Overview of basic concepts

Descriptive and mathematical (inductive) statistics. The most common statistical parameters. Normal distribution and the central limit theorem. T-, Chi-squared- and F-distributions. Sampling and statistical independence, correlation.

Basic tests, confidence intervals

The z-test and various types of t-test, the F-test for equality of variances. One- and two-sided tests, ANOVA for one and more factors. Decomposition of variability using different types of sums of squares. Confidence intervals and their relation to hypothesis tests.

Regression models

Their purpose and ways to use them. Linear regression and logistic regression. Multivariate models. Survival analysis, Cox models.

Tests for categorical (qualitative) variables

Chi-squared test of independence (Pearson‘s chi-squared test). Dummy coding for linear and logistic regression.

Pairing

Paired tests, randomization, (randomized) blocking.

Nonparametric methods

The usage of nonparametric methods. Permutation tests, Fisher‘s exact test, the rank-sum test (Mann-Whitney U-test), Wilcoxon‘s test, the Kruskal-Wallis test and the Friedland test.

Classification tasks

Clustering, (linear) discriminant analysis.

Planning of experiments

Design of Experiments (DoE), factorial designs, PCA, statistical power.

Processing of results

Verifying the assumptions, exclusion of outliers, missing values, meta-analysis.