Estimates of Sampling Error
Sampling errors, on the other hand, can be evaluated statistically. The sample of respondents selected in the 1998 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 1998 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 1998 Kenya Demographic and Health Survey (KDHS) is the ISSA Sampling Error Module. This module uses 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 1998 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, and for the seven surveyed provinces. For each variable, the type of statistic (mean, proportion, or rate) and the base population are given in Table B.1 of the appendix in the Final Report. Tables B.2 to B.11 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 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 aged 15-49) can be interpreted as follows: the overall average from the national sample is 2.895 and its standard error is 0.034. Therefore, to obtain the 95 percent confidence limits, one adds and subtracts twice the standard error to the sample estimate, i.e., 2.895±2×0.034. 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 2.827 and 2.962. (The confidence interval should not be interpreted to mean that all values between 2.827 and 2.962 are equally likely to be the true value. Indeed, based on the assumption that the sample design is unbiased, the estimated value of 2.895 is the best estimate (most likely single value) of the average number of children ever born that can be inferred from the KDHS data.)
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 0.2 percent and 22.5 percent with an average of 4.2 percent. The highest relative standard errors are for estimates of very low values (e.g., Women currently using contraceptive implants, or Norplant). If estimates of very low values (less than 1 percent) were removed, than the average would drop to 2.4 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 (i.e. rare occurences). The relative standard error for the total fertility rate is small, 2.3 percent. However, for the childhood mortality rates, the average relative standard error is much higher, 5.5 to 8.0 percent.
There are differentials in subnational estimates of the relative standard error. For example, for the variable With Secondary Education or higher, the relative standard errors (i.e., as a percentage of the estimated proportion) for the whole country, for the urban areas, and for the Coast region are 3 percent, 3.9 percent, and 10.4 percent, respectively.
For the total sample, the value of the design effect (DEFT), averaged over all variables, is 1.26. This which means that, due to the sample design which involves multi-stage clustering, the average standard error is increased by 26 percent over that in an equivalent simple random sample.