Table 3 Description of sample size calculation
\(\boldsymbol{m}=\frac{{\left({\boldsymbol{Z}}_{\mathbf{1}-\boldsymbol{\alpha} /\mathbf{2}}+{\boldsymbol{Z}}_{\mathbf{1}-\boldsymbol{\beta}}\right)}^{\mathbf{2}}\ \mathbf{2}{\boldsymbol{\sigma}}^{\mathbf{2}}}{{\boldsymbol{\Delta}}^{\mathbf{2}}}\left(\mathbf{1}+\left(\boldsymbol{n}-\mathbf{1}\right)\boldsymbol{\rho} \right)\) | |
where? m = sample size per study arm | = 1.96 at the type 1 error of 5% = 0.842 at 80% power |
σ = the standard deviation of primary outcome in the population | • Based on Uganda STEP survey [2], the standard deviation of waist circumference for women aged 18 to 49 years = 13.73. |
△ = effect size = 7.4cm. | • Effect size was calculated based on Bendall, Mayr [41] , impact of the Mediterranean diet on central obesity. • Only studies with a duration below 12 months were included in the calculation as the proposed study duration is below 12 months. |
(1 + (n − 1)ρ)= design effect (DE) to compensate for cluster randomisation. ▪ n = number of individuals per cluster ▪ ρ = Intra-Cluster Correlation coefficient | • For our intervention, n = 27 • ρ = 0.001 ▪ There is no data available on the intra-Cluster Correlation coefficient of waist circumference across villages for communities within Kampala. A range of 0.001 to 0.10 is demonstrated as a cost - effective and safe choice to account for the variability. |