Normrank Correlations for Testing Associations and for Use in Latent Variable Models

Abstract

Pearson’s correlation is widely used to test for an association between two variables and also forms the basis of several multivariate statistical procedures including many latent variable models. Spearman’s ρ\rho is a popular alternative. These procedures are compared with ranking the data and then applying the inverse normal transformation, or for short the normrank transformation. Using the normrank transformation was more powerful than Pearson’s and Spearman’s procedures when the distributions have less than normal kurtosis (platykurtic), when the distributions have greater than normal kurtosis (leptokurtic), and when the distribution is skewed. This is examined for testing if there is an association between two variables, identifying the number of factors in an exploratory factor analysis, identifying appropriate loadings in these analyses, and identifying relations among latent variables in structural equation models. R functions and their use are shown.

Keywords

• robust statistics
• latent variable models
• structural equation modelling
• statistical power