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This study introduces a novel method for interpreting correlation coefficients, avoiding data loss from dichotomizing variables. The new approach estimates probabilistic advantages and disadvantages, enhancing theoretical specificity.

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Area of Science:

  • Psychology
  • Statistics

Background:

  • Interpreting correlation coefficients is complex, with existing methods like coefficient of determination and binomial effect size displays having limitations.
  • Coefficient of determination (r²) quantifies variance explained but can be misinterpreted.
  • Binomial effect size displays (BESD) require dichotomizing continuous variables, leading to information loss.

Purpose of the Study:

  • To present a novel, tutorial-based procedure for interpreting correlation coefficients.
  • To estimate probabilistic advantages and disadvantages implied by correlation coefficients.
  • To introduce gain-probability diagrams as a new interpretive tool.

Main Methods:

  • The proposed method estimates probabilistic (dis)advantages of correlation coefficients.
  • It involves constructing gain-probability diagrams.
  • Crucially, it avoids dichotomizing continuous dependent variables, preserving information.

Main Results:

  • The new procedure offers a third interpretive method for correlation coefficients.
  • It does not involve dichotomizing continuous variables, thus preventing information loss.
  • The method facilitates nuanced comparisons of correlation coefficients, enhancing theoretical specificity.

Conclusions:

  • A new, information-preserving method for interpreting correlation coefficients is presented.
  • This approach enhances theoretical specificity by allowing for subtle comparisons.
  • The gain-probability diagrams offer a valuable tool for understanding probabilistic implications of correlations.