Question 6: Were they correct?
When the number of clusters is very small and the number of individuals within a cluster is large, as in this study, clustering can have a major effect. The design effect, by which the estimated sample size should be multiplied, is DEFF = 1 + (m – 1) × ICC = 1 + (750 – 1/ ×0.005 = 4.745. Thus the estimated sample size for any given comparison should be multiplied by 4.745.
Looking at it another way, the effective sample size is the actual sample size, 3,000, divided by 4.745, about 632.
Further, sample size calculations should take into account degrees of freedom. In large sample approximation sample size calculations, power 80% and alpha 5% are embodied in the multiplier ƒ(α,P) = ƒ(0.05,0.80) = (1.96 + 0.85)2 = 7.90. For a small sample calculation using the t test, 1.96 must be replaced by the corresponding 5% point of the t distribution with the appropriate degrees of freedom, here 2 degrees of freedom giving t = 4.30. Hence the multiplier is (4.30 + 0.85)2 = 26.52, 3.36 times that for the large sample. The effect of the small number of clusters would reduce the effective sample size even more, down to 630/3.36 = 188. Thus the 3,000 men in two groups of two clusters would give the same power to detect the same difference as 188 men randomised individually.
The applicants resubmitted a proposal with many more clusters.
Back to Exercise: estimation of sample size.
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Last updated: 3 February, 2020.