Work out cluster sample design effect instantly with clear inputs, formula shown and shareable results.
Cluster sampling loses efficiency because people within a cluster resemble each other. The design effect is 1 + (m-1)ICC, so clusters of 25 with an ICC of 0.05 give 2.2 - meaning 400 participants under simple random sampling becomes 880, spread across 36 clusters. Even a small ICC is costly when clusters are large.
Design effect
DEFF = 1 + (cluster size - 1) x ICC
Adjusted sample
adjusted = simple random sample x design effect
Because it is multiplied by cluster size. An ICC of 0.02 with clusters of 100 still gives a design effect near 3.
More clusters, almost always. Adding participants within a cluster adds little new information once the cluster mean is estimated.