## APUNAP32 Data Processing and Statistics

Institute of physics in Opava
winter 2022
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Stanislav Hledík, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Stanislav Hledík, Ph.D.
Institute of physics in Opava
Timetable
Wed 14:45–16:20 SM-UF
• Timetable of Seminar Groups:
APUNAP32/A: Mon 10:35–12:10 LPS, A. Hofer
Prerequisites (in Czech)
( FAKULTA ( FU ) && TYP_STUDIA ( B ))
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course acquaints students with the basics of the probability theory, with the basics of descriptive and inferential statistics, including the presentation of statistical data, and with the basics of data modeling. The explanation is complemented by interactive computer demonstrations based on real data and cases.
Learning outcomes
After completing the course, the student will:
- master standard statistical methods to the extent necessary for the specialization;
- be able to interpret the data obtained;
- be able to correctly design an experiment;
- capable of skeptical thinking and critical evaluation
Syllabus
• 1. Basic concepts of probability theory. Repetition, combinatorics. Concept of probability, random experiment, random phenomenon, definition and properties of probability. Independence of phenomena, conditional probability. Discrete and continuous random variable, probability distribution function (probability density, PDF) and (cumulative) distribution function (CDF).

2. Probability distribution characteristics. Moments, mean, variance, standard deviation, skewness, kurtosity, other measures of variability. Median, quantiles, mode. Random variable transformation.

3. Basic one-dimensional distribution functions. Discrete distribution functions. Continuous distribution functions.

4. Random vector. Distribution functions and probability densities of multidimensional distributions. Marginal distribution, correlation (contingency) table. Distribution moments, covariance, linear correlation coefficient, uncorrelated and independent quantities. Multinomic distribution, two-dimensional normal distribution.

5. Limit theorems of the number of probabilities. Bernoulli's theorem, law of large numbers (Chebyshev's theorem), central limit theorem.

6. Statistics - introduction and statistical surveys. Basic concepts. Qualitative and quantitative variables and their statistical characteristics. Sample surveys, methods, types and errors. Sample distributions and their characteristics - population vs. selective, frequencies. Distribution of statistics in selections from the normal distribution.

7. Basics of estimation theory. Point and interval estimation, unbiased and best unbiased estimation. Asymptotic properties of estimation, consistent estimation. Construction of point estimation. Construction of interval estimation.

8. Testing statistical hypotheses. Hypothesis testing methodology, statistical hypothesis, null and alternative hypothesis, test statistics, level of statistical significance, p-value, number of degrees of freedom, error of the first and second kind.

9. Selected parametric tests. Arithmetic mean and variance testing (Student's t-test and F-test), goodness-of-fit tests (chi square, K-S test). Dependency analysis. Analysis of variance (ANOVA), post hoc analysis.

10. Selected nonparametric tests. Mann-Whitney test, Kruskal-Wallis test, Spearman coefficient, Kendall's tau. Tests for dependent selections (Friedman's test).

11. Regression and correlation analysis. Model, model coefficients. Linear regression model. Point estimates (point estimation of regression line parameters, significance of point estimates), model verification, model stability, residue testing. Generalized linear regression (structural matrices, normal equations, multicollinearity). Determination index, partial correlation coefficients.

12. Examples of case studies and applications of statistical methods and data modeling.
Literature
required literature
• RICE, John A. Mathematical Statistics and Data Analysis (with CD Data Sets). 3 edition. Belmont, CA: Thomson/Brooks/Cole, 2007. ISBN 0-534-39942-8. info
recommended literature
• E.T. Jaynes. Probability Theory: The Logic of Science. Cambridge University Press (June 9, 2003). ISBN 978- 0521592710.
Teaching methods
lectures; exercises
Assessment methods
Active participation in exercises and solving all homework. During the oral exam, students demonstrate knowledge and overview of statistics and data processing in the range of lectures.
Language of instruction
Czech