In a cluster randomized trial of a health education intervention in villages, the design effect (DEFF) is calculated as 2.8. This means the effective sample size is:

• A 2.8 times larger than a simple random sample of the same total n
• B 2.8 times more precise than simple random sampling
• C Effectively 1/2.8 times a simple random sample of the same total n ✓
• D Unaffected if intraclass correlation coefficient (ICC) is <0.05

Explanation

The design effect (DEFF) accounts for within-cluster similarity (measured by the intraclass correlation coefficient, ICC). A DEFF of 2.8 means the variance of the estimate is 2.8 times larger than if the same number of individuals had been selected by simple random sampling. The effective sample size = total n/DEFF, so the clustered sample is less informative (equivalent to 1/2.8 of a simple random sample). This is why cluster trials must inflate their sample size by the DEFF.

Reference: Park's Textbook of Preventive and Social Medicine, 27th ed.

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