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RegisterFieller’s (‘fiducial’) confidence interval [General Statistics]
posted by Helmut 
– Vienna, Austria, 2019-11-29 11:03 (1989 d 02:43 ago) – Posting: # 20894
Views: 4,547
Hi ElMaestro,
Nope. Hauschke et al.1 use $$H_0:\frac{\mu_T}{\mu_R}\leqslant\theta_1\,\textrm{or}\,\frac{\mu_T}{\mu_R}\geqslant\theta_2\;\textrm{versus}\;H_1:\theta_1<\frac{\mu_T}{\mu_R}<\theta_2\tag{3}$$and \((\theta_1,\theta_2)=(0.8,1.25)\) as well (see the figures and paragraphs below them).
It never hurts to read the primary document.2
❝ […] powerTOST's nomenclature seems to differ a bit (?) from Hauschke's in that it uses theta1 and theta2 where Hauscke would use f1 and f2. In powerTOST theta1 defaults to 0.8 when the limit for the ratio is actually 0.8*mu(R), or so I am reading it.
Nope. Hauschke et al.1 use $$H_0:\frac{\mu_T}{\mu_R}\leqslant\theta_1\,\textrm{or}\,\frac{\mu_T}{\mu_R}\geqslant\theta_2\;\textrm{versus}\;H_1:\theta_1<\frac{\mu_T}{\mu_R}<\theta_2\tag{3}$$and \((\theta_1,\theta_2)=(0.8,1.25)\) as well (see the figures and paragraphs below them).
❝ […] the important part of this post is how the CI for the ratio is actually derived.
It never hurts to read the primary document.2
- Hauschke D, Kieser M, Diletti E, Burke M. Sample size determination for proving equivalence based on the ratio of two means for normally distributed data. Stat Med. 1999;18(1):93–105. doi:10.1002/(SICI)1097-0258(19990115)18:1<93::AID-SIM992>3.0.CO;2-8.
- Fieller EC. Some Problems in Interval Estimation. J Royal Stat Soc B. 1954;16(2):175–85. JSTOR:2984043.
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Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz
The quality of responses received is directly proportional to the quality of the question asked. 🚮
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Complete thread:
- On CI calculation, untransformed metrics ElMaestro 2019-11-29 03:40
![[Mix]](https://static.bebac.at/img/mix.png "open in Mix view")
- Fieller’s (‘fiducial’) confidence intervalHelmut 2019-11-29 10:03
- Fieller’s (‘fiducial’) confidence interval ElMaestro 2019-11-29 15:53
- Fieller’s (‘fiducial’) confidence interval d_labes 2019-11-29 17:20
- Fieller’s (‘fiducial’) confidence interval ElMaestro 2019-11-30 05:11
- power.TOST with logscale=FALSE d_labes 2019-11-30 14:01
- Fieller’s (‘fiducial’) confidence interval ElMaestro 2019-11-30 05:11
- Fieller’s (‘fiducial’) confidence interval d_labes 2019-11-29 17:20
- Fieller’s (‘fiducial’) confidence interval ElMaestro 2019-11-29 15:53
- On CI calculation, untransformed metrics PharmCat 2019-11-29 12:05
- Fieller’s (‘fiducial’) confidence intervalHelmut 2019-11-29 10:03
Ing. Helmut Schütz