ANSWER AND REASONINGE. Precision is overstated and the study may be underpowered because the design effect was omitted
Cluster trials contain fewer independent units than their raw participant count suggests. Ignoring the design effect produces standard errors that are too small and an inadequate sample-size target.
Why every option is right or wrong
A. The intervention effect is necessarily biased toward benefit: Ignoring clustering primarily affects precision; the direction of the point estimate is not predetermined.
B. Allocation concealment becomes impossible in principle: Clusters can still be allocated with concealment before assignment.
C. The effective sample size increases because patients share a hospital: Correlation reduces, rather than increases, independent information.
D. Only external validity is affected: Within-cluster correlation directly affects variance, confidence intervals and power.
E. Precision is overstated and the study may be underpowered because the design effect was omitted: Outcomes within hospitals correlate; sample size and analysis must account for intracluster correlation and cluster size.
What if the scenario changed?
If the intracluster correlation were zero, the design effect would be one and individual-level precision calculations would coincide with the clustered design.