I have $n$ measures and I would like to get a p-value to know if the mean is significantly different from 0. However, each measure belongs to a cluster and hence all the $n$ measures are not perfectly independent. Therefore, I would like to take the cluster information into account for a valid statistical inference. Note that the size of each cluster varies, most of them are 1 but some go to 6.
A valid approach is to average the measures within each cluster but I suspect this is not the most efficient in terms of statistical power.
Frow what I read on the topic I understood that a linear regression could be suitable (e.g. here) but I'm really not familiare with inference based on linear regression and I don't understand the procedure.