In most of the literature , we find design effect taken as 2 while calculating sample size in cluster sampling technique? Any specific reasons for taking the value?
Well a reasonable approximation of 1.96 is 2. Best wishes David Booth
Kish developed the design effect (deff), which is the variance of the more complex design, here cluster sampling, divided by the variance had the same sample size been used in a simple random sample. There are different variables involved. In the case of cluster sampling, you have both within and between cluster variance to consider.
In general, stratified random sampling is more efficient than simple random sampling, so the deff will be less than 1. Cluster sampling is less efficient, so the deff is greater than 1. It depends on the different variances. Cluster sampling, though less efficient (efficiency refers to the variance, less efficient meaning a larger overall variance), is often used because it can be more practical. If you have to travel to locations, it may be cheaper, even though you collect more data to do the job.
[Clusters have other roles too, as in describing a certain phenomenon, but not important here.]
If you have seen 2 used often for cluster sampling, I suppose that might be a close approximation in various practical applications. I don't know, but would not be surprised.
Sure the deff would depend on both design and estimate. For instance, according to Petterson and do Nascimento Silva (2005), in developing countries, the two-stage selection of households provides a design effect that can range from 2 to 6. It is a crucial information for calculating the sample size for a complex design survey. The deff can be estimated from a previous survey using e.g. an estimate of the intra cluster correlation (icc): deff=1+(m-1)*icc where m is le cluster size. In absence of previous information, approximate values are used depending on the design. I usually consider an initial value of 3 or 4 for the deff when calculating sample size for a multi stage survey; and then I would consider lower values to keep the sample size at a reasonable level
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