Estimates of Sampling Error
The estimates from a sample survey are affected by two types of errors: (1) non-sampling error, and (2) sampling errors. Nonsampling errors are the results of mistakes made in implementing data collection and data processing, such as failure to locate and interview the correct household, misunderstanding of the questions on the part of either the interviewer or the respondent, and data entry errors. Although numerous efforts were made during the implementation of the 2008 BAIS III to minimise these type of errors, non-sampling errors are impossible to avoid and difficult to evaluate statistically.
Sampling errors, on the other hand, can be evaluated statistically. The sample of respondents selected in the 2008 BAIS III is only one of many samples that could have been selected from the same population, using the same sample 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 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.
The standard error can also be used to compute 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 indicates that the sample design is as efficient as simple random sample: a value greater than 1 indicates that increase in the sampling error is due to the use of more complex and less statistically efficient design.
If the sample of respondents had been selected as a simple random sample, it would have been possible to use straightforward formulae for calculating standard errors. However, the BFHS sample is the results of a stratified two stage design which is considered a complex design, hence special methods and softwares are required to take into account the complexity of the design.
WesVar 4.3 statistical software (supported by WESTAT) was used to obtain standard errors, confidence intervals and design effect for selected indicators. It is a powerful tool for statistical data analysis from complex survey designs which includes multi-stage, stratification and unequal probability samples. Jackknife replication method was applied which forms part of the replication options within this software. To estimate variances using the jackknife method requires forming replications from the full sample by randomly eliminating one sample cluster (enumeration area) from a domain or stratum at a time. Then a pseudo-estimate is formed from the retained EAs, which are re-weighted to compensate for the eliminated unit. Thus, for a particular stratum containing k clusters, k replicated estimates are formed by eliminating one of these, at a time, and increasing the weight of the remaining(k - 1) clusters by a factor of k /(k - 1). This process is repeated for each cluster.
Note: See detailed sampling error calculation which is presented in 2008 BAIS-III final report.
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