A gain-probability way to interpret correlation coefficients: A tutorial

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.