# Sampling and Households

Senturia et al. (1994) describe a survey taken to study how many children have access to guns in their households. Questionnaires were distributed to all parents who attended selected clinics in the Chicago area during a one-week period for well or sick child visits. Suppose that the quantity of interest is percentage of the households with guns. Describe why this is a cluster sample. What is the psu? The ssu? Is it a one-stage or two-stage cluster sample? How would you estimate the percentage of households with guns, and the standard error of your estimate?

What is the sampling population for this study? Do you think this sampling procedure results in a representative sample of households with children? Why, or why not? Solution: This is a cluster sample because all the elements within the clusters are selected. (Example: All parents who attended selected clinics in the Chicago). The primary sampling unit (psu): Clinics in the Chicago. The secondary sampling unit (ssu): Households with guns (parents who attended selected clinics in the Chicago area during a one-week period for well or sick child visits).

## Sampling and Households Essay Example

This is a two stage cluster sample because subsample only some of the element within a sampled cluster. We can estimate the percentage of households with guns based on the information available but in this study, the information is not available. We can assume in the case of selecting clinics, the sample size is 10 and the population size is 100, and those are the parameters that define the probability, 10/100. For households, calculation of the percentage is slightly different because we do not know, in advance of the study, how many households are to be selected in each sample clinic.

We are simply instructed to select 1 in 5 of all of them, so that if there is a total of 100 in Clinic A and 75 in Clinic B, we would select 20 and 15 respectively. Still, the percentage of selecting a household is 1/5, irrespective, of the population size or the sample size (20/100 = 1/5 but so does 15/75). By the formula, we simply estimate( t) ? unb= N/n ? t_i. When the population value is known, we can know the sampling error and we use this error for the purpose of our statistical test. The standard error of a percentage is always pq/n. Standard error (( t) ? unb) = Nv((1-n/N) (S^2 t)/n) .

The sampling population for this study is households with guns in the Chicago. Yes, this sampling procedure results in a representative sample of households with children because where there is sub-sampling within the clusters chosen at the first stage, the term multistage sampling will applies. The population is regarded as being composed of a number of first stage or primary sampling units (PSU’s) each of them being made up of a number of second stage units in each selected PSU and so the procedure continues down to the final sampling unit, with the sampling ideally being random at each stage.

Using cluster samples ensures fieldwork is materially simplified and made cheaper. That is, cluster sampling tends to offer greater reliability for a given cost rather than greater reliability for a given sample size. With respect to statistical efficiency, larger numbers of small clusters is better. All other things being equal than a small number of large clusters.