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Lecturer(s)
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Meloun Milan, prof. RNDr. DrSc.
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Course content
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1. Metrology, theory of errors, errors of instrumental measurements. 2. Propagation-of-errors law in experimental operations. 3. Exploratory data analysis and construction of sample distribution function. 4. Power and Box-Cox transformation and assumption about univariate sample. 5. Classical analysis of univariate data and analysis of small samples with Horn procedure. 6. Robust analysis of univariate data and statistical data testing. Accuracy tests. 7. ANOVA. One-way ANOVA. Two-way-ANOVA. 8. Analysis of linear regression models. Regression model building and testing. 9. Analysis of multivariate regression models with the use of the regression triplet. 10. Regression diagnostics and statistical analysis of various residuals. Calibration in analytical chemistry. 11. Data correlation. Global, pair and partial correlation coefficients. Pearson and Spearman tests. 12. Nonlinear regression models. Statistical analysis in nonlinear regression and the goodness-of-fit test. 13. Interpolation, approximation and curve smoothing. Spline function. Piecewise regression. 14. Shewhart regulation diagrams of quality control.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Methods of individual activities, Skills training
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- 30 hours per semester
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- 20 hours per semester
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- 40 hours per semester
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- 30 hours per semester
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Learning outcomes
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The application of computer oriented statistical methods in scientific and technical fields enables not only the use of information hidden in data and the generalization of combined results from different sources, but also the creation of models, optimizations, and possible solutions. It is a multi-disciplinary movement on the frontier of the scientific disciplines of statistics and informatics, which have led to the rise of new fields such as chemometrics, biometrics, psychometrics, econometrics, technometrics and others. The goal of data processing and the level of expertise of the problems solved are always determinant factors, which affect the analysis approach and selection of methods used. Solving practical exercises allows one to better understand the limits and possibilities of various methods and to select through analogy the manner for processing one's own exercises. This is exploratory data analysis to verify the basic assumptions about data with regard to the basic data model statistical method. The construction of statistical models here is more for illustration and the interpretation of results is merely general. The comprehensive statistical data analysis approach is made therefore in the ADSTAT and QC-Expert statistics packages. The diagnosis of interactive data analysis means looking for all relations and peculiarities hidden in data. This is not possible using a standard approach without computer support.
The subject is intended for undergraduates and graduate students in chemistry, other natural sciences, and chemical engineering, and for all who engage in applied research in all fields of chemistry. The subject introduces the use of interactive data treatment by personal computer. It provides the basis for adequate understanding of the interactive use of exploratory and confirmatory techniques, with examples, and requiring only a relatively unsophisticated level of mathematical knowledge. Interactive statistical data analysis is introduced here as a form of numerical or graphical detective work. The exploratory data analysis represents here the first step in an adaptive statistical analysis of experimental data. Then the concept of exploratory and confirmatory data analysis by interactive work with "user-friendly" software is described. It is important in chemical data analysis to understand what you can do before you learn to measure how well you seem to have done it. Learning first what you can do will help you to work more easily and effectively. Exploratory data analysis consists of looking at data to see what it seems to say. It concentrates on simple arithmetic and easy-to-draw pictures. The confirmatory data analysis looks at a sample, and at what that sample has told us about the population from which it came, and attempts to assess the precision with which the inference from sample to population is made. Since regression is a popular research area, regression analysis is an everchanging collection of techniques. The regression methods are taught as a state-of-the-art regression methodology so called the regression triplet: data analysis, model analysis and method analysis what represents quite a new modern approach to this technique.
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Prerequisites
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There is no special request on preliminary knowledge of statistics or mathematics. The active work with computer and software (Microsoft Office) is supposed only namely the work with the text and figures is welcomed when creating and solving tasks in the semestral assay.
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Assessment methods and criteria
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Written examination, Home assignment evaluation
The practical data treatment using the computer-assisted interactive statistical analysis is proven by student with computation of 10 tasks and the writing a semestral work which represents 40% of the final exam. Theoretical knoledge of the computer-assisted interactive statistical analysis is proven by student in the written form of an exam which represents 40% of the final exam.
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Recommended literature
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M. Meloun, J. Militký. KOMPENDIUM STATISTICKÉHO ZPRACOVÁNÍ DAT. Academia Praha, 2002. ISBN 80-200-1008-4.
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M. Meloun, J. Militký. KOMPENDIUM STATISTICKÉHO ZPRACOVÁNÍ DAT. Academia Praha, 2006. ISBN 80-200-1396-2.
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M. Meloun, J. Militký, M. Hill. Počítačová analýza vícerozměrných dat v příkladech. Academia Praha, 2005. ISBN 80-200-1335-0.
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M. Meloun, J. Militký. Sbírka úloh pro Statistické zpracování experimentálních dat. Univerzita Pardubice 1996, 1996. ISBN 80-7194-075-5.
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M. Meloun, J. Militký. STATISTICKÁ ANALÝZA EXPERIMENTÁLNÍCH DAT v chemometrii, biometrii, ekonometrii a v dalších oborech přírodních, technických a společenských věd, . Praha, 2004. ISBN 80-200-1254-0.
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M. Meloun, J. Militký. STATISTICKÁ ANALÝZA EXPERIMENTÁLNÍCH DAT v chemometrii, biometrii, ekonometrii a v dalších oborech přírodních, technických a společenských věd,. EAST PUBLISHING Praha, 1998. ISBN 80-7219-003-2.
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Meloun, M.; Militký, J.; Forina, M. Chemometrics for Analytical Chemistry, Volume 1: PC-Aided Statistical Data Analysis. Ellis Horwood, Chichester, 1992. ISBN 0-13-126376-5.
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Meloun, M.; Militký, J.; Forina, M. Chemometrics for Analytical Chemistry, Volume 2: PC-Aided Regression and Related Methods. Ellis Horwood, Chichester, 1994. ISBN 0-13-123788-7.
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