Analysis of variance in R

The bachelor thesis focuses on the One-way ANOVA and its nonparametric counterpart the Kruskal-Wallis test. The aim of this bachelor thesis is to analyse the ANOVA's test validity and power in case of assumptions (e. g. normal distribution, homoscedasticity and sample size) violations. The conclusions of the One-way ANOVA are compared with the Kruskal-Wallis test. The analysis is performed using Monte Carlo simulations implemented in the statistical software R. Based on the simulations, it is found out that the One-Way ANOVA is not significantly sensitive to the violation of normality, if the homoscedasticity assumption is met within each of four samples. On the other hand it is found out that the One-Way ANOVA is significantly sensitive to the violation of homoscedasticity at the particular specification. The Kruskal-Wallis test yields in better results if the homoscedasticity assumption is violated. In case that the One-Way ANOVA and the Kruskal-Wallis test are valid, the ANOVA provides higher power of the test