Where
is the mean in the total sample and
is the mean in the sub-group,
and
are their respective effective sample sizes, and
is the proportion of the total population in sub-group
:
,
where:
,
,
,
,
,
is the Standard Error of
,
is 1 if Bessel's correction is selected for Proportions in Statistical Assumptions and 0 otherwise,
and
are the estimated standard deviations for the total sample and sub-groups respectively,
and
are the estimated standard error of the means for the total sample and sub-groups respectively,
is Extra Deff, and
is the proportion of the Population represents by the sub-group.