# Sample Size Calculation for Cluster Sampling

I'm being asked to calculate a necessary sample size for a cluster sampling protocol. I don't have much experience with cluster sampling, so thought I'd come here. The situation is as follows:

1) Clusters: We have two separate groups to run analysis on. One with 75 clusters and one with 150 clusters.

2) Cluster size: Cluster size is uniform - 20 people per cluster.

3) Data of interest: What we're interested in is a repeated measure. An index is calculated at the start of an intervention, and then again at the end of the intervention (18 months later). We would like to answer the following question:

If we assume that without intervention, the end value would increase by 15 points (out of a scale of 100), is the intervention more effective? (There is rationale for this assumption, I just won't get into it here).

4) Desired alpha is .05, desired power is .8, we would like to measure an effect size of at least .5 SDs, however there are budgetary and time constraints so we may adjust those to bring down the sample size. Not ideal, but it may have to be done.

The proposed design is that some people (minimum 2) will be interviewed from each cluster to ensure that each cluster gets representation, but I believe the same results could be achieved by taking a random sample of clusters and then a random sample of people within the selected clusters. I'm just not sure if that's correct and, if it is, how to calculate the # of clusters needed and the # of people within the clusters to pick.

Thanks for the help! Let me know if any more information is needed.

• Is the intervention at the cluster level, or the individual level? That is, does everyone in the same cluster get the same treatment (intervention or control)? May 14, 2014 at 17:44
• Everyone is getting the same treatment in all clusters. We don't have any active control clusters - the control has already been established as the 15 point increase I mentioned in point 3. May 14, 2014 at 19:32
• Update: The group, as I advised, has decided to go with a blocked t-test design instead of cluster analysis, since it more naturally fits their situation. I'm still interested in reading more about cluster analysis if anyone has any good resources. May 15, 2014 at 16:53