Bias and correction for the log response ratio in ecological meta‐analysis
Abstract
Ecologists widely use the log response ratio for summarizing the outcomes of studies for meta‐analysis. However, little is known about the sampling distribution of this effect size estimator. Here I show with a Monte Carlo simulation that the log response ratio is biased when quantifying the outcome of studies with small sample sizes, and can yield erroneous variance estimates when the scale of study parameters are near zero. Given these challenges, I derive and compare two new estimators that help correct this small‐sample bias, and update guidelines and diagnostics for assessing when the response ratio is appropriate for ecological meta‐analysis. These new bias‐corrected estimators retain much of the original utility of the response ratio and are aimed to improve the quality and reliability of inferences with effect sizes based on the log ratio of two means.
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The log response ratio is a reliable measure of ecological change only when its numerator and denominator refer to the same or equivalent observational units across time.
“The log response ratio is a reliable measure of ecological change only when its numerator and denominator refer to the same or equivalent observational units across time, ensuring that observed differences reflect real change rather than differences in sample composition (Hedges et al. 1999;Lajeunesse 2015).”
From Flawed analysis invalidates claim of a strong Yellowstone trophic cascade after wolf reintroduction: A comment on Ripple et al. (2025) (2025) · cites this paper as Lajeunesse 2015
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Distribution Theory for Glass's Estimator of Effect Size and Related Estimators
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The impact of hunting on tropical mammal and bird populations
Benítez-López, A., Alkemade, R., Schipper, A. M., Ingram, D. J., Verweij, P. A., Eikelboom, J. A. J., & Huijbregts, M. A. J. (2017) · Science · doi:10.1126/science.aaj1891 · Cited by 663 · see citing works
Wallace, B. C., Lajeunesse, M. J., Dietz, G., Dahabreh, I. J., Trikalinos, T. A., Schmid, C. H., & Gurevitch, J. (2017) · Methods in Ecology and Evolution · doi:10.1111/2041-210x.12708 · Cited by 421 · see citing works
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“Moreover, Lajeunesse (2015) derived estimators that correct for biases that arise when quantifying response ratios for studies with small sample sizes.”
BackgroundMacNulty, D. R., Cooper, D., Procko, M., & Clark-Wolf, T. J. (2025) · Global Ecology and Conservation · doi:10.1016/j.gecco.2025.e03899 · Cited by 1 · see citing works
“…measure of ecological change only when its numerator and denominator refer to the same or equivalent observational units across time, ensuring that observed differences reflect real change rather than differences in sample composition (Hedges et al., 1999; Lajeunesse, 2015; Engeman et al., 2017).”
MacNulty, D., Cooper, D., Procko, M., & Clark-Wolf, T. (2025) · doi:10.32942/x2qq0c
- Authors
- Lajeunesse, M. J.
- Affiliations
- University of South Florida (US)
- Corresponding author
- Lajeunesse, Marc J.
- ORCID
- Lajeunesse, Marc J.
- Venue
- Ecology
- Publisher
- Wiley
- Published
- 2015-08
- Volume
- 96
- Issue
- 8
- Pages
- 2056-2063
- ISSN
- 0012-9658 (ISSN-L)
- 1939-9170
- OpenAlex
- W1950153927
- Cited by
- 244
- References
- 4
- Citations by year
- 2026: 29 · 2025: 25 · 2024: 42 · 2023: 31 · 2022: 24 · 2021: 17 · 2020: 25 · 2019: 19 · 2018: 7 · 2017: 16 · 2016: 7
- FWCI
- 8.34
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Ecology (publishedVersion)
- PubMed (publishedVersion)
- Funders
- Division of Biological Infrastructure
- Topics
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Physical Sciences › Environmental Science › Nature and Landscape Conservation › Ecology and Vegetation Dynamics Studies
- Keywords
- log response ratio, small sample bias, bias correction, sampling distribution, variance estimation, Monte Carlo simulation
- MeSH terms
- Computer Simulation, Data Interpretation, Statistical, Models, Biological, Monte Carlo Method, Sampling Studies, Meta-Analysis as Topic, Linear Models, Ecosystem, Risk Assessment
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