Population models and simulation methods: The case of the Spearman rank correlation

Area of Science:

• Statistics
• Social and Behavioral Sciences

Background:

• The Spearman rank correlation is a widely used non-parametric statistic.
• Misconceptions regarding its application persist in research due to a lack of population definition.
• A robust population model is needed for accurate simulation studies.

Purpose of the Study:

• To highlight the importance of a population model for Spearman rank correlation.
• To guide the design and interpretation of simulation studies.
• To address misconceptions in the published literature.

Main Methods:

• Utilizing copula distribution theory to present a population model for Spearman rank correlation.
• Exploring the model's properties theoretically and through simulation.
• Applying the Iman-Conover algorithm to specify the rank correlation as a population parameter.

Main Results:

• Simulation studies reveal that previous conclusions change when data generation matches the population parameter.
• Issues like small sample bias and lack of power in statistical tests diminish.
• The proposed copula model demonstrates flexibility and encompasses existing mathematical literature.

Conclusions:

• A population model is crucial for accurate Spearman rank correlation analysis and simulation.
• Clarifying the population definition resolves common statistical issues in simulation studies.
• The copula-based model offers a unified framework for understanding Spearman rank correlation properties.