Application of measures of dependence between quantitative variables

This bachelor thesis focuses on a simulation study and applied analysis using measures of dependence, with an emphasis on examining the impact of assumption violations on the results of the analysis. The simulation study included seven scenarios: linear dependence, nonlinear dependence, outliers, heteroskedasticity, monotonic dependence, nonlinear non-monotonic dependence, and white noise. The results indicated that nonparametric measures such as Spearman’s ρs and Kendall’s τb are more robust to nonlinearity and outliers than Pearson’s ρ. When applied to the real datasets, we have found that heteroscedasticity does not significantly affect correlation results; it can also be addressed effectively using standard nonparametric measures of dependence. Modern measures of dependence are, on the other hand, more suitable for complex patterns or in situations, where information about the direction of the relationship is not required.