| Course Unit Code | 639-3021/01 |
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| Number of ECTS Credits Allocated | 4 ECTS credits |
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| Type of Course Unit * | Optional |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | |
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| Semester when the Course Unit is delivered | Winter Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | English |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| TOS012 | Ing. Filip Tošenovský, Ph.D. |
| Summary |
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| The primary aim of the subject is an exposition of the theory of estimation of population parameters, hypothesis testing, modelling of technological processes with regression models and their assessment by correlation analysis. Multivariate regression is taught under the required theoretical conditions. Correlation analysis shows ways of measuring dependence for various types of variables. |
| Learning Outcomes of the Course Unit |
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Knowledge of basic statistical methods
Analysis of real data
Ability to process correctly experimental data
Managing work with Excel
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| Course Contents |
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1. Introduction to statistics – explanation of its use in metallurgy. Graphical representation of data samples, assessment of data type. General principles of testing.
2. Confirmation of data sample homogeneity using graphs. Outliers – their depiction, detection (box plot) and solution.
3. Confirmation of data independence using graphs. Effect of data dependence on quality of data sample processing.
4. Confirmation of normality: normal distribution, Gauss curve and its parameters, empirical histogram. Reasons why normality is required, and procedures to be followed if the normality condition is not met.
5. Descriptive characteristics of location, variability, skewness and kurtosis. The notion of robustness of numerical characteristics.
6. Student’s distribution, Fisher’s distribution, Pearson’s distribution and their graphs. Examples of using the distributions. Use of tables of quantiles and critical values.
7. Point estimation and confidence intervals. „Confidence level“ and „nivel of test“.
8. Analysis of two data samples. Testing the difference of expected values and variances. Two-sample t-test, F-test.
9. Evaluating a measure of dependence (correlation) of two variables: Pearson’s correlation coefficient, Spearman’s rank correlation coefficient.
10. Regression analysis – simple (paired) linear regression. Estimation of regression coefficients by least squares. Assessment of significance and quality of the regression function. Simple nonlinear regression models (power, exponential, logarithmic, quadratic and polynomial models).
11. Regression analysis – multivariate linear regression. Assessment of significance of the model and its regression coefficients. Use of multivariate regression. |
| Recommended or Required Reading |
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| Required Reading: |
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JAMES, G., D. WITTEN, T. HASTIE a R. TIBSHIRANI. An Introduction to Statistical Learning. NY: Springer, 2013. ISBN 978-1-4614-7138-7.
DRAPER, N. R. and H. SMITH. Applied Regression Analysis. NY: Wiley, 1998. ISBN 978-0471170822.
RYAN, T. P. Modern Regression Methods. NY: Wiley, 2008. ISBN 978-0470550441.
ASHENFELTER, O. B.,P. B. LEVINE and D. J. ZIMMERMAN. Statistics and Econometrics: Methods and Applications. NY: Wiley, 2006. ISBN-13: 978-0470009451.
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ANDĚL, J. Základy matematické statistiky. Praha: MATFYZPRESS, 2011. ISBN 978-80-737-8162-0.
TOŠENOVSKÝ, J. Základy statistického zpracování dat. Ostrava: VŠB - Technická univerzita Ostrava, 2015. ISBN 978-80-248-3733-8.
HEBÁK,P., J.HUSTOPECKÝ, E.JAROŠOVÁ a I. PECÁKOVÁ.Vícerozměrné statistické metody.
Praha: Informatorium,2004. ISBN 80-7333-025-3. |
| Recommended Reading: |
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MONTGOMERY, D. C. Applied Statistics and Probability for Engineers. NY: Wiley, 2010. ISBN-13 978-1-1185-3971-2.
SHESKIN, D. J. Handbook of Parametric and Nonparametric Statistical Procedures. NY: Chapman and Hall, 2003. ISBN 1-58488-440-1.
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MELOUN, J. a J. MILITKÝ. Statistické zpracování experimentálních dat. Praha: Ars magna, 1998. ISBN 80-7219-003-2.
HANOUSEK, J. a P. CHARAMZA. Moderní metody zpracování dat. Matematická
statistika pro každého. Praha: EDUCA, 1992. ISBN 80-85623-31-5.
TOŠENOVSKÝ, J. a D. NOSKIEVIČOVÁ. Statistické metody pro zlepšování jakosti.
Ostrava: Montanex, 2000. ISBN 80-7225-040-X.
LIKEŠ, J. a J. MACHEK. Matematická statistika. Praha: SNTL, 1983.
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| Planned learning activities and teaching methods |
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| Lectures, Tutorials |
| Assesment methods and criteria |
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| Tasks are not Defined |