analyses:miller1978
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analyses:miller1978 [2021/12/20 15:38] – Wolfgang Viechtbauer | analyses:miller1978 [2022/08/03 11:19] (current) – Wolfgang Viechtbauer | ||
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The '' | The '' | ||
- | Note that one can find two different definitions of the Freeman-Tukey transformation in the literature that differ only by the multiplicative constant $1/2$. The '' | + | **Note:** One can find two different definitions of the Freeman-Tukey transformation in the literature that differ only by the multiplicative constant $1/2$. The '' |
==== Back-Transformation of Individual Values ==== | ==== Back-Transformation of Individual Values ==== | ||
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Model Results: | Model Results: | ||
- | estimate | + | estimate |
- | 0.6131 | + | 0.6131 |
--- | --- | ||
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Now '' | Now '' | ||
<code output> | <code output> | ||
- | xi ni pi | + | xi ni pi |
- | 1 0 10 0.0 0.0000 0.0000 0.1652 | + | 1 0 10 0.0 0.0000 0.0000 0.1652 |
- | 2 4 10 0.4 0.4000 0.1131 0.7238 | + | 2 4 10 0.4 0.4000 0.1131 0.7238 |
- | 3 9 15 0.6 0.6000 0.3382 0.8371 | + | 3 9 15 0.6 0.6000 0.3382 0.8371 |
- | 4 16 20 0.8 0.8000 0.5921 0.9513 | + | 4 16 20 0.8 0.8000 0.5921 0.9513 |
5 20 20 1.0 1.0000 0.9157 1.0000 | 5 20 20 1.0 1.0000 0.9157 1.0000 | ||
</ | </ | ||
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<code rsplus> | <code rsplus> | ||
forest(dat.back$yi, | forest(dat.back$yi, | ||
- | | + | |
| | ||
addpoly(pred$pred, | addpoly(pred$pred, | ||
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{{ analyses: | {{ analyses: | ||
Now the estimated average and the results from the individual studies are correctly back-transformed. | Now the estimated average and the results from the individual studies are correctly back-transformed. | ||
+ | |||
+ | ==== Note of Caution ==== | ||
+ | |||
+ | It turns out that there are some concerns with bias when back-transforming a pooled Freeman-Tukey (double arcsine) transformed proportion using the back-transformation suggested by Miller (1978) that uses the harmonic mean of the sample sizes in the back-transformation. For details, see Schwarzer et al. (2019). Alternatively, | ||
==== References ==== | ==== References ==== | ||
- | Freeman, M. F., & Tukey, J. W. (1950). Transformations related to the angular and the square root. //Annals of Mathematical Statistics, 21//(4), 607--611. | + | Freeman, M. F., & Tukey, J. W. (1950). Transformations related to the angular and the square root. //Annals of Mathematical Statistics, 21//(4), 607--611. |
+ | |||
+ | Miller, J. J. (1978). The inverse of the Freeman-Tukey double arcsine transformation. //American Statistician, | ||
- | Miller, J. J. (1978). The inverse of the Freeman-Tukey double arcsine transformation. //American Statistician, 32//(4), 138. | + | Schwarzer, G., Chemaitelly, |
analyses/miller1978.txt · Last modified: 2022/08/03 11:19 by Wolfgang Viechtbauer