Type-M robust measures of correlation

Correlation analysis determine the degree and direction of the relationship between two variables. The well known correlation is Pearson's correlation. But it is not robust when normality and homoscedasticity assumptions are violated. Therefore, robust methods are improved to minimize effect of violation of assumptions. Robust measures of correlations are classified into two types. First type protects against outliers among the marginal distributions without taking into account the overall structure of the data (Type-M) and second type that take into account the overall structure of the data when dealing with outliers (Type-O). In this study, five Type-M robust correlations (percentage bend correlation, Winsorized correlation, biweight midcorrelation, Kendall's Tau and Spearman's rho) are analyzed and compared when they are used with a heteroscedastic test procedure in terms of actual significance level. The percentage bend, Kendall's tau and Spearman's rho correlations saved nominal significance level much better Winsorized and Biweight correlations with using percentile bootstrap method according to simulation study