# variance of proportion

#### bhdn

##### New Member
I am taking a stratified sampling approach to estimating the proportion of the estimated total items of interest in a population that are in a subset of the population (a subset of the strata). My question is how to calculate the variance for that proportion.

For example, suppose I have a population partitioned into 8 strata (say, A - H), and I am interested in the proportion of the full population's total items of interest that are contained in 4 strata (say, A - D).

It is easy enough to get an estimate and variance for the denominator of the proportion (using conventional estimation procedures on all 8 strata); it is also easy enough to get an estimate and variance for the numerator of the proportion (using conventional estimation procedures on the 4 strata A - D).

My question is how to calculate the variance of the resulting proportion estimator. One might think about using Gaussian Error Propagation, but that requires the assumption that numerator and denominator of the proportion are independent when, in the case under consideration, the numerator estimate is derived from a subset of the strata that are the basis for the derivation of the denominator estimate.

Any thoughts would be appreciated. Thank you.

#### Xenu

##### New Member
It is easy enough to get an estimate and variance for the denominator of the proportion (using conventional estimation procedures on all 8 strata); it is also easy enough to get an estimate and variance for the numerator of the proportion (using conventional estimation procedures on the 4 strata A - D).
Missed this question so my answer is probably too late. Anyways, can you estimate the covariance between the denominator and the numerator? If so, taylor approximation of the variance could be used.