Table 1.

Summary of notation.

			Stage 1		Stage 2		Stages 1 and 2
Selected	Sub‐	True parameter	Sample	Variance of	Sample	Variance of	Naive	Sufficient	Unbiased
population	population	value	mean	sample mean	mean	sample mean	estimator	statistic	estimator
S	S	θ S	X	${\sigma }_X^2$	U	${\tau }_U^2$	D S,N	Z S	D S,U
	S c	${\theta }_{S^c}$	Y	${\sigma }_Y^2$	—	—	—	—	—
F	S	θ S	X	${\sigma }_X^2$	V	${\tau }_V^2$	$D_{S,N}^F$	$Z_S^F$	$D_{S,U}^F$
	S c	${\theta }_{S^c}$	Y	${\sigma }_Y^2$	W	${\tau }_W^2$	$D_{S^c,N}^F$	$Z_{S^c}$	$D_{S^c,U}^F$
	S + S c	θ F	Z	—	—	—	D F,N	—	D F,U