# 4706564: Statistics

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Semester:SS 19
Type:Module
Language:German
ECTS-Credits:6.0
Scheduled in semester:2
Semester Hours per Week / Contact Hours:60.0 L / 45.0 h
Self-directed study time:135.0 h

## Description

Descriptive statistics with numerical measures, graphical and tabular representations (measures of location, measures of variability, measures of association between two variables, pie charts, dot plots, bar charts, histograms, box plots, scatter plots, contingency tables), simple linear regression (ordinary least squares, ANOVA-table, R-squared, residual standard error, Tukey-Anscombe plot)
Probability theory (definition of a probability space, general addition rules, Laplace models, combinatorics, decision trees, Bayes' theorem, random variables and their distributions, measures of location, variability, skewness and curtosis as measures for the shape of distribution, calculation rules for expectations, variances and covariances, binomial, normal, t-, chi-square and F-distributions, central limit theorem), Statistical inference (basic notions of statistical testing procedures like hypotheses, type 1 error, type 2 error, test statistic, decision rule, p-value, power; applications of binomial, t-, F- and chi-square-tests; point and interval estimates for probabilities and means)

## Qualifications

• Know about the roles of quantiles, variances, standard deviations and correlations to measure risks.
• Know the axioms of a discrete probability space.
• Know the most important distributions and their properties.
• Know the importance of the central limit theorem.
• Can describe univariate and bivariate data according to the level of scale using numerical measures and graphical representations.
• Can explain the content of the axioms of a discrete probability space while modelling a random experiment.
• Use the law of large numbers to interpret a probability as a relative frequency in the long run.
• Can explain why and when a certain distribution is used to model economic situations.
• Can name the basic idea of testing hypotheses referring to the possible types of errors.
• Name the basic ideas of standard testing procedures.
• Calculate the critical values in the decision rules of binomial tests.
• Can explain the meaning of confidence intervals and indicate the duality between confidence intervals and testing hypotheses.
• Use the principle of ordinary least squares to estimate the parameters of a regression model.
• Run simple linear regressions, set up the ANOVA-table and judge the residual plot.
• Calculate probabilities using addition rules, decision trees and combinatorics.
• Can explain the results of Bayes' theorem.
• Use limits theorems to approximate distributions and probabilities.
• Use calculations rules for expectations and variances correctly and can explain their meanings in the context of risk measuring.
• Calculate the critical values of binomial tests and the resulting probability of a type 2 error.
• Evaluate the test statistics of standard procedures, read the corresponding critical values from statistical tables and formulate the conclusion of the testing procedure correctly in the given context.
• Calculate confidence intervals and interpret them correctly in a given context.
• Interpret measures as quantiles, variances, standard deviations, correlations, skewness, curtosis correctly.
• Use the vocabulary introduced to them to describe graphical representations correctly and include the advantages and disadvantages of such representations while interpreting them.
• Judge the certainty or uncertainty of statistical conclusions and formulate their interpretations accordingly.
• Judge the practical relevance of a linear regression in the given context.
• Judge the uncertainty in the conclusions from statistical testing procedures correctly.
• Know the central statistical techniques that are often used in business applications.
• Understand the meaning of statistical notions.
• Use the introduced concepts in a purposeful way, interpret the results in the context and formulate their conclusions correctly.
• Use basic commands of the software package R to analyze data graphically and numerically.
• Apply standard learning techniques in abstract contexts so that they get used to working with scientific publications on their own.
• Analyze data to justify decisions in business applications.
• Analyze business cases using methods of probability theory.
• Can critically check the content of statistical results while planning economic actions.
• Argue in a precise and rational way in their comments.
• Strengthen their skills to argue rationally in a scientific environment.
• Judge the relevance of statistical conclusions and their limitations correctly.
• Judge arguments critically whether they are sound, reasonable and consistent.
• Judge the uncertainties in statistical conclusions correctly.
• Cooperate while working out problems or while preparing themselves for the final exam.
• Formulate the findings from the analyses of empirical data using the terminology made available to them, to indicate the degree of uncertainty in the conclusions correctly.
• Are able to argue in a rational and controversial way in a scientific environment and include different points of view in their considerations.
• Internalize the use of standard learning and working techniques to learn on their own.