## Fieller’s (‘fiducial’) confidence interval [General Sta­tis­tics]

Hi ElMaestro,

» […] 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

1. 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.
2. Fieller EC. Some Problems in Interval Estimation. J Royal Stat Soc B. 1954;16(2):175–85. JSTOR:2984043.

Dif-tor heh smusma 🖖
Helmut Schütz

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