Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
A priori power calculations were conducted for the primary outcome, Kendall’s τ (tau), a measure of ranking consistency. With a total sample size of N = 180 (90 per arm), an alpha level of 0.05 (two-tailed), and assuming a standard deviation of τ derived from pilot data or prior literature (estimated SD ≈ 0.25), the design achieves 80% power to detect a minimum detectable effect (MDE) of approximately 0.20 in Kendall’s τ. This corresponds to a small-to-moderate standardized effect size (Cohen’s d ≈ 0.40). The calculation assumes no clustering and uses an independent two-sample t-test. If the achieved sample size reaches the upper target of N = 240 (120 per arm), the MDE decreases proportionally.