Statistics

1. Define basic statistical concepts (population, sample, variable, observation, distribution, sampling distribution, error of the first and second type, power of a statistical test)
2. Distinguish nominal, ordinal, interval and ration variables.
3. Apply appropriate descriptive methods on a data set.
4. Analyze statistical association between variables using appropriate methods.
5. Evaluate validity of assumptions of statistical methods.
6. Interpret results of a statistical data analysis.
7. Appraise suitability of the learned statistical techniques for solving problems in their profession.

Lectures accompanied by computer presentation introduce students to new concepts through relevant examples and teach theoretical basis of the course.

In computer labs students use statistical environments R and RStudio. By solving concrete problems students reinforce theoretical concepts and models, link them to applications and practice independent problem solving.

Course descriptions, the literature list, lecture handouts and presentations, online tests and examples of solved problems, and links to other statistical resources are available through the Learning Management System Merlin. Downloading and uploading of lab and home assignments are implemented in Merlin. Solving of a graded online test on current course content is a prerequisite for downloading lab assignments and uploading their solutions. Online self-assessment test is available, formed as a random selection of 20 questions from covered course content. There is a forum with official information and a forum for questions and answers in Merlin. Results of all grades awarded through the continuous assessment are published on Merlin.

Through homework and online tests students practice independent problem solving through application of theoretical concepts and methods.

1. Lectures: What is statistics? Data table, variable, observation, population and sample, measurement scale. Computer lab: Demonstration of R and R-Studio systems and Rmarkdown package. Practice – writing, reading and saving R markdown documents, reading data from an excel file and a plain text file, computation with R.
2. Lectures: Graphical and numerical summary of one or two qualitative variables, bar chart, pie chart, mosaic graph, frequency tables. Computer lab: Practice – analysis of qualitative variable – graphical and numerical summaries in R.
3. Lectures: Graphical and numerical summary of a quantitative variable, histogram, distribution (shape, center and spread), 5 number summary, box-plot, outliers, comparison of distributions. Computer lab: Practice – analysis of quantitative variable – graphical and numerical summaries in R.
4. Lectures: Standardization, shift and scale, normal distribution model, percentile, quantile, qq plot, association and correlation, scatterplot, correlation coefficient. Computer lab: Standardization of a quantitative variable, graphical and correlation analysis of association between quantitative variables in R.
5. Lectures: Linear regression - descriptive, linear model, reziduals, prediction, least squares, regression coefficients, assumptions, diagnostics. Computer lab: Practice – linear regression and its diagnostics using R.
6. Lectures: Probability and randomness, random event, outcome, trial, law of large numbers, probability of a complement and a complex event, conditional probability, Bayes rule, discreet and continuous random variable, distribution function, variance, standard deviation, covariance. Computer lab: Demonstration of the law of large numbers through simulation in R, application of rules for calculating probability of events.
7. Mid-term exam
8. Lectures: Data collection, population, sample, randomization, bias, sample size, population parameter, sample statistics, simple random sample, sampling frame, sampling variability, types of samples. Computer lab: Demonstration – simulation of random variables for standard distributions in R, sampling variability through simulation.
9. Lectures: Sampling distribution, sampling variability, sampling distribution of a proportion, sampling distribution of a mean, central limit theorem. Interval and numerical estimate of a proportion. Computer lab: Demonstration of the central limit theorem and confidence intervals through simulation in R.
10. Lectures: Hypotheses testing, hypotheses on proportions, null-hypothesis, alternative hypothesis, one-sided and two-sided test, p-value, z-test, errors type I and II, power of a test. Computer lab: Demonstration of hypotheses testing, the I. and the II. Type errors and power through simulation in R. Practice – estimation and testing hypotheses about proportions in R.
11. Lectures: Comparing two proportions, sampling distribution of a difference between two proportions, variance of a difference between two independent random variables, confidence interval of a difference, z-test Computer lab: Practice – testing hypotheses on difference between two proportions in R.
12. Lectures: Inference about a mean, Student’s t-distribution, degrees of freedom, confidence interval based on t-distribution, testing hypotheses on mean. Comparing means on independent and paired samples, box-plots, t-test, confidence intervals for the mean Computer lab: Practice – Demonstration of sampling distribution and confidence interval in R. Testing hypothesis about means in R, interpretation of results.
13. Lectures: Inference on frequencies contingency table, cell, chi-square model, chi-square distribution, Computer lab: Practice – analysis of frequencies and contingency tables in R, interpretation of results
14. Lectures: Inference on linear regression, assumptions, t-test for regression coefficients, confidence interval for predicted mean and individual observation Computer lab: Practice – application of linear regression to data analysis with testing of hypotheses on regression coefficients and model diagnostics, interpretation of results.
15. Final exam