Table 1.

Internal pilot study notation for testing H₀ : θ = Cβ = θ₀

	Symbol	Definition
Design parameters	α t	Target Type I error rate
	Pt	Target power
	θ *	‘Scientifically important’ value of θ
	${\sigma }_0^2$	Variance value used for planning
	n 0	Planned sample size for αt, Pt, θ*, ${\sigma }_0^2$
Sample size allocation	π	Proportion of n0 used in internal pilot
	n1 = πn0	Internal pilot sample size
	n 1 +,min	Minimum size of final sample
	n +,max	Maximum size of final sample
Unknown parameters	σ 2	True variance
	$\gamma ={\sigma }^2∕{\sigma }_0^2$	Ratio of true to initial variance value
	θ	True value of secondary parameter