Estimates of Sampling Error
Sampling errors, on the other hand, can be evaluated statistically. The sample of respondents selected in the 2006-07 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 formulas for calculating sampling errors. However, the 2006-07 NDHS sample is the result of a multi-stage stratified design, and, consequently, it was necessary to use more complex formulae. The computer software used to calculate sampling errors for the 2006-07 NDHS is the 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.
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 the increase in the sampling error 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 2006-07 DHS are calculated for selected variables considered to be of primary interest for woman's survey and for man's surveys, respectively. The results are presented in an appendix of the Final Report for the country as a whole, for urban and rural areas, and for each of the eleven 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.17 present the value of the statistic (R), its standard error (SE), the number of unweighted (N-UNWE) and weighted (N-WEIG) 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 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 child-bearing.
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 4.390 and its standard error is 0.078. Therefore, to obtain the 95 percent confidence limits, one adds and subtracts twice the standard error to the sample estimate, i.e., 4.39 ± 2 × 0.078. 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 4.234 and 4.546.
Sampling errors are analyzed for two separate groups of estimates: (1) means and proportions, and (2) complex demographic rates. At the national level, mostly relative standard error values (SE/R) for the means and proportions are below 10 percent, however the highest relative standard error values are for indicators with very low values (i.e., less than 2 percent). So in general, the relative standard errors for most estimates for the country as a whole are small, except for indicators with very small values, i.e., for estimates which are rare in the population. For example, the relative standard error for the total fertility rate (TFR 0-3 years) is small (2.6 percent) since births are a fairly common event. However, for the mortality rates which are rarer events, the average relative standard error value is higher; for example, the relative standard error for the 0-4 year estimate of infant mortality is 7.1.
The relative standard error varies across sub-populations. For example, for the variable children ever born to women age 40-49, the relative standard errors as a percent of the estimated mean for the whole country, for the urban areas and for the rural areas are 1.8 percent, 3.1 percent and 2.0 percent, respectively.
For the total sample, the value of the design effect (DEFT), averaged over all selected variables, is 1.291 which means that, due to multi-stage clustering of the sample, the average standard error is increased by a factor of 1.291 over that in an equivalent simple random sample.