Syllabus
The course will cover following topics:• Statistical decision making: Formulation of null and alternative hypotheses. 1st /2nd -type errors, the significance level, p-level of the test.• One-sample tests: Parametric tests of mean value, esp. in normal and binomial distribution. Nonparametric tests.• Two-sample tests: Two-sample t-test, two-sample nonparametrictests.
Prerequisites for using parametric tests and verification of the assumptions.• Paired tests: Paired t-test, nonparametric paired tests.• Multiple samples: Analysis of variance (on-way, multiple-way). Inter-actions.
Kruskal-Wallis test.• Distribution difference testing: Kolmogorov-Smirnov test. Testingnormality - Shapiro-Wilk test, d’Agostino and Anscombe test.• Testing of homogeneity of variances : Fisher's and Levene's test.• Continuous variables dependency testing:- Correlation and its testing.
Coherence of several characters - partial coefficientcorrelation.- regression models: Regression linear model. Parameter estimates.
Coefficientof determination. Connection with ANOVA.
Generalization of the linear model:quadratic and multidimensional regression. analysis of residuals.• Testing the dependence of nominal variables: - contingency tables (independence, homogeneity of samples, symmetry, residues, graphical representation). Measures of association.
Use of χ 2 statistics to verify the fit of the distribution.• Testing the dependence of ordinal quantities: Spearman's test, Kendall'sτ and derived measures.
Annotation
Based on the prequel course Statistics I, this course will introduce basic methods of testing the statistical hypotheses.
The key take-away is ability to select the right method for given problem as well as the skill in interpretation of the results.
Repetitive enrollment is allowed.