A dependence measure flow tree through Monte Carlo simulations,

In applied psychological, behavioral and sociological research the majority of data are typically mixed (continuous and discrete) or, if continuous, they violate the normality condition. Given a dependent and an independent variables: (a) both the variables may appear with distinct values (continuous variables); (b) the dependent variable may present distinct values (continuous variable) and the independent variable tied values (discrete variable); (c) the dependent variable may present tied values (discrete variable) and the independ- ent variable distinct values (continuous variable). The dependence relationship between the variables could be assessed through the common correlation coefficients, i.e., the Pearson’s, Spearman’s and Kendall’s coefficients, jointly with a recently revisited monotonic dependence coefficient, called “Monotonic Dependence Coefficient”. But, the choice of the most suitable dependence measure in different scenarios may become problematic. The aim of the paper is to show which dependence measure to use to discover dependence rela- tionships. A flow tree displaying how to find the best dependence measures is proposed by means of a Monte Carlo simulation study. Both Normal and non-Normal distributions pro- ducing continuous and discrete data, together with the possibility of transforming discrete data into continuous ones, are considered. Finally, validation of simulation findings on real data is also introduced.