In a cluster randomized trial of a school-based nutrition intervention, the intra-class correlation coefficient (ICC) is 0.05. The design effect (DEFF) for a cluster size of 40 children per school is:
- A 2.95 ✓
- B 1.95
- C 3.5
- D 1.0
Correct answer: A. 2.95
Explanation
Design Effect (DEFF) = 1 + ICC × (cluster size − 1) = 1 + 0.05 × (40−1) = 1 + 0.05 × 39 = 1 + 1.95 = 2.95. This means the sample size for a cluster trial needs to be 2.95 times larger than for a simple random sample of the same size to achieve equivalent statistical power, because children within the same school are more similar to each other (correlated) than children randomly drawn from the population. ICC quantifies within-cluster correlation; higher ICC or larger cluster size inflates DEFF.
Reference: Park's Textbook of Preventive and Social Medicine, 27th ed.
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