Di Plinio Simone
Department of Neuroscience Imaging and Clinical Sciences, "G. D'Annunzio" University of Chieti-Pescara, Chieti, Italy.
Front Psychol. 2022 May 26;13:860213. doi: 10.3389/fpsyg.2022.860213. eCollection 2022.
Correlation coefficients are often compared to investigate data across multiple research fields, as they allow investigators to determine different degrees of correlation to independent variables. Even with adequate sample size, such differences may be minor 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. The methods tested were Cohen's q, Fisher's method, linear mixed-effects models (LMEM), and an developed procedure that integrates bootstrap and effect size estimation. Correlation strengths and sample size was varied across a wide range of simulations to test the power of the methods to reject the null hypothesis (i.e., the two correlations are equal). Results showed that Fisher's method and the LMEM failed to reject the null hypothesis even in the presence of relevant differences between correlations and that Cohen's method was not sensitive to the data structure. Bootstrap followed by effect size estimation resulted in a fair, unbiased compromise for estimating quantitative differences between statistical associations and producing outputs that could be easily compared across studies. This unbiased method is easily implementable in MatLab through the bootes function, which was made available online by the author at MathWorks.
相关系数常被用于跨多个研究领域的数据比较，因为它们能让研究者确定与自变量的不同相关程度。即便样本量充足，这些差异可能很小，但仍具有科学相关性。迄今为止，尽管已投入大量精力开发估计相关系数差异的方法，但针对不同样本量和相关强度的适用工具仍有待检验。本研究评估了四种检测两个相关性之间差异的不同方法，并通过对多种数据结构进行模拟来测试每种方法的适用性。所测试的方法包括科恩q检验、费舍尔方法、线性混合效应模型（LMEM）以及一种将自助法和效应量估计相结合的改进程序。在广泛的模拟中改变相关强度和样本量，以测试这些方法拒绝零假设（即两个相关性相等）的能力。结果表明，即使相关性之间存在相关差异，费舍尔方法和线性混合效应模型也未能拒绝零假设，并且科恩方法对数据结构不敏感。先进行自助法再进行效应量估计，在估计统计关联之间的定量差异以及生成可在不同研究间轻松比较的结果方面，是一种合理、无偏的折衷方法。这种无偏方法通过作者在MathWorks网站上提供的bootes函数，在MatLab中很容易实现。
