The ubiquitous regression to the mean (RTM) effect complicates statistical inference regarding the relationship between baseline levels of a biological variable and its subsequent change. We demonstrate that common RTM correction methods are problematic: the Berry et al. method, popularized by Kelly & Price in The American Naturalist, is unreliable for hypothesis testing or effect-size estimation, leading to systematic bias and inflated error rates. Conversely, while the Blomqvist method is theoretically unbiased, its high sampling variance limits its practical utility in small-to-moderate datasets. Using a structural linear model, we show that the most robust approach to navigating RTM is not to correct the data, but to evaluate the uncorrected crude slope against a structural null expectation derived from measurement repeatability-the proportion of total variance attributable to true individual differences. We illustrate this approach using empirical data from studies on lizard thermal physiology and bird telomere dynamics. Ultimately, we argue that any conclusion regarding a differential treatment effect is statistically unfounded without a clear understanding of the experiment's repeatability.

翻译：普遍存在的回归到均值（RTM）效应使得关于生物变量基线水平与其后续变化之间关系的统计推断变得复杂。我们证明常见的RTM校正方法存在问题：由Kelly与Price在《美国博物学家》中推广的Berry等人方法在假设检验或效应量估计方面不可靠，会导致系统性偏差和错误率膨胀。相反，虽然Blomqvist方法在理论上无偏，但其高抽样方差限制了其在小到中等规模数据集中的实际效用。通过使用结构线性模型，我们证明处理RTM最稳健的方法并非校正数据，而是根据测量重复性（即总变异中可归因于真实个体差异的比例）推导出的结构零期望来评估未校正的原始斜率。我们使用蜥蜴热生理学和鸟类端粒动态研究的实证数据阐述了这一方法。最终我们认为，若未清晰理解实验的重复性，任何关于差异处理效应的结论在统计学上都是缺乏依据的。