Which of the variance estimation methods in this chapter would be suitable for estimating the proportion of beds that have bed nets for the Gambia bed net survey in Example 7.1? Explain why each method is or is not appropriate.

Example 7.1

Malaria is a serious health problem in The Gambia. Malaria morbidity can be reduced by using bed nets that are impregnated with insecticide, but this is only effective if the bed nets are in widespread use. In 1991 a nationwide survey was designed to estimate the prevalence of bed net use in rural areas. The survey is described and results reported in D'Alessandro et al. (1994). The sampling frame consisted of all rural villages of fewer than 3000 people in The Gambia. The villages were stratified by three geographic regions (eastern, central, and western) and by whether the village had a public health clinic (PHC) or not. In each region five districts were chosen with probability proportional to the district population as estimated in the 1983 national census. In each district four villages were chosen, again with probability proportional to census population: two PHC villages and two non-PHC villages. Finally, six compounds were chosen more or less randomly from each village, and a researcher recorded the number of beds and nets, along with other information, for each compound. In summary, the sample design is the following:

To calculate estimates or standard errors using formulas from the previous chapters, you would start at stage 3 and work up. The following are steps you would use to estimate the total number of bed nets (without using ratio estimation):

1 Record the total number of nets for each compound.

2 Estimate the total number of nets for each village by (number of compounds in the village) x (average number of nets per compound). Find the estimated variance of the total number of nets, for each village.

3 Estimate the total number of nets for the PHC villages in each district. Villages were sampled from the district with probabilities proportional to population, so formulas from Chapter 6 need to be used to estimate the total and the variance of the estimated total. Repeat for the non-PHC villages in each district.

4 Add the estimates from the two strata (PHC and non-PHC) to estimate the number of nets in each district; sum the estimated variances from the two strata to estimate the variance for the district.

5 At this point you have the estimated total number of nets and the estimated variance, for each district. Now use two-stage cluster-sampling formulas to estimate the total number of nets for each region.

6 Finally, add the estimated totals for each region to estimate the total number of bed nets in The Gambia. Add the region variances as called for in stratified sampling.