I have to recruit a sample of 300 secondary sampling units (elements) from X number of Clusters ( primary sampling units), how do I determine X when my primary sampling frame has 93 clusters. I will then do mapping in X clusters to get a sampling frame for the secondary sampling units and select a random sample of 300 among those. The assumption is that each cluster has aporoximately 50 elements.
Select a simple random sample of your 93 clusters, if I understand your question correctly. In any case, compare stratified and two stage cluster sampling as described e.g. in the following book.
https://www.amazon.com/Elementary-Survey-Sampling-Richard-Scheaffer/dp/0840053614/ref=sr_1_1?s=books&ie=UTF8&qid=1529460185&sr=1-1&keywords=Elementary+Survey+Sampling
Best, David Booth
@David and Andrew thank you for the response. That is the idea for stage 1 i.e. taking a random sample from the 93 clusters (Mind you 93 is the sampling frame), what I am unsure about is what should be the sample size (no of clusters)?
In my opinion, you should pick up at least 6 clusters randomly among 93 to reach 300 as a sample. So, you should add all elements in that 6 clusters to your sample.
Zohaib -
As David noted, you might want to compare stratified random sampling with the two-stage cluster sampling that you describe. Stratified random sampling is generally more efficient than random sampling, and cluster sampling is less efficient. When cluster sampling is chosen, it is usually because it is more practical for data collection, such as when people have to travel, rather than collect data by mail, email, or other Internet response.
Also, generally your concern should be reaching certain low levels of standard errors for key variables with the smallest sample size possible. If you must use a cluster sample, then what combination of number of primary units and selections from within them will give you the fewest total number of secondary unit selections and obtain a given accuracy for given attributes/variables/questions?
(The goal re sample size problems is generally low standard error, which depends upon design, estimator, standard deviation(s), and sample size(s), assuming bias is not an issue, which may be a bad assumption at times.)
But you seem to already be constrained to a two-stage sample selection, and a total number of secondary units of 300, for which I assume you want the lowest overall standard errors for given means or totals. For the sake of stability, I also assume you don't want too few primary units (clusters). Assuming that is not a problem, because you will reassess if the following considerations only give you four or five of them from which to draw your total of 300 cases, there are the following considerations, which parallel considerations for strata:
(1) How much variability is there within each cluster? Here, if the variability within clusters is low, then you can pick fewer cases within each cluster, and therefore pick more clusters in the first place. (2) How much do the clusters vary from each other overall? You won't need as many primary unit selections (clusters), if they don't differ from each other so much. In addition to these two considerations, you could also consider using unequal probability sampling, based on varying cluster sizes.
Here are three more books that you might consider as you research "cluster sampling," "multistage sampling," "two-stage sampling," and "subsampling":
Thompson, S.K.(2012), Sampling, 3rd ed, John Wiley & Sons.
Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons.
Lohr, S.L(2010), Sampling: Design and Analysis, 2nd ed., Brooks/Cole.
Note that primary units and second-stage units are described well on page 274 in Cochran(1977). I have found that it's easy to forget which one is labeled 'primary.' The actual units of interest, regarding sample size, are the secondary selections.
So you see that with two-stage sampling it is complicated to figure out the optimum number of clusters. You need information about how data may be distributed, including how it might be 'clumped' in places. A pilot study might help with that.
Perhaps you have already preceded to a point where this may not help you this time, but perhaps next time, or perhaps you have run into problems, and though it is best to plan ahead, perhaps some data you have now may serve as a pilot study if you have not gone too far.
I hope I have not misunderstood your question, or made any other error, and that something above might be helpful.
Cheers - Jim
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