# Determining if observations within the same cluster are correlated for categorical data

Suppose I have:

• 66 observations
• 22 clusters
• 3 observations per cluster
• Each observation can take on a value of $$k\in\{0, 1, 2, 3, 4, 5, 6\}$$
• Each cluster is independent of every other cluster

I want to asses whether observations within the same clusters have a meaningful correlation (ie. are each of the 3 observations per cluster independent or not).

What statistical method could I use in this situation?