I am studying the topic of cluster sampling. I have learnt that intracluster correlation ($\rho$) measures the correlation over all clusters between distinct elements in the same cluster. I do not quite understand what this means. Can someone explain please and give an example if possible?
In general ICC tells you about the
"degree of similarity in the responses of individuals from the same cluster for the outcome" (Eldridge, Ukoumunne and Carlin, 2009)
describes how strongly units in the same group resemble each other (Wikipedia)
So it tells you if the clusters are made of similar individuals versus being a random mixture of individuals. However this measure could be misleading and you should not take it at a face value.