1990 POPULATION CENSUS Detailed data based on a 2 per cent representative sample (1992)

IV. SAMPLING ERROR OF THE ESTIMATES

IV. SAMPLING ERROR OF THE ESTIMATES The 2 per cent representative sample of the 1990 Census was based on a two-stage stratified design, thus the sampling error of the estimates cannot be determined by the well-known variance formula derived under the assumption of srs (simple random sampling). This is not a serious difficulty, since in the case of the given sample design (i.e. two-stage selection with stratification) sampling errors can be estimated by means of analytical expressions. In order to provide the Reader with proper information on the limits within which the data of this volume may be used somé sampling errors pertaining to data of different nature from tables of the previous chapters will be listed below. Data were selected for this purpose by the following aspects: — every main topic (demography, occupation, etc.) be represented by somé tables or variables and by the corresponding sampling errors; — data at the national level and those pertaining to different groups of the population should equally be considered. Combining these aspects with technical limits such as space considerations the following tables were selected for sampling error computations: Demography, educational attainment: 2.1.1, 2.1.2, 2.1.7 Occupation: 2.2.1, 2.2.4.1, 2.2.5.1, 2.2.6 Household, family: 2.3.1, 2.3.3, 2.3.6, 2.3.9, 2.3.11 Housing: 2.4.2, 2.4.4, 2.4.6 If sampling error had been calculated for each data occurring in these tables, the result would have been a data set still too large to be handled, therefore a second round of selections was made among the data themselves. The set of data remaining after this reduction is still large enough to represent the different effects on sampling errors, first of all those of the nature of the variable and the number of underlying observations; our list of sample estimates and their sampling errors would therefore enable the Reader to find a guess on the reliability of any data in this volume. The sampling error computations are based on the sample design described in the previous chapter, i.e. on two-stage stratified sampling. Two types of estimates occurred in the computations, namely, — estimated totals, and — ratio estimates obtained as ratios of two estimated totals such as the number of persons per 100 households. In what follows first the method of computing the variance of estimated totals will be described. As subsamples were drawn independently in the strata, the variance of an estimated totál is equal to the sum of variances of the subtotals pertaining to the strata. It is sufficient therefore to consider only the variance of somé subtotal in one of the strata. Introduce the following notations: M — the number of primary sampling units or PSU's (i.e. ED's) within the stratum in the population; m — the number of sample PSU's in the stratum (m ~ M/5); 241