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

IV. SAMPLING ERROR OF THE ESTIMATES

2 and Sj» are aggregates, l.e. they pertain to somé geographical units consisting of several strata. (In the case of the data listed below they are actually aggregates at national level.) Note that the expectation of Z is close to 0, but this does not hold in generál for its coraponents Zj = Yj - RX^, Z

2 = ' "

x2> et

c- belonging to the strata. Standard error (or standard deviation) of the estimates is obtained both for totals and ratios as the positive square root of the variance, and the relative standard error or coefficient of variation (CV) is the ratio of the standard error to (the absolute value of the) estimite. By sampling error at the 95 per cent confidence level we mean 1.96 times the standard error; the relative sampling error is analogously defined in terms of the CV. The üst below contains both absolute and relative sampling errors of the data selected. The definition of absolute sampling error implies that the true value of ^ome data is covered with 95 per cent probability by the interval whose centre is the estimate and vrfiose length is twice the absolute standard error; thus e.g. in Table 2.1.1 the sampling error 7257 belonging to the estimate 327550 of the number of males aged 4549 enables us to state with 95 per cent confidence that the true number lies between the limits 320293 and 334807. Similar reasoning yields in the same Table that with 95 per cent confidence the true number of females aged 45-49 is between 335517 and 350183, hence at the given level of confidence the females outnumber the males significantly in the cohort of persons aged 45-49. Confidence limits implied by our results listed below indicate that somé data in this volume may be used only as information on the order of magnitude. Though — as was mentioned earlier — there is no functional relationship between sampling error and the number of observations in the case of the sample design used, the following rule of thumb may be recommended: data based on 50 or even less observations, i.e. totals not exceeding 2500 should be used with specific care. To check the efficiency of the sample the design effect was alsó computed in somé cases. This means that for somé data tíie sampling error was alsó calculated under the assumption that the estimate came from a simple random sample which is of the same size as the actual one. These computations showed that there was only a slight difference between the actual sampling errors (based on the actual sample design) and those coming from the assumption of a srs; e.g. the absolute sampling error of the estimated number of inactive earners and dependents per 100 active earners for all households in Table 2.3.1 equalled 1.1 in both cases. In the majority of cases, however, the two-stage stratified sampling actually in use resulted in slightly greater sampling errors than what would have been obtained from a simple random sample provided that both samples have the same number of units. 243