COMPARISON OF COEFFICIENTS AMONG POLY CHORIC CORRELATION, PEARSON CORRELATION AND RANK CORRELATION OF RANK DATA

[Objective] To compare polychoric correlation coefficients, Pearson correlation coefficients and Spearman correlation coefficients of two rank variables with continuous latent variables. [Methods] Two variables with size 10 000 were generated from bivariate normal distribution by SAS, and they were transformed into rank variables. The coefficients of Pearson correlation, Spearman correlation and polychoric correlation were calculated. [Results] The polychoric correlation coefficients were much closer to real coefficients than Pearson correlation coefficients and Spearman correlation coefficients if two rank variables had continuous latent variables. And if the absolute value of real coefficients was closer to 1, Pearson correlation and Spearman correlation coefficients had bigger deviation. [Conclusion] The polychoric correlation coefficients are not affected by rank, and Pearson correlation and Spearman correlation coefficients are affected by unequally-spaced rank.