[Variance estimation methods in samples from household surveys]

Knowledge of sampling errors is essential for correctly interpreting the results from household surveys and evaluating their sampling designs. The composition of household samples used in surveys gives rise to situations of complex estimation. In this light, the study was conducted with the aim of evaluating the performance of the variance estimators in surveys carried out among urban populations in Brazil.

The reference population was the sample drawn by the Fundação Sistema Estadual de Análise de Dados Estatísticos (SEADE - State Statistical Data Analysis System Foundation) for carrying out an employment and unemployment survey in the metropolitan region of São Paulo. Three techniques were used for estimating variance: Taylor linearization and Jackknife and BRR replication. Repeated samples were selected from the reference population, using stratified cluster sampling in two stages (census tracts and households). Three different designs were used and 2,000 samples were drawn within each design. To obtain an estimator ratio, the accuracy of the variance estimators was evaluated by means of the mean square error and the confidence interval coverage.

According to the mean square error, the three techniques provided similar accuracy. The bias ratios were approximately 0.10, for the smaller samples. The confidence interval coverage indicated that the confidence levels observed were lower than what was set (95%), and were around 90% for the smaller samples.

The variance estimators showed similar performance with regard to accuracy and confidence interval coverage. The bias was irrelevant in relation to the magnitude of the standard error. Although the real confidence levels were lower than the nominal levels for normal distribution, the changes did not prevent construction of interval estimates with reasonable confidence.