therefore be covered both during the lectures and in the computer lab. In particular, astronomical examples will be used to demonstrate the application of various statistical tools.
During the computer lab sessions, each student will work individually (using either the lab computers or their own laptop), but exercises will be tackled collectively whenever possible, in order to encourage participation and the exchange of ideas and opinions among students.

In the final month of the course, students will carry out a hands-on lab project in groups (typically of three students) using a Geiger counter, applying statistical concepts discussed during the course (typically 3–4 hours per group).
At the end of the course, students will be required to submit a written report on an exercise (assigned by the instructor) carried out during the computer lab sessions, and a written report on the Geiger counter experiment.

Attendance to the course (both lectures and computer lab sessions) is strongly recommended for a better understanding of the subject. Participation in the Geiger counter experiment is mandatory.

Readings/Bibliography

The following books are not mandatory but are suggested for further reading (particularly for non-attending students). Study materials are available on the Virtuale platform, including all lecture slides (provided in advance) and any supplementary notes for further explanations. The slides are sufficient for exam preparation for students who have regularly attended the course.

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

• Lectures with electronic teaching materials (powerpoint presentations).
• Participation in the Geiger counter lab project in groups of three students. This experience is mandatory in order to take the exam.
• Participation in computer lab sessions (individual work).
• Given the nature of the activities and the teaching methods used, attendance requires prior completion of Safety Training Modules 1 and 2 (https://elearning-sicurezza.unibo.it/ ) in e-learning format.

Assessment methods

The oral exam is held at the desk (i.e., students write on paper, not on the board). Submission of the written reports (typically at least one week before the exam date) is a prerequisite to take the exam. The reports are not graded; they serve only as preparation for the oral exam and have no impact on the final grade. At the beginning of the exam, the reports are discussed, and any errors may prompt the first question. The rest of the exam (average duration 25–30 minutes) will focus on topics covered in the lectures, including proofs presented during the course.

The final grade is based on the following criteria:

• Grade 18–22: The student demonstrates a limited understanding of the course content, with significant difficulties in proofs and mathematical aspects.
• Grade 23–25: Satisfactory but incomplete preparation, with gaps in some topics or uncertainty in proofs.
• Grade 26–28: Good overall understanding of the entire syllabus, with solid command of the mathematical content and good ability to answer and connect different topics.
• Grade 29–30L: Excellent and comprehensive understanding of the entire syllabus and proofs, with a strong grasp of terminology and ability to interrelate the course topics.

No notes or books are allowed during the exam.
Students may not decline a grade more than twice. The most recent grade will be recorded (not the highest one).

Students with special needs are kindly asked to contact the dedicated UniBO service in advance: https://site.unibo.it/studenti-con-disabilita-e-dsa/en

Teaching tools

PowerPoint presentations and blackboard will be used. All slides presented during the lectures, as well as the Python programs and notebooks used in the computer lab sessions, will be made available.

Office hours

See the website of Alessio Mucciarelli