## Exact (Owen’s Q) [Power / Sample Size]

Hi Imph,

❝ […] which formula to choose to calculate the number of subjects among all the formulas published: Dilleti, Chow, Julious,...

Diletti (1981), which is exact based on Owen’s Q function. Julious is based on an approximation by the noncentral t-distribution and fine as well.

❝ For now I am using chow's formula, I would like to know if there is a plausible reference that supports its use.

Don’t. Chow’s is based on the shifted central t-distribution and the paper contains typos. See also this post.

I suggest to estimate sample sizes with functions of the -package PowerTOST. All three methods are im­ple­ment­ed, where the exact one is the default.
Whilst in many cases sample sizes based on the shifted central t-distribution will be equal to the others, sometimes estimated sample sizes are larger than necessary. The background is shown in an article.

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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