Demographic and Health Survey 1999

Sampling errors, on the other hand, can be evaluated statistically. The sample of respondents selected in the 1999 KDHS 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 1999 KDHS 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 1999 KDHS 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.

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 clusters in the calculation of the estimates. Pseudo-independent replications are thus created. In the 1999 KDHS, there were 251 non-empty clusters. Hence, 251 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 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 1999 KDHS 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 six survey regions, and for three ethnic groups (Kazakh, Russian, and other ethnic groups).

The confidence interval (e.g., as calculated for children ever born to women age 15-49) can be interpreted as follows: the overall average from the national sample is 2.924 and its standard error is 0.079. Therefore, to obtain the 95 percent confidence limits, one adds and subtracts twice the standard error to the sample estimate, i.e., 2.924±2×0.079. There is a high probability (95 percent) that the true average number of children ever born to all women age 15 to 49 is between 2.765 and 3.082.

Sampling errors are analyzed for the national woman sample 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 32.3 percent with an average of 6.8 percent; the highest relative standard errors are for estimates of very low values (e.g., women currently using pills). If estimates of very low values (less than 10 percent) were removed, than the average would drop to 3.6 percent. So, in general, the relative standard errors for most estimates for the country as a whole are small, except for estimates of very small proportions. The relative standard error for the total fertility rate is small, 6.2 percent. However, for mortality rates, the average relative standard error is much higher, 18.3 percent.

There are differentials in the relative standard error for estimates of subpopulations. For example, for the variable children ever born to women over 40, the relative standard errors as a percent of the estimated mean for the whole country, for the urban areas, and for the South region are 2.7 percent, 5.0 percent, and 5.9 percent, respectively.

For the total sample, the value of the design effect (DEFT), averaged over all variables, is 1.21, which means that due to multistage clustering of the sample the average standard error is increased by a factor of 1.1 over that in an equivalent simple random sample.