Unequal Weighting and Design Effects
Unequal weights inflate variance estimates. This is expressed through unequal weighting effects and design effects.
Description
The base weight of a survey sample is the inverse of the selection probability. If all cases are selected from a single stratum in a SRS, this naturally leads to equal weights.
Often, some information (e.g., response propensity) or research objectives (e.g., propensity to be in population of interest) are used to allocate sample disproportionately across strata. This leads to differential selection probabilities, and ultimately unequal weights. Furthermore, information is incorporated into weight adjustments for measurable bias, or to post-stratify
The design effect is the ratio of the estimated variance for some estimate θ given a sample design over the variance that would have been achieved given a SRS. It can be interpreted as how much a sample design inflates variance for some measure.
Generally, design effects are greater than 1. It is possible to achieve an effect below 1 however. For example, sample could be allocated across strata such that the differential sampling probabilities perfectly counteracts differential response rates.
The unequal weighting effect is 1 plus the ratio of the average variance of weights over the squared average weight.
