Testing the Magnitude of Correlations Across Experimental Conditions

Abstract

Comparisons between correlation coefficients are used to investigate data across multiple research fields, as they allow investigators to determine different degrees of correlation to independent variables. Such differences may be small, even with adequate sample size, but still scientifically relevant. To date, although much effort has gone into developing methods for estimating differences across correlation coefficients, adequate tools for variable sample sizes and correlational strengths have yet to be tested. The present study evaluated four different methods for detecting the difference between two correlations and tested the adequacy of each method using simulations with multiple data structures. These methods were Cohen's q, Fisher's method, linear mixed-effects models (LMEM), and an ad-hoc developed procedure that integrates bootstrap effect size estimation. Results showed that Fisher's method and the LMEM tended to reject the null hypothesis even in the presence of relevant differences between correlations and that Cohen's method was not sensitive to data structure. Bootstrap followed by effect size estimation resulted in a favorable, unbiased compromise for estimating quantitative differences between statistical associations and producing outputs that could be easily compared across studies.

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