In a cross-sectional survey of 1,200 adults, cluster sampling was performed by randomly selecting 30 villages and then interviewing all adults in each selected village. The design effect (DEFF) was 2.1. What does this imply about the effective sample size?

• A The effective sample size is 2,520
• B The DEFF corrects for non-response, not clustering
• C The effective sample size is approximately 571 ✓
• D DEFF > 1 indicates that clustering improved precision over simple random sampling

Explanation

The design effect (DEFF) is the ratio of the variance under the actual complex sampling design to the variance under simple random sampling of the same size. An effective sample size is calculated as n/DEFF = 1200/2.1 ≈ 571. A DEFF > 1 means clustering has reduced precision (increased variance) compared with simple random sampling of equal size, because individuals within clusters tend to be similar (intracluster correlation > 0). The effective sample size of 571 conveys the true precision-equivalent sample. DEFF does not correct for non-response.

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

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