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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