Analysis of Experimental Uncertainty

obligatory courses

It is essential to know the differential calculus and the ability to use a spreadsheet.

Objectives:

- introduction to modern methods of data analysis and evaluation of uncertainty of the results with the use of elements of statistics,

- methods of data presentation

- introduction to methods of statistical hypothesis testing.

Profile : academic

Form: stationary

Subject: obligatory, module "Rudiments of physics"

Branch of science and Discipline of science: Physical sciences, physics

Year/Semester: 1 year/2 semester, first degree (undergraduate) study (general physics)

Prerequisites: passed exams on Introduction to physics, skill in using Worksheet.

Didactic units: lecture 15 hrs., laboratory 15 hrs.

Didactic methods: Lecture in the form of a multimedia presentations (lecture notes available on e-learning); laboratory: performing computer excersises related to lecture subjects.

ECTS credits: 2

Balance the workload of the average student: participation in lectures (15 hrs.), OSH training - 1 hr., participation in laboratory excercises (15 hrs.), active participation in the consultations (3 hrs.), preparation to computer classes - 15 hrs., preparing for written test and participation in the test - 6 hrs. 55 hrs. in total.

Quantitative indicators: classes with academic teacher - 34 hrs., 2 ECTS, practical classes (with students activity) - 15 hrs. (ca. 1 ECTS).

Lecture topics:

1. Introduction, system of physical units, methods of experimental data presentation (graphic, histogram, tables, equations).

2. Basic definitions related to experiment, simple and complex quantities, sources and classification of experimental errors and uncertainties.

uncertainty of complex-valued quantity.

3. Rounding and comparison of the results, precision of the results, position and significant digits.

4. Basis of statistical data analysis, result of the measurement as a random variable, probability distribution for random variables (expected value, variance, standard deviation, moments of a distribution), cumulative distribution function.

5. Examples of probability distribution function (discrete uniform distribution, binomial distribution, uniform distribution, Poisson distribution, normal distribution, χ^2, distribution, t-Student distribution).

6. Statistical analysis of uncertainties of direct and indirect measurements (type A evaluation of uncertainties), most important estimators of a sample measurement obeying normal distribution, combined contributions to the uncertainty of complex quantity.

7. Type B evaluation of uncertainties.

8. Analysis of linearly dependent data, the method of least squares, linear regression, correlation coefficient.

9. Examples of evaluation of parameters of nonlinear functions matching the distribution of some measurement results.

10. Testing of statistical hypothesis using χ^2 test and t-Student test. Planning of the measurements.

Laboratory topics:

1. Methods of experimental data presentation (graphic, histogram, tables, equations).

2. Rounding and comparison of the experimental results, precision of the results, position and significant digits.

3. Evaluation of parameters of some probability distribution functions.

4. Analysis of random uncertainties of direct and indirect measurements (type A), combined contributions to the uncertainty of complex quantity.

5. Type B evaluation of uncertainties.

6. Analysis of linearly dependent data, the method of least squares, linear regression, correlation coefficient.

7. Examples of fitting of composite curves to the experimental data.

8. Testing of statistical hypothesis using χ^2 test and t-Student test.

Literature:

1. E.Żukowski - Manuscript of the lecture.

2. GUM: Guide to the Expression of Uncertainty in Measurement (2008), PDF file.

Student will be able to:

- achieve awareness of the importance of the experiment as a method of verification of theoretical concepts and awareness of experimental uncertainty,

- know the limits of applicability of selected physical theories, models, and description of physical phenomena,

- knows how understanding and critically use literature and Internet resources in relation to the problems of basic physics.

In addition, the student:

- knows how to plan simple experiments in the field of different branches of physics, to critically analyze the results and present them,

- takes skills in laboratory teamwork, taking the role of contractor or coordinator of the experiment,

- acquires the ability to organize the laboratory teamwork and take responsibility for the results of its work.

Written practical exam with the use of Worksheet

No