Survey ID Number
Demographic and Health Survey 1988-1989, Kenya
Estimates of Sampling Error
The sample of women selected in the KDHS is only one of many samples that could have been selected from the same population, using the same design and expected size. Each one would have yielded results that differed somewhat from the actual sample selected. The sampling error is a measure of the variability between all possible samples; although it is not known exactly, it can be estimated from the survey results. Sampling error is usually measured in terms of the "standard error" of 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 one can be reasonably assured that, apart from non-sampling errors, the true value of the variable for the whole population falls. For example, for any given statistic calculated from a sample survey, the value of that same statistic as measured in 95 percent of all possible samples with the same design (and expected size) will fall within a range of plus or minus two times the standard error of that statistic.
If the sample of women had been selected as a simple random sample, it would have been possible to use strightforward formulas for calculating sampling errors. However, the KDHS sample design depended on stratification, stages, and clusters; consequently, it was necessary to utilize more complex formulas. The computer package CLUSTERS was used to assist in computing the sampling errors with the proper statistical methodology.
In addition to the standard errors, CLUSTERS 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; 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.
Sampling errors are presented in Table B.2 through B.4 in the Appendix to the Final Report for 45 variables considered to be of major interest. Results are presented for the whole country and for urban and rural areas. In Tables B.5 through B,11, results are presented by province for 30 variables. Finally, Table B.12 contains sampling errors for current contraceptive use for the 13 targctted districts. For each variable, the type of statistic (mean, proportion) and the base population are given in Table B.1. For each variable, Tables B.2 through B.12 present the value of the statistic, its standard error, the number of unwcighted and weighted cases, the design effect, the relative standard error, and the 95 percent confidence limits.
The confidence interval has the following interpretation. For current use of family planning (CURUSE), the overall proportion of married women using is 0.269 or 26.9 percent and its standard error is 0.010. Therefore, to obtain the 95 percent confidence limits, one adds and subtracts twice the standard error to the sample estimate, i.e., 0.269 + or -(2 x 0.010), which means that there is a high probability (95 percent) that the true contraceptive prevalence rate falls within the interval of 0.250 to 0.288 (25 to 29 percent).
The relative standard error for most estimates for the country as a whole is not large, except for estimates of very small proportions. The magnitude of the error increases as estimates for subpopulations such as particular provinces or districts are considered. For contraceptive prevalence, for example, the relative standard error (as a percentage of the cstimated proportion) for the whole country, urban areas, Nairobi and Kilifi District is, respectively, 3.6 percent, 6.2 percent, 7.6 percent, and 23.3 percent. By district, this means that the prevalence rate of 31.3 for Murang'a District cannot be said with certainty to differ from the rate of 20.2 for Kisii District, since the confidence intervals overlap. Similarly, the difference between the rates for Kirinyaga (52.2 percent) and Machakos Districts (40.4 percent) might be explained by sampling error.