Interpretation and reporting issues

Common Error 12: Lack of Attention of Moderation Effect Size

While ΔR² is the appropriate measure of moderation effect size (Chin et al., 2003; Hair et al., 2022), 71.53% of articles in our review either failed to report it or mistakenly relied solely on the interaction coefficient (b₃) (Becker et al., 2023; Rasoolimanesh et al., 2021). Statistical significance (b₃) and effect size (ΔR²) are distinct; they are equal only under perfect measurement (Carte & Russell, 2003). Relying solely on b₃ is misleading. Researchers must report ΔR² or f² to quantify the interaction term's unique explanatory power. The f² statistic is recommended as a complementary measure (Aiken et al., 1991). A ΔR² of ~0.02 is a common benchmark for a small effect (Cohen et al., 2014). A complete assessment requires integrating significance (b₃), effect size (ΔR²/f²), and simple slope plots.

调节分析:常见问题十二  忽视调节效应量的报告与解读

在多元调节回归中，ΔR²（模型解释方差的变化）是评估调节效应大小的恰当指标（Chin等, 2003）。然而，我们的综述发现高达71.53%的研究存在误区：要么完全不报告效应量，要么错误地仅以交互项的系数（b₃）大小来代表效应强弱（Becker等, 2023）。

问题实质：

b₃的显著性（p值）只能回答“调节效应是否存在”，而 ΔR²或f²才能回答“这个效应有多大” 。除非在完美的无测量误差且方差相等的理想情况下，否则b₃与ΔR²并不等价。仅依赖b₃会导致对调节变量实际重要性的误判：一个微小的b₃可能对应着可观的方差解释增量，而一个很大的b₃可能仅解释了因变量极小的变异。

解决建议：

1. 必须报告效应量：在报告交互项显著性的同时，必须计算并报告ΔR²或等效的f²统计量。Cohen（1988）的基准（f² ≥ 0.02为小效应）可作为参考，但需结合具体领域判断。

2. 多维综合评估：切勿依赖单一指标。应结合交互项显著性（b₃）、效应量（ΔR²/f²）以及简单斜率分析图进行综合解读，以获得对调节效应的全面、严谨的理解。

Reference

• Becker, J. M., Cheah, J. H., Gholamzade, R., Ringle, C. M.,      & Sarstedt, M. (2023). PLS-SEM's most wanted guidance. International      Journal of Contemporary Hospitality Management, 35(1), 321-346.

• Carte, T. A., & Russell, C. J. (2003). In pursuit of moderation: Nine common errors and their solutions. MIS Quarterly,      27(3), 479-501.

• Chin, W. W., Marcolin, B. L., & Newsted, P. R. (2003). A      partial least squares latent variable modeling approach for measuring interaction effects. Information Systems Research, 14(2), 189-217.

• Hair, J. F., Hult, G. T. M., Ringle, C. M., & Sarstedt, M.      (2022). A Primer on Partial Least Squares Structural Equation Modeling      (PLS-SEM) (3rd ed.). SAGE Publications.

• Rasoolimanesh, S. M., Wang, M., Mikulić, J., &      Kunasekaran, P. (2021). A critical review of moderation analysis in tourism and hospitality research toward robust guidelines. International      Journal of Contemporary Hospitality Management, 33(12), 4311-4333.

• Xu, Y., & Shiau, W. L. (2026). Moderation analysis in business and management research: Common issues, solutions, and guidelines for future research. International Journal of Information      Management, 86, 102995.