Estimates of Sampling Error
The sample of women selected in the UDHS 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 UDHS 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 Tables in appendice of the Final Report for 35 variables considered to be of major interest. Results are presented for the whole country, for urban and rural areas, for women in three broad age groups, and for the six regions. For each variable, the type of statistic (mean, proportion) and the base population are given in Table B.1 of the Final Report. For each variable, Table presents the value of the statistic, its standard error, the number of unweighted and weighted cases, the design effect, the relative standard error, and the 95 percent confidence limits. The confidence interval has the following interpretation. For the mean number of children ever born (CEB), the overall average from the sample is 3.493 and its standard error is 0.049. Therefore, to obtain the 95 percent confidence limits, one adds and subtracts twice the standard error to the sample estimate, i.e., 3.493 + or - (2 x 0.049), which means that there is a high probability (95 percen0 that the true average number of children ever born falls within the interval of 3.395 to 3.592.
The relative standard error for most estimates for the country as a whole is small, except for estimates of very small proportions. The magnitude of the error increases as estimates for subpopulations such as particular age groups, and especially geographical areas, are considered. For the variable CEB, for example, the relative standard error (as a percentage of the estimated mean) for the whole country, rural areas, and Kampala is, respectively, 1.4 percent, 1.4 percent, and 7.1 percent. This means that the survey can provide estimates of CEB only with a margin of uncertainty (at the 95 percent confidence level) of +/- 2.8 percent, 2.8 percent, and 14.2 percent respectively for these three domains.