Survey ID Number
Malaria Indicator Survey 2012
SAMPLING FRAME AND STRATIFICATION
Malawi is administratively divided into 3 regions and 28 districts. The 2012 MMIS sample was designed to provide estimates for the country as a whole, for urban and rural areas separately, and for each of the regions:
Northern Region: Chitipa, Karonga, Likoma, Mzimba, Nkhata Bay, and Rumphi
Central Region: Dedza, Dowa, Kasungu, Lilongwe, Mchinji, Nkhotakota, Ntcheu, Ntchisi, and Salima
Southern Region: Balaka, Blantyre, Chikhwawa, Chiradzulu, Machinga, Mangochi, Mulanje, Mwanza, Neno, Nsanje, Mwanza, Neno, Nsanje, Phalombe, Thyolo, and Zomba
Each district is subdivided into traditional authorities. For statistical purposes, each traditional authority is subdivided into standard enumeration areas (SEAs). The 2008 National Population and Housing Census demarcated these SEAs and determined the number of households in each one. The sampling frame of the 2012 MMIS is the list of SEAs developed from the 2008 census, stratified by region and urban and rural strata.
To improve the precision of the trend analysis, the 2012 MMIS was conducted in the same 140 standard enumeration areas (SEAs) selected for the 2010 MMIS.
SAMPLE ALLOCATION AND SELECTION
To meet the objective of providing reliable estimates for key indicators of the sample domains, a total sample of 140 SEAs-44 in urban areas and 96 in rural areas- and 3,500 households was allocated among regions in proportion to the 2008 population of each region. Urban areas were over-sampled within regions in order to produce robust estimates for that domain. Therefore, the MMIS sample was not proportional to the population for residence (urban-rural area) and required a final weighting adjustment to provide valid estimates for every domain of the survey.
The SEAs were selected with probability proportional to size from a list of approximately 12,474 SEAs covered in the 2008 census. The SEA size was the number of residential households recorded in the census. Once the households were allocated to the different strata, the number of SEAs to be selected was calculated based on an average cluster take of 25 completed interviews of all respondents.
In the second stage, 25 households were selected in each selected SEA using systematic sampling from a list of households in the SEA. Because it has been almost four years since the census, a fresh household listing was undertaken before the survey was fielded. The National Statistical Office (NSO) assisted in listing the households in the SEAs. As part of this exercise, the listing teams also drew up the necessary maps and recorded the geographic coordinates of each SEA.
SELECTION OF HOUSEHOLDS
The frame of households was obtained from the listing of all households in the selected SEAs. Upon completion of household listing, the households were given new numbers, which were sampling serial numbers assigned to each household in the cluster. The sampling numbers were assigned sequentially within each SEA starting from 1. The total number of households in the SEA was equal to the last serial number assigned.
In summary, the following steps were used to select the households:
- The sampling interval for each category was calculated:
where B is the number of households listed in the selected SEA and b is the number of households to be selected in that SEA.
- A random number (R) between 1 and the interval I was generated; the first selection will hence be R.
- The interval to the random number to get the next selection was added.
- The interval was repeatedly added until the desired sample size was achieved.
The sampling procedures are fully described in Appendix A of "Malawi Malaria Indicator Survey 2012 - Final Report" pp.49-52.
Estimates of Sampling Error
Sampling errors, on the other hand, can be evaluated statistically. The sample of respondents selected in the 2012 Malawi MIS 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 among all possible samples. Although the degree of variability is not known exactly, it can be estimated from the survey results.
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 2012 Malawi MIS sample is the result of a multi-stage stratified design, and, consequently, it was necessary to use more complex formulae. Sampling errors are computed in either ISSA or SAS, using programs developed by ICF International. These programs use the Taylor linearization method of variance estimation for survey estimates that are means, proportions, or ratios like the ones in the Malawi MIS survey.
In addition to the standard error, the design effect (DEFT) for each estimate is also calculated. The design effect 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. Relative standard errors and confidence limits for the estimates are also calculated.
Sampling errors for the 2012 Malawi MIS are calculated for selected variables considered to be of primary interest. The results are presented in this appendix for the country as a whole, for urban and rural areas, and for the three regions in the country: Northern, Central, and Southern. For each variable, the type of statistic (mean, proportion, or rate) and the base population are given in Table B.1. Tables B.2 through B.7 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 sampling errors for mortality rates are presented for the five-year period preceding the survey for the whole country and for the ten-year period preceding the survey by residence and region. The DEFT is considered undefined when the standard error considering a 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 childbearing.
The confidence interval (e.g., as calculated for child has fever in last two weeks can be interpreted as follows: the overall average from the national sample is 0.317, and its standard error is 0.013. Therefore, to obtain the 95 percent confidence limits, one adds and subtracts twice the standard error to the sample estimate, i.e., 0.317±2×0.013. There is a high probability (95 percent) that the true average number of children ever born to all women age 40 to 49 is between 0.291 and 0.344.
For the total sample, the value of the DEFT, averaged over all variables, is 1.8. This means that, due to multi-stage clustering of the sample, the average standard error is increased by a factor of 1.8 over that in an equivalent simple random sample.
The sampling errors are fully described in Appendix B of " Malawi Malaria Indicator Survey 2012 - Final Report" pp.55-58.