In a cluster randomised trial of a school-based health intervention, the intra-cluster correlation coefficient (ICC) is 0.05 and cluster size is 40. What is the design effect (DEFF)?

• A 1.95
• B 2.05
• C 3.25
• D 2.95 ✓

Explanation

Design effect (DEFF) = 1 + (cluster size − 1) × ICC = 1 + (40 − 1) × 0.05 = 1 + 39 × 0.05 = 1 + 1.95 = 2.95. The DEFF reflects the loss of efficiency due to clustering; a DEFF of 2.95 means the effective sample size is approximately one-third of the actual sample size. Ignoring ICC and DEFF in cluster trials leads to underestimation of standard errors and inflated type I error rates.

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

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