|Authors:||Ronny Klæboe, Berit Grue|
An ad hoc two stage cluster sampling scheme used for the National Travel Survey in 1998 has not previously been documented. The sampling scheme consists of a simple random sample of households from a national telephone directory, whereafter the person over 13 years of age and that last celebrated their birthday is selected. The sampling fraction at the second stage is thus inversely proportional to cluster size causing simple sample means to be biased estimators for their respective population means. In this document it is shown that the size of these biases are substantial but that Ratio to size estimators can be used instead. In addition to the weighting for household size the datafile is however also weighted with county weights in order to take advantage of the improved precision provided by the inclusion of data from three regional samples. The complexity of the sampling scheme makes the use of a package like WesVar necessary assessing the precision of the resulting estimators by numerical means. The results provided by WesVar using replication methods are shown to be reasonable and close to those derived analytically under simplifying assumptions. Weighting the datafile with the number of persons over 13 years old in the household provides estimators that for all practical purposes are unbiased. The standard errors of the estimators are somewhat larger than that of a simple random sample of the same size. The incorporation of data from 3 regional travel surveys by means of a poststratification stage restores precision.