Estimates of Sampling Error
The results from sample surveys are affected by two types of errors: (1) nonsampling error and (2) sampling error. Nonsampling error is due to mistakes made in carrying out field activities, such as failure to locate and interview the correct h0usehold, errors in the way questions are asked, misunderstanding of the questions on the part of either the interviewer or the respondent, data entry errors, etc. Although efforts were made during the design and implementation of the Sri Lanka Demographic and Health Survey to minimize this type of error, nonsampling errors are impossible to avoid entirely and difficult to evaluate statistically.
Sampling errors, on the other hand, can be evaluated statistically. The sample of women ~selected in the SLDHS is only one of many samples of the same size that could have been selected from the same population, using the same design. Each one of these samples would have yielded results somewhat different from the sample that was actually selected. The variability observed between all possible samples constitutes sampling error, which, although it is not known exactly, 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 of the statistic across all possible samples of equal size and design. The standard error can be used to calculate confidence intervals within which one can be reasonably sure 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 of identical size and design will fall within a range of plus or minus two times the standard error of that statistic.
If simple random sampling had been used to select women for the SLDHS, it would have been possible to use straightforward formulas for calculating sampling errors. However, the SLDHS sample design depended on stratification, stages, and clusters and 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 one indicates that the sample design is as efficient as a simple random sample and a value greater than one indicates the increase in the sampling error due to the use of a more c0mplex and less statistically efficient design.
Sampling errors are presented in Table A.1 of the survey Final Report for 32 variables considered to be of major interest. Results are presented for the whole country, for urban and rural areas, for three age groups, and for the seven zones. For each variable, the type of statistic (mean, proportion) and the base population (all women, currently married women) are given in Table A.1. For each variable, Table A.I presents the value of the statistic, R, its standard error, SE, the actual number of cases, N, the weighted number of cases, WN, the DEFT value, and the relative standard error, SE/R. In addition to these indicators, for the entire country ROH and the 95 percent confidence limits, R-2SD and R+2SD are presented. ROH is is a measure of homogeniety. A value of ROH closer to zero indicates more homogeniety in the cluster.
In general, the sampling errors for the country as a whole are small, which means that the SLDHS results are reliable. For example, for the variable children ever born, the overall average from the sample is 3.009 and its standard error is 0.030. Therefore, to obtain the 95 percent confidence limits~ one adds and subtracts twice the standard error to the sample estimate, i.e., 3.009 +-(2 * 0.030), which means that there is a high probability (95 percent) that the true average nnmher of children ever born for all Sri Lankan women falls within the interval of 2.949 to 3.069. This same type of calculation can be made for any other of the variables listed.