Probability of bivariate superiority: A non-parametric common-language statistic for detecting bivariate...

Area of Science:

• Statistics
• Data Analysis

Background:

• Traditional bivariate correlation (r) relies on linearity and parametric assumptions.
• Existing methods struggle with non-normal data, limiting accurate bivariate relationship assessment.

Purpose of the Study:

• Introduce a new nonparametric statistical model, probability of bivariate superiority (PBS), for evaluating bivariate relationships.
• Develop an estimator (B_p) for PBS, extending previous work to directly estimate the probability of paired variable concordance above/below their respective means.
• Provide a robust alternative to correlation (r) that is less sensitive to parametric assumption violations.

Main Methods:

• Specified the copula underpinning the PBS model.
• Developed an algorithm for estimating PBS from sample data.
• Conducted a Monte Carlo simulation across 448 conditions to evaluate the B_p estimator's performance.

Main Results:

• The B_p estimator for PBS demonstrated robustness to violations of parametric assumptions.
• PBS analysis revealed significant effects where traditional correlation (r) did not, and vice versa.
• The B_p estimator provides a reliable method for assessing probability-of-superiority relationships in bivariate data.

Conclusions:

• The probability of bivariate superiority (PBS) model and its estimator B_p offer a valuable, robust tool for bivariate data analysis.
• PBS captures a different aspect of bivariate relationships than correlation (r), uncovering potentially overlooked effects.
• This new statistical procedure can be applied to future research and re-analysis of past studies to identify significant findings.