National Demographic and Health Survey 2003

Sampling errors, on the other hand, can be evaluated statistically. The sample of respondents se­lected in the 2003 NDHS 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. Sampling errors are 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.

A sampling error is usually measured in terms of the standard error for a particular statistic (e.g., mean, percentage), 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 respondents had been selected as a simple random sample, it would have been possible to use straightforward formulas for calculating sampling errors. However, the 2003 NDHS sam­ple is the result of a multistage stratified design, and consequently, it was necessary to use more complex formulas. The computer software used to calculate sampling errors for the 2003 NDHS is the Integrated System for Survey Analysis (ISSA) Sampling Error Module. This module used the Taylor linearization method of variance estimation for survey estimates that are means or proportions. The Jackknife repeated replication method is used for variance estimation of more complex statistics, such as fertility and mortal­ity rates.

The Jackknife repeated replication method derives estimates of complex rates from each of sev­eral replications of the parent sample and calculates standard errors for these estimates using simple for­mulas. Each replication considers all but one cluster in the calculation of the estimates. Pseudo-independent replications are thus created. In the 2003 NDHS, there were 819 non-empty clusters; hence, 818 replications were created.

In addition to the standard error, ISSA 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 DEFT 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 that the increase in the sampling errors is due to the use of a more complex and less statistically efficient design. ISSA also computes the relative error and confidence limits for the estimates.

Sampling errors for the 2003 NDHS were calculated for selected variables considered to be of primary interest for the women's survey and for the men's survey. The results are presented in an ap­pendix to the Final Report for the country as a whole, for urban and rural areas, and for each of the 17 regions. For each vari­able, the type of statistic (mean, proportion, or rate) and the base population are given in Table B.1 of the Final Report. Ta­bles B.2 to B.21 present the value of the statistic (R), its standard error (SE), the number of unweighted cases (N) and weighted cases (WN), the design effect (DEFT), the relative standard error (SE/R), and the 95 percent confidence limits (R±2SE) for each variable. The DEFT is considered undefined when the standard error considering the simple random sample is zero (when the estimate is close to 0 or 1). In the case of the total fertility rate, the number of unweighted cases is not relevant, as there is no known un­weighted value for woman-years of exposure to childbearing.

The confidence interval (e.g., as calculated for children ever born to women age 40-49) can be in­terpreted as follows: the overall average from the national sample is 4.321, and its standard error is 0.065. Therefore, to obtain the 95 percent confidence limits, one adds and subtracts twice the standard error to the sample estimate (i.e., 4.32 ± 2 × 0.065). There is a high probability (95 percent) that the true average number of children ever born to all women age 40 to 49 is between 4.192 and 4.451.

Sampling errors were analyzed for the national sample of women and for two separate groups of estimates: 1) means and proportions and 2) complex demographic rates. The relative standard errors (SE/R) for the means and proportions range between 0.1 and 29.1 percent, with an average of 3.27 per­cent; the highest relative standard errors are for estimates of very low values (e.g., currently using male sterilization). If estimates of very low values (less than 10 percent) are removed, then the average drops to
1.81 percent. So in general, the relative standard error for most estimates for the country as a whole is small, except for estimates of very small proportions. The relative standard error for the total fertility rate is small (1.9 percent). However, for the mortality rates, the average relative standard error is much higher
(8.95 percent).

There are differentials in the relative standard error for the estimates of subpopulations. For ex­ample, for the variable “want no more children,” the relative standard errors as a percent of the estimated mean for the whole country and for the urban areas are 0.9 and 1.4 percent, respectively.

For the total sample, the value of the DEFT, averaged over all variables, is 1.167, which means that, because of multistage clustering of the sample, the average standard error is increased by a factor of
1.167 over that in an equivalent simple random sample.