Modified Signed Log-Likelihood Ratio Test for Comparing the Correlation Coefficients of Two Independent Bivariate Normal Distributions

TL;DR

This paper introduces a modified signed log-likelihood ratio test for comparing correlation coefficients between two independent bivariate normal distributions, showing improved performance over existing methods especially with unequal sample sizes.

Contribution

The paper proposes a new modified signed log-likelihood ratio test for correlation comparison, demonstrating its superiority through simulations and real data application.

Findings

Proposed method outperforms Fisher's Z-transform and generalized test variable.

Better size and power properties, especially with unequal sample sizes.

Validated with real data analysis.

Abstract

In this paper, we use the method of modified signed log-likelihood ratio test for the problem of testing the equality of correlation coefficients in two independent bivariate normal distributions. We compare this method with two other %competing approaches, Fisher's Z-transform and generalized test variable, using a Monte Carlo simulation. It indicates that the proposed method is better than the other approaches, in terms of the actual sizes and powers especially when the sample sizes are unequal. We illustrate performance of the proposed approach, using a real data set.