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

posted by Helmut Homepage – Vienna, Austria, 2019-11-29 10:03 (426 d 03:07 ago) – Posting: # 20894
Views: 1,906

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
[image]

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

Complete thread:

Activity
 Admin contact
21,317 posts in 4,447 threads, 1,489 registered users;
online 13 (1 registered, 12 guests [including 4 identified bots]).
Forum time: Thursday 13:11 CET (Europe/Vienna)

Always listen to experts.
They’ll tell you what can’t be done and why.
Then do it.    Robert A. Heinlein

The Bioequivalence and Bioavailability Forum is hosted by
BEBAC Ing. Helmut Schütz
HTML5