Question

In a cluster sampling wherein the units within same cluster are highly correlated, suppose \(S_w^2\) represents the variance within the clusters and \(S_b^2\) between clusters, then which option is correct?
1. \(S_w^2\) is greater than and equal to \(S_b^2\)
2. \(S_w^2 \) is equal to \(S_b^2\)
3. \(S_w^2\) is lesser than and equal to \(S_b^2\)
4. \(S_w^2 \) and \(S_b^2\) are not comparable

Answer 1

Correct Answer - Option 3 : \(S_w^2\) is lesser than and equal to \(S_b^2\)

Explanation

In cluster sampling, researchers divide a population into smaller groups known as clusters.  They then randomly select among these clusters to form a sample.

Cluster sampling is a method of probability sampling that is often used to study large populations, particularly those that are widely geographically dispersed. Researchers usually use pre-existing units such as schools or cities as their clusters.

In cluster sampling the variance within the clusters is lesser than the variance between clusters

∴ S²_w is lesser than and equal to S²_b