Evaluation and analysis issues

Common Error 6: Low Statistical Power

Moderation tests are known to have lower statistical power than main effect analyses due to various factors (Aguinis et al., 2017; Carte & Russell, 2003; Dawson, 2014; Memon et al., 2019). While neglect of this issue has decreased from 43.41% (Aguinis et al., 2017) to approximately 15.33% in our review, low power remains a critical risk. Progress is likely due to larger samples and better handling of measurement issues.

To ensure adequate power, we strongly recommend: (1) conducting a priori power analysis (e.g., using G*Power) to determine necessary sample size (Faul et al., 2009; Sarstedt et al., 2023), and (2) always computing and reporting observed statistical power and the effect size f², regardless of significance. This allows assessment of whether non-significant results reflect a true null or inadequate power. The effect size f² is calculated as (R²₂ - R²₁) / (1 - R²₂), where R²₁ and R²₂ are from models without and with the interaction term, respectively. Conventional benchmarks are 0.02 (small), 0.15 (medium), and 0.35 (large) (Cohen, 1988), though context is key.

常见问题六：统计功效不足

调节检验的统计功效通常低于主效应分析，这是由变量间相关、测量误差、范围限制等多种因素导致的经典难题。虽然学术界对此问题的认识已显著提高（我们综述中忽视该问题的研究比例已降至约15.33%，相较于Aguinis等人2017年报告的43.41%有巨大进步），但功效不足的风险依然存在，可能导致真实的调节效应被遗漏（假阴性）。

问题实质：

检测调节效应就像在嘈杂环境中辨识一个微弱信号。如果“放大器”的功率（统计功效）不足，即使信号真实存在，你也可能听不见。

解决建议：

Ÿ  进行先验功效分析：在收集数据前，使用G*Power等工具，基于预期的效应大小（如小效应f²=0.02）计算所需的样本量，确保研究有足够的“探测能力”。

Ÿ  报告观测功效与效应量：无论结果是否显著，都应计算并报告实际观测到的统计功效及调节效应的效应量（如f²）。这能让读者判断一个不显著的结果，究竟是源于关系真的不存在，还是仅仅因为功效不足。f²的计算公式为：，其中R²₁和R²₂分别代表不含与包含交互项的模型R²。

Ÿ  扩大样本量是根本：在可行范围内，更大的样本量是提升功效最直接有效的方法（Memon等, 2019）。

Reference

• Aguinis, H., Edwards, J. R., & Bradley, K. J. (2017).      Improving our understanding of moderation and mediation in strategic      management research. Organizational Research Methods, 20(4),      665-685.

• 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: Results from a Monte Carlo simulation study and an      electronic-mail emotion/adoption study. Information Systems Research,      14(2), 189-217.

• Dawson, J. F. (2014). Moderation in management research: What,      why, when, and how. Journal of Business and Psychology, 29(1),      1-19.

• Memon, M. A., Cheah, J. H., Ramayah, T., Ting, H., Chuah, F.,      & Cham, T. H. (2019). Moderation analysis: Issues and guidelines. Journal      of Applied Structural Equation Modeling, 3(1), i-xi.

• 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.