does this approach introduce serious biases in the results and make it difficult to calculate the sampling errors, unless one assumes that the districts not covered are similar to those that are which is a very big assumption.? on the other hand, sampling all districts would have serious financial and logistic implications. what is the standard practice? .
Hi Sarah -
Yes, one stage and multiple stage cluster sampling are accepted randomized designs. Standard errors can be estimated. There are a number of good textbooks that cover this. An "oldie but a goodie" would include this one:
Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons.
The purpose of such a design is to alleviate "financial and logistic" problems.
Note that when you move from a simple random sample to a stratified random sample, your efficiency improves. But when you go to a cluster sample, the opposite occurs. You may have felt that intuitively. But the idea is that it is more cost effective logistically, so you may be able to afford a bigger sample.
Just be careful of accidentally increasing your nonsampling error, such as measurement error, if your sample size becomes too large, in any case.
Cheers - Jim
PS - Note that the problem with any probability of selection/randomized/design-based sample is that you are hoping that a randomized selection will give you a "representative" sample, but the chances that that did not happen are built into your standard error estimate. However, oddly distributed data could increase the standard error of your standard error. (Also, note that bias is always a concern.) If you can use auxiliary data for model-assisted design-based sampling and estimation, that can greatly improve results. Consider the following, for example:
Särndal, CE, Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling, Springer-Verlang
But that is probably beyond the scope of your current project. However, you might keep this in mind in the future for continuous data.
The main point is to clarify which are the population units. If they were the districts in clusters of regions of a country, and the study pretends obtain inference over the districts of the country, then you could use cluster sampling of regions with subsampling of ditricts.
Other possibility is to take stratified sampling by regions, and in each stratum or region to take a sample of districts with proportional allocation to the size of the region.
As I noted above, the same efficiency (variance) can be achieved with a smaller sample size using stratified random sampling, but Sarah's question appears to be a classic example of the need for the use of cluster sampling due to logistical issues.
If you will research "cluster sampling" Sarah, that should address your issue. (Note that not all online resources are equally reliable, and I just noticed a definition on a popular resource that I believe is not quite correct, so if using the internet, i suggest checking multiple sources.)
Hi Sara,
if I'm understanding well you have a study area partitioned into regions and you want to select only one district within each region. In my opinion this is the well-known one-per-stratum stratified sampling. There is no problem to achieve unbiased estimation by means of the Horvitz-Thompson criterion. The only problem is the estimation of variance. As to some literature see Breidt FJ (1995) Markov chain designs for one-per-stratum sampling. Survey Methodology, 21, 63-70. Recently I have outlined the effectivenerss of this scheme in spatial sampling (sampling spatial units from a regular grid). Give a look at Fattorini et al, Environmetrics, 2015, 26, 216-228
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