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Correlation and Causation

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Statistical tests can calculate whether there is a relationship, or correlation, between independent and dependent variables. An indirect relationship of the variables signifies a correlation, while a direct relationship shows causation. If it is determined that no connection exists between the variables, then the correlation is a coincidence.
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In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is mathematically expressed by the correlation coefficient, which describes the strength and direction of the relationship between two variables. The coefficient is symbolically represented by 'r' and ranges from -1 to +1. A positive value indicates a positive correlation where the two variables move in the same direction. A negative value suggests a...
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In statistics, two variables are said to be correlated if the values of one variable are associated with the other variable. Depending on the relationship between two variables, correlation can be of three types– positive correlation, negative correlation, and zero correlation.
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Dimensional analysis simplifies complex physical problems and guides experimental investigations, but it does not provide complete solutions. It identifies the dimensionless groups that influence a phenomenon, but experimental data is needed to establish the specific relationships and validate theoretical predictions.
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The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.
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Introduction to correlation networks: Interdisciplinary approaches beyond thresholding.

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Constructing correlation networks from data is complex. This review explores diverse methods beyond simple thresholding, offering best practices for analyzing these networks across scientific fields.

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Area of Science:

  • Interdisciplinary Network Science
  • Statistical Modeling
  • Data Analysis

Background:

  • Empirical networks frequently derive from correlational data across diverse fields like psychology, neuroscience, and finance.
  • Specialized network analysis methods exist in various domains, but cross-disciplinary communication is limited.
  • Transforming correlation matrices into networks presents challenges, with thresholding being common but problematic.

Purpose of the Study:

  • To review and compare various methods for constructing and analyzing correlation networks.
  • To highlight limitations of common methods like thresholding.
  • To propose best practices and identify open questions in correlation network analysis.

Main Methods:

  • Review of existing literature on correlation network construction and analysis.
  • Discussion of methods including thresholding, weighted networks, regularization, dynamic networks, and threshold-free approaches.
  • Comparison with null models and consideration of unweighted vs. weighted networks.

Main Results:

  • Thresholding correlation matrices can lead to suboptimal network representations.
  • A variety of advanced techniques exist, offering improvements over basic thresholding.
  • No single method is universally superior; the choice depends on the specific application.

Conclusions:

  • Cross-disciplinary insights are crucial for advancing correlation network analysis.
  • Recommended practices and open research questions are proposed for the field.
  • Further research is needed to optimize network construction from correlational data.