10 papers analyzed
These studies suggest that the Pearson correlation coefficient is suitable for light-tailed distributions and bivariate normal distributions, can be decomposed for detailed analysis, and has modern methods to improve accuracy, while alternative methods like Spearman's rank correlation and new coefficients like $phi_K$ are preferable for heavy-tailed distributions, outliers, and non-linear dependencies.
The Pearson correlation coefficient (r) is a widely used statistical measure that quantifies the linear relationship between two variables. It is commonly applied in various fields, including psychology, neuroscience, and biomedical research. This synthesis explores the key insights from multiple research papers on the Pearson correlation coefficient, its applications, limitations, and comparisons with other correlation measures.
Comparison with Spearman Correlation:
Applications in EEG Connectivity Analysis:
Extension to Nonlinear Relationships:
Robustness and Limitations:
New Correlation Coefficients:
Historical Context and Development:
Standard Error Calculation:
Decomposition of Pearson Correlation:
The Pearson correlation coefficient remains a fundamental tool for measuring linear relationships between variables. It is most effective for normally distributed data but has limitations in the presence of outliers and non-linear relationships. Extensions like the correlation curve and new coefficients like φK address some of these limitations. Additionally, the complex Pearson correlation coefficient offers valuable insights for EEG connectivity analysis. Understanding the robustness and proper calculation of standard errors is crucial for accurate application in research.
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