Assessing the Accuracy of the Median in a Stratified Double Stage Cluster Sample by Means of a Nonparametric Confidence Interval: Application to the Swiss Salary Structure Survey

• Activity Number: 312
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 10:30 AM to 12:20 PM
• Sponsor: Section on Government Statistics*
• Author(s): Monique Graf*+
• Affiliation(s): Swiss Federal Statistical Office
• Keywords: stratified sampling ; median ; nonparametric estimation ; double stage cluster sampling ; coefficient of variation ; salary structure survey

Abstract

The median is a relevant location measure for skewed data, but although the construction of nonparametric confidence intervals based on the empirical distribution function is well established in general statistics, few applications exist for survey data. The Swiss salary structure survey is a biennial study constructed on a stratified double stage cluster sampling scheme. Different weighted medians (overall, by strata and some domains) are computed. In order to assess the accuracy of a median, each salary is replaced by a binary variable, which is 1 if the salary is less than the median. Variance calculation fully considering the structure of the sample and the extrapolation weights is done on the transformed data and a 95% confidence interval is computed. The images of the confidence bounds by the inverse weighted empirical distribution function define a nonparametric 95% confidence interval for the median. This interval is not based on an estimation of the standard error and is not necessarily symmetrical around the estimated median. A coefficient of variation is thus not readily available. We derive a synthetic coefficient of variation directly from the confidence interval.