Hi,

The sample size is multiplied by the design effect in cluster sampling because observations within clusters tend to be more similar than observations in a simple random sample, which reduces the effective sample size.

Hope this helps.

In cluster sampling, the sample size is adjusted by multiplying it by the design effect. This adjustment is important because clustering can increase variability when comparing samples taken from groups rather than randomly selected individuals. Since individuals within the same cluster tend to be more similar, the effective sample size is reduced, which means that each additional sample from the same cluster provides less new information. The following could be the main reasons why this adjustment is necessary:

• Loss of Independence
• Intra-Cluster Homogeneity
• Variance Adjustment

Thank you