Estimates of Sampling Error
Sampling errors, on the other hand, can be evaluated statistically. The sample of respondents selected in the 2001 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 (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 respondents had been selected as a simple random sample, it would have been possible to use straightforward formulae for calculating sampling errors. However, the 2001 NDHS sample is the result of a multistage stratified design, and consequently, it was necessary to use more complex formulae. The computer software used to calculate sampling errors for the 2001 NDHS is the ISSA Sampling Error Module (ISSAS). 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 formulae. Each replication considers all but one cluster in the calculation of the estimates. Pseudo-independent replications are thus created. In the 2001 NDHS, there were 251 nonempty clusters (PSUs). Hence, 251 replications were created.
In addition to the standard error, ISSAS 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 the increase in the sampling error due to the use of a more complex and less statistically efficient design. ISSAS also computes the relative error and confidence limits for the estimates.
Sampling errors for the 2001 NDHS 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, for the three ecological zones (mountains, hills, and terai), and for each of the 13 subdomains in the country. 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.4 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±2SE) for each variable. The DEFT is considered undefined when the standard error considering simple random sample is zero (when the estimate is close to 0 or 1).
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 subpopulations. For example, for the variable “currently using any contraceptive method” for currently married women age 15-49, the relative standard errors as a percentage of the estimated mean for the whole country, for urban areas, and for rural areas are 2.8 percent, 3.2 percent, and 3.2 percent, respectively.
The confidence interval (e.g., as calculated for “currently using any contraceptive method” for currently married women age 15-49) can be interpreted as follows: the overall national sample proportion is 0.393 and its standard error is 0.011. Therefore, to obtain the 95 percent confidence limits, one adds and subtracts twice the standard error to the sample estimate, i.e. 0.393±2(0.011). There is a high probability (95 percent) that the true average proportion of contraceptive use for currently married women age 15-49 is between 0.371 and 0.415.