When correcting for regression to the mean is worse than no correction at all
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| Format: | Preprint |
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2025
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| _version_ | 1866912997081874432 |
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| author | Fontanari, José F. Santos, Mauro |
| author_facet | Fontanari, José F. Santos, Mauro |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_04718 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | When correcting for regression to the mean is worse than no correction at all Fontanari, José F. Santos, Mauro Methodology Data Analysis, Statistics and Probability Quantitative Methods 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. |
| title | When correcting for regression to the mean is worse than no correction at all |
| topic | Methodology Data Analysis, Statistics and Probability Quantitative Methods |
| url | https://arxiv.org/abs/2509.04718 |