Survey ID Number
Demographic and Health Survey 1992, Zambia
Estimates of Sampling Error
Sampling errors, on the other hand, can be evaluated statistically. The sample of women selected in the ZDHS is only one of many samples that could have been selected from the same population, using the same design and expected size. Each of these samples would yield results that differ somewhat from the results of the actual sample selected. The sampling error is a measure of the variability between all possible samples. Although the degree of variability is not known exactly, it can be estimated from the survey results.
Sampling error is usually measured in terms of the standard error for a particular statistic (mean, percentage, etc.), which is the square root of the variance. The standard error can be used to calculate confidence intervals within which the true value for the population can reasonably be assumed to fall. For example, for any given statistic calculated from a sample survey, the value of that statistic will fall within a range of plus or minus two times the standard error of that statistic in 95 percent of all possible samples of identical size and design.
If the sample of women had been selected as a simple random sample, it would have been possible to use straightforward formulas for calculating sampling errors. However, the ZDHS sample is the result of a three-stage stratified design, and, consequently, it was necessary to use more complex formulas. The computer package CLUSTERS, developed by the International Statistical Institute for the World Fertility Survey, was used to compute the sampling errors with the proper statistical methodology.
In addition to the standard errors, CLUSTERS computes the design effect (DEFT) for each estimate, which is defined as the ratio between the standard error using the given sample design and the standard error that would result if a simple random sample had been used. A DEbT value of 1.0 indicates that the sample design is as efficient as a simple random sample, while a value greater than 1.0 indicates the increase in the sampling error due to the use of a more complex and less statistically efficient design. CLUSTERS also computes the relative error and confidence limits for the estimates.
Sampling errors for the ZDHS are calculated for selected variables considered to be of primary interest. The results are presented in an appendix to the Final Report for the country as a whole, for urban and rural areas, and for the nine provinces. For each variable, the type of statistic (mean or proportion) and the base population are given in Table B.1 of the Final Report. Tables B.2 to B. 13 present the value of the statistic (R), its standard error (SE), the number of unweighted (N) and weighted (WN) cases, the design effect (DEFT), the relative standard error (SE/R), and the 95 percent confidence limits (R-~SE), for each variable.
In general, the relative standard error for most estimates for the country as a whole is small, except for estimates of very small proportions. There are some differentials in the relative standard error for the estimates of sub-populations such as geographical areas. For example, for the variable EVBORN (children ever born to women aged 15-49), the relative standard error as a percent of the estimated mean for the whole country, for urban areas and for rural areas is 1.3 percent, 1.7 percent, and 1.9 percent, respectively.
The confidence interval (e.g., as calculated for EVBORN) can be interpreted as follows: the overall average from the national sample is 3.105 and its standard error is .040. Therefore, to obtain the 95 percent confidence limits, one adds and subtracts twice the standard error to the sample estimate, ie. %105+.080. There is a high probability (95 percent) that the true average number of children ever born to all women aged 15 to 49 is between 3.025 and 3.185.