There are multiple design effects; it depends on the design. It's a measure of efficiency of the design. The one I see most often is for clustering / two stage sampling.

Deff = 1 + (m-1)*rho

where m is the average cluster size and rho is the intra-class correlation.

Total N = m * n where n is the number of clusters. So if you can plan for the number of clusters and typical cluster size you can account for the design effect if you can estimate rho. There's several studies publishing typical ICCs for different fields and you can use that as a guideline. So not guesswork, but still lots of room for misestimation. I'd usually estimate a plausible range for Deff based on likely high and low ICCs.

e.g., 10 clusters (n) and 20 observations per cluster gives N = 200. If rho is .10 then Deff = 1 + (9)*.1 = 1.9.

So effective sample size is 200/1.9 or approx 105.

Other design effects probably allow you to estimate the effective sample size for planning a study in similar ways. The wikipedia article on this is quite good, but I've never had to use any of the others.

Yes, the **design effect (DEFF)** is primarily used in sampling techniques **other than simple random sampling (SRS)**. Here's why: ### **1. What is Design Effect?** The design effect (DEFF) measures how much the variance of an estimate increases due to the sampling design compared to simple random sampling. It is given by: DEFF = 1 + (m - 1) \rho where: - **m** = Average cluster size - **ρ (rho)** = Intraclass correlation coefficient (ICC), which indicates the similarity within clusters A **DEFF > 1** means the actual sampling variance is greater than that of SRS, requiring a larger sample to achieve the same precision. ### **2. When is Design Effect Used?** - **Cluster Sampling:** Used because individuals in the same cluster tend to be similar, reducing variability between clusters but increasing variance overall. - **Stratified Sampling:** If proportional allocation is used, DEFF may be close to 1, but for disproportionate stratification, adjustments are needed. - **Systematic Sampling:** If there is an underlying pattern in the population, DEFF is considered. - **Multistage Sampling:** Similar to cluster sampling, DEFF is applied due to potential intra-cluster similarities. ### **3. Why is DEFF Not Used in SRS?** In **simple random sampling (SRS)**, every individual is selected independently, leading to **minimum variance**. Since SRS assumes no clustering or grouping effects, the design effect is **1** (i.e., no increase in variance), so it is not needed. ### **Conclusion** The **design effect is used in all sampling techniques except SRS**, where individuals are randomly selected with equal probability, eliminating any clustering effects. If you're working with stratified or cluster samples, it's essential to adjust for DEFF when determining sample size and variance estimates. Would you like an example of how DEFF affects sample size calculations?

Abowak Ulfata Megersa -

If you look at page 56 of Kish, L.(1995), “Methods for Design Effects,” Journal of Official Statistics, Vol. 11, No. 1, pp. 55‐57, which is available from JOS by just searching on the paper name with quotes on the internet, you may see that a deff is shown as the variance for a mean you obtain with your sample design, divided by that variance obtained with simple random sampling.  My understanding has been that it is a way to see the effect of your sampling design with regard to efficiency (variance). Kish discusses further.

Thus if you use a deff as defined on page 56 of Kish(1995), your result for a simple random sample, as stated in your question, will be 1. If you use a different design and get a lower variance for the same sample size, then that will be more "efficient" than simple random sampling. That would generally happen with stratified random sampling, for example. An example of a less efficient random sampling design would be cluster sampling, but that generally makes up for the inefficiency in sample size by ease of data collection.

For similar questions you may find good background material by searching for your term along with the following words: Pennsylvania State University.

Cheers - Jim

PS - I am not familiar with what Thom Baguley has above, but I do know that cluster sampling should be less efficient than a simple random sampling design, and since i see Deff = 1 + (m-1)*rho in his answer, that seems like it could work. Also, I know Thom supplies good responses.