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Fig. 1 | Substance Abuse Treatment, Prevention, and Policy

Fig. 1

From: Universal cannabis outcomes from the Climate and Preventure (CAP) study: a cluster randomised controlled trial

Fig. 1

Power to detect differences in binary outcomes as a function of prevalence and effect size. Power was calculated using a method for three-level binary data randomized at the third level [34], using the function: \( \upvarphi =\Phi \left\{\frac{\left|{p}_1-{p}_0\right|\sqrt{N_1{N}_2{N}_3/{f}_3}-{\Phi}^{-1}\left(1-\upalpha /2\right)\sqrt{2\overline{p}\left(1-\overline{p}\right)}}{\sqrt{p_0\left(1-{p}_0\right)+{p}_1\left(1-{p}_1\right)}}\right\} \) where N1 is the size of the level 1 units (repeated observations of participants in the current study); N2 the size of level 2 units (participants per school); N3 the number of level 3 units (schools); p1 and p0 the prevalence of the outcome in the treatment and control groups respectively; \( \overline{p}=\left({p}_0+{p}_1\right)/2 \); f3 = 1 + N1(N2 – 1)ρ2 + (N1 – 1)ρ1; ρ1, ρ2 the correlations within level 1 and level 2 units. Power calculations for the trial analyses were performed using N1 = 5, N2 = 80, N3 = 5, ρ1 = 0.36, ρ2 = 0.03. Contour lines join regions with equal power in increments of 0.1, with the power of some contours labelled in white

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