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Double arcsine transform not appropriate for meta‐analysis
Abstract
The variance‐stabilizing Freeman–Tukey double arcsine transform was originally proposed for inference on single proportions. Subsequently, its use has been suggested in the context of meta‐analysis of proportions. While some erratic behavior has been observed previously, here we point out and illustrate general issues of monotonicity and invertibility that make this transform unsuitable for meta‐analysis purposes.
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![FIGURE 1 Illustration of the double arcsine transform for varying sample sizes N . Effectively, proportions (or proportion estimates ) corresponding to different sample sizes are not mapped to a common scale; even the ranges of possible θ values are only partly overlapping. The dashed line shows the limiting ( ' single ' ) arcsine transform [Colour figure can be viewed at wileyonlinelibrary.com]](/paper-figures/08f9d3e965dd4b2897aff607d7ac32e8/double-arcsine-transform-not-appropriate-for-metaanalysis-figure-1.png)
![FIGURE 2 Illustration of the double arcsine transformation for the example data from Table 1 [Colour figure can be viewed at wileyonlinelibrary.com]](/paper-figures/e99653c85edf467699bad275aee82f07/double-arcsine-transform-not-appropriate-for-metaanalysis-figure-2.png)
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“which has been proved to generate more adequate results than the double arcsine transformation when dealing with varying sample sizes228,229”
From Prevalence and severity of mental health problems in early-career researchers: a systematic review and meta-analysis (2026) · cites this paper as [228]
In the citing paper
“Hence, prevalence rates were transformed prior to analysis, using the single (not double) arcsine transformation to stabilize the variance, which has been proved to generate more adequate results than the double arcsine transformation when dealing with varying sample sizes228,229:transformedES=ASIN(√ES),transformedvar=1/4n.”
From Prevalence and severity of mental health problems in early-career researchers: a systematic review and meta-analysis (2026) · cites this paper as [228]
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Research works printed but not linked: 14
- 10.1214/aoms/1177729756 · DOI
- 10.1016/j.spl.2009.04.010 · DOI
- 10.1002/jrsm.1348 · DOI · Paper page
- 10.1093/biomet/35.3‐4.246 · DOI · Paper page
- 10.2307/2983678 · DOI
- Eisenhart C, 1947, Selected Techniques of Statistical Analysis for Scientific and Industrial Research and Production Management Engineering, 395
- Freeman MF, 1949, Transformation Related to the Angular and the Square Root. Memorandum Report 24, Statistical Research Group
- 10.1093/biomet/43.1‐2.235 · DOI
- 10.1080/00031305.1978.10479283 · DOI
- 10.1002/hsr2.178 · DOI
- 10.1136/jech‐2013‐203104 · DOI · Paper page
- 10.1111/jebm.12445 · DOI
- 10.1097/EDE.0000000000001232 · DOI · Paper page
- 10.1007/s11606‐021‐07098‐5 · DOI
Cited by
Sorted by citations
Dreisoerner, A., Goetz, V., Frohnmayer, D., Tran, U. S., Voracek, M., & Nater, U. M. (2026) · Nature Human Behaviour · doi:10.1038/s41562-026-02505-5 · Cited by 2
Metadata
- Authors
- Röver, C., & Friede, T.
- Venue
- Research Synthesis Methods
- Publisher
- Wiley
- Published
- 2022-07-22
- Volume
- 13
- Issue
- 5
- Pages
- 645-648
- ISSN
- 1759-2879
- 1759-2887
- Cited by
- 31
- References
- 0
- Language
- en
- Funders
- Deutsche Forschungsgemeinschaft (FR 3070/3‐1)
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- Röver, C., & Friede, T. (2022). Double arcsine transform not appropriate for meta‐analysis. Research Synthesis Methods. https://doi.org/10.1002/jrsm.1591
