Correlation Analysis

This chapter discusses different approaches to correlation. Beginning with the most common Pearson's correlation, we discuss various assumptions that the data are required to meet for undertaking Pearson's correlation. We also discuss the approach to test these assumptions, followed by the procedure to undertake Pearson's correlation. We then explain the concept of partial correlation when there are other (control) variables influencing the relationship between the variables of our interest. We, then, explain Spearman's rho and Kendall's tau approaches to undertake correlation, when the bivariate normality assumption is violated. This is followed by polychoric correlation, which is used when the data are measured on Likert-type scales and are likely to have several ties when ranking them. The procedure for Cramer's V is then discussed for nominal scale variables with polytomous responses and with underlying continuity. We then explain the biserial and point biserial correlations for one of the variables is dichotomous, with and without underlying continuity respectively, whereas the other is measured on interval/ratio. We end the chapter with a discussion on phi coefficient for both the variables measured on nominal scale, with or without continuity.