How to determine the correct number of clusters

#1
Hi all

I am coming up with some sample sizes for a study and want some advice on how to determine how many clusters is an adequate number (n) from a total number of clusters (N). I have a list of clusters (schools) and have the population of students in each cluster. I want to determine an adequate number of clusters (n out of N), from which I will then do further stages of sampling (stratified random sampling of n clusters, and random selection of students). I have tried searching online to figure out how to determine n with the information I have, but cannot get a clear answer. I hope somebody can help!

Thanks
 

Miner

TS Contributor
#2
Determining the best number of clusters is more art and judgment than a science. Some recommend slicing the dendrogram, but that takes a really good eye. I plot the similarity values by the number of clusters as shown in the attached graph. I look for break points then create the dendrograms for each breakpoint (examples attached). I then used judgment to determine which make the most sense. The best number of clusters will depend on your specific needs.
 

Karabiner

TS Contributor
#3
Great contribution, Miner! Nevertheless, I guess that the OP did not refer to cluster analysis, but to some kind of sample size determination in case of a clustered data structure.

Since terms like "correct number" and "adequate number" are used by the OP without further qualification, and since the whole research project is described very sparsely, I suppose the question will not easily be answered.

Karabiner