Statistical Experiment Design – Design of Experiment (DoE)

Establishment of research hypotheses

What is the population?

  • Scale levels: Nominal scale, Ordinal scale, Interval scale, Ratio scale
  • Development of experimental plans: screening plans (complete experimental plans, partial factor plans), response surface plans
  • Conception of surveys / questionnaires / tests
  • Specify sample size / number of subjects / number of groups & control groups
  • Conducting surveys / online surveys / experiments / experiments
  • Save test results
  • Documentation / logging of test results
  • Cleanup of data / incorrect data
  • Technical implementation of online surveys
  • Import / export of data
  • Convert data / various file formats
  • Recognize first trends with descriptive / descriptive stat.
  • Representation of data: histogram, boxplot, scatterplot, pie chart, Q-Q plot, etc.

Absolute and relative frequencies

Calculation of measures / position parameters: arithmetic mean, median, mode, sums of squares, standard errors, variance, empirical variance, span, quantiles, empirical covariance, correlation coefficient, etc.

  • Linear regression
  • cluster analysis
  • Data Analysis / Data Evaluation (Inductive Stat.)
  • Formulate research hypotheses as null hypotheses and alternative hypotheses
  • Set significance level
  • Choice of statistical test
  • Verification of distribution assumptions (eg, normal distribution assumption): chi2 fit test, Kolmogorov-Smirnow test, Shapiro-Wilk test, Anderson-Darling test, etc.
  • Confidence intervals / Confidence areas / Confidence intervals / Expected ranges
  • Decision rule: interpretation of test size / test statistic, critical value / p-value
  • Power analysis, test strength
  • Parametric hypothesis tests: t-test, z-test, F-test, chi2 homogeneity test, etc.
  • Nonparametric Hypothesis Tests: Wilcoxon Mann Whitney Test, Kruskal Wallis Test, Wilcoxon Sign Rank Test, Friedman Test, etc.
  • One-Factor Variance Analysis and Multi-Variance Analysis of Variance (ANOVA), Multivariate Analysis of Variance (MANOVA)
  • Correlation, partial correlation, pseudo-correlation, rank correlation, Pearson chi2 test
  • Linear Regression, Nonlinear Regression, Logistic Regression, Multiple Regression, Moderator Analysis, Mediator Analysis, Generalized Linear Models, Multi-Level Analysis, Path Analysis / Structural Equation Models
  • Factor analysis / main axis model / main component model, correspondence analysis
  • Time series analysis
  • Statistical Modeling
  • Basics / background knowledge about stochastics
  • Combinatorics, Bernoulli chains
  • Random variables, events, probabilities, conditional probabilities, z-values, tabulation of probabilities
  • Statistical independence and dependence
  • Discrete distributions: binomial distribution, uniform distribution, Poisson distribution
  • Continuous distributions: normal distribution, exponential distribution
  • Test distributions: distribution, distribution, F distribution

Law of large numbers and the meaning of the central limit theorem

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