A robust Spearman correlation coefficient permutation test

Area of Science:

• Statistics
• Statistical inference
• Hypothesis testing

Background:

• Standard tests for Spearman's rank correlation coefficient (ρ) assume bivariate normality.
• Commonly used tests for ρ are theoretically flawed and perform poorly when normality assumptions are violated or sample sizes are small.
• Deviations from bivariate normality can severely impact the type I error control of existing tests.

Purpose of the Study:

• To identify theoretical inaccuracies in standard Spearman's correlation coefficient tests.
• To develop a robust permutation test for hypothesis testing of Spearman's ρ.
• To demonstrate the asymptotic validity and practical performance of the proposed test.

Main Methods:

• Development of a robust permutation test using a studentized statistic.
• Asymptotic validity analysis of the proposed permutation test.
• Comprehensive simulation studies to evaluate performance under various conditions (e.g., small sample sizes, deviations from normality).

Main Results:

• The proposed permutation test demonstrates robust type I error control, even with small sample sizes.
• Simulation studies confirm the theoretical validity of the test in general settings.
• The test effectively addresses the limitations of standard Spearman's correlation tests.

Conclusions:

• The developed robust permutation test provides a reliable alternative for hypothesis testing of Spearman's rank correlation coefficient.
• This method ensures accurate statistical inference when bivariate normality assumptions are not met or sample sizes are limited.
• The test is applicable in real-world scenarios, offering improved statistical rigor.