### Appendix D (Loss in Precision of Estimate Due to Weighting in Household Surveys)

While overall survey weights help decrease three different sources of bias (coverage, nonresponse, and sampling), the variability of the weights also can increase the sampling variance in household surveys. The following formula is a simple model to measure the loss in precision ($$L_{w}$$) due to weighting. It assumes that the weights and the variable of interest are not related: $$(L_{w}=\left [ \frac{\sum\limits_{i=1}^n w_{i}^{2}}{\left (\sum\limits_{i=1}^n w_{i} \right )^2} \right ](n)-1)$$.

• For example, if $$L_{w}$$ = .156, then the sampling variance of the estimate increased by 15.6% due to differential weighting.
• $$L_{w}$$ can also be calculated for subgroups.
• Note: This formula does not apply to surveys of institutions or business establishments where differential weighting can be efficient.
• This is only one method for measuring the variability of the weights.