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An upper bound for the relative bias of the design effect

Keywords: Variance of variances, Confidence interval, Coefficient of variation

Design effects are typically used to compute sample sizes or standard errors from complex surveys. In this paper, we show that the design effect estimator is biased and an upper bound to the ratio of the bias of the design effect estimator to the standard error is presented. A simulation study was conducted to assess the size of the bound for the relative bias with samples drawn from two artificially generated populations using stratified and two-stage cluster sampling.