C2170 Statistical Methods in Chemistry

Faculty of Science
Spring 2025
Extent and Intensity
1/2/0. 3 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
doc. Mgr. Dominik Heger, Ph.D. (lecturer)
Bc. Jan Novotný (lecturer)
Guaranteed by
doc. Mgr. Dominik Heger, Ph.D.
Department of Chemistry – Chemistry Section – Faculty of Science
Supplier department: Department of Chemistry – Chemistry Section – Faculty of Science
Prerequisites
Basics in mathematics
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Statistics help us to draw the right conclusions based on the measured data. The aim of this basic course is to teach you how to think about data, explain some basic concepts of statistics, and be able to apply these skills to examples mostly from the sciences. The course consists of three parts: 1. Descriptive statistics, 2. Probability, 3. Inference. Understanding the differences and connections between these parts is one of the important goals. Statistics is needed by everyone who wants to make sense of this world full of data. We have built this course taking into account our personal experience as a natural scientist working in physical chemistry (Dominik Heger) and as an applied statistician (Jan Novotný). Finding a common interdisciplinary language is a challenge and an opportunity for our own growth. We hope that this course will enable you to understand the language of statistics, to solve basic problems independently, and to know what literature to open when solving more complex problems.
Learning outcomes
The student will be able to - apply descriptive statistics and understand the basics of inference - the student will be familiar with the important concepts of statistics and will have mastered basic statistical methods - be able to read advanced statistical texts with understanding
Syllabus
  • Outline 1. Descriptive statistics. Position characteristics: mean, median, mode, quantiles; box plot. Sorted statistical ensemble. Histogram, transition to the density of a continuous probability distribution. Different kinds of averages: arithmetic, geometric, etc. 2. Types of statistical signs: categorical, numerical, etc. Characteristics of variability: variance, standard deviation. General and central moments, skewness and peakedness. Recalculation of characteristics in linear transformations. Normal distribution. 3. Multivariate trait (2D), marginal frequencies, histogram in 2D. Scatter plot. Correlation, covariance matrix. Correlation vs causality. Basics of linear regression. 4. Basics of probability: random phenomena, phenomenon field, Kolmogorov's axioms of probability. Independence of phenomena, conditional probability. Complete probability, Bayes formula. Differences between discrete and continuous probability. 5. Counting with probabilities. Selected discrete distributions: binomial, geometric, uniform. Selected continuous distributions: uniform, "simple skew (example)", normal. Galton's board, Pascal's triangle. 6. Random variable. Mean, variance and standard deviation for discrete and continuous random variables (sum and integral). Probability function and probability density; distribution function and quantile function. 7. Random selection vs population. Correlation and differences. Mean as a random variable (statistics) and its distribution, law of large numbers. Chebyshev and Markov inequalities, types of convergence v  probability (comment only). 8. Central limit theorem. Derivation of the probability distribution of particle velocities in an  ideal gas, possibly also the Maxwell-Boltzmann distribution. Multivariate normal distribution. 9. Inference: point and interval estimates. 10. Hypothesis testing theory: principle, 1st and 2nd order error, power of test. Various tests (t-test, z-test, etc.); multiple sample hypotheses. 11. Error propagation via total differential 12. Linear regression with calculation of confidence intervals. 13. ANOVA.
Literature
  • • https://www.edx.org/course/uc-berkeleyx/uc-berkeleyx-stat2-1x-introduction-1138#.VBhMghaqIhY • http://www.stat.berkeley.edu/~stark/SticiGui/ • Jerrold H. Zar: Biostatistical Analsis • Statistics by Freedman, Pisani, and Purves; W.W. Norton, 2007
Teaching methods
The teaching will be based on a presentation with the help of a blackboard, sometimes presentations will be prepared. Theory will be demonstrated by examples which will be solved in the lessons. Each lesson will end with summary questions which will be discussed by the students at the beginning of the next lesson. There will be recommended readings from each week's online scripts to study, which will also include demonstration examples. We will also incorporate IS-assessed homework.
Assessment methods
Assessment method: homework 25%, mid-term tests 25%, final written work 50%. The final grade of A > 92%, B > 84%, C > 76%, D > 68%, E > 60% may be changed by grade on the basis of an oral retest.
Náhradní absolvování (in Czech)
Test probrané látky bez nutnosti absolvovat cvičení. V~takovémto případě bude detailně testována hloubka porozumění.
Language of instruction
Czech
Teacher's information
https://stdt.cz/
The course is also listed under the following terms Autumn 2010 - only for the accreditation, Autumn 2010, Autumn 2011 - acreditation, autumn 2021, Autumn 2022, Spring 2024.
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