The effect of normality and outliers on bivariate correlation coefficients in psychology: A Monte Carlo simulation

This study aims to examine the effects of the underlying population distribution (normal, non-normal) and OLs on the magnitude of Pearson, Spearman and Pearson Winzorized cor- relation coefficients through Monte Carlo simulation. The study is conducted using Monte Carlo simulation method- ology, with sample sizes of 50, 100, 250, 250, 500 and 1000 observations. Each, underlying population correlations of 0.12, 0.20, 0.31 and 0.50 under conditions of bivariate Normality, bivariate Normality with Outliers (discordant, contaminants) and Non-normal with different values of skewness and kur- tosis. The results show that outliers have a greater effect com- pared to the data distributions; specifically, a substantial effect occurs in Pearson and a smaller one in Spearman and Pearson Winzorized. Additionally, the outliers are shown to have an impact on the assessment of bivariate normality using Mardia’s test and problems with decisions based on skewness and kurtosis for univariate normality. Implications of the results obtained are discussed Abstract Introduction The concept of normality Assumption of normality in psychology Outliers and their importance in correlations Method Generation of data Data analysis Results First stage of the analysis Second stage of the analysis Discussion Conclusions Funding Orcid References