Estimating means and percentages in a complex sampling survey: application to a French national survey on sexual behaviour (ACSF). Analyse des Comportements Sexuels en France.

Two-phase stratification sampling with unequal selection probabilities is a relatively cost-efficient strategy to address problems on a nationwide basis and to perform comparative analyses of specific subgroups. This was the case with the ACSF survey. Specific procedures to estimate the variances of unbiased estimators in complex sampling designs are not included in standard statistical packages and no specialized software is available for two-phase sampling. A detailed synthesis of general basic rules for inference about a target population from a probability sample is first presented. We follow with a standard procedure to estimate means and percentages with their confidence intervals according to the design. Finally, numerical results are discussed.