 2.5.3 Sample Size Estimations The sample size is based on the principles cluster randomised trials 16 using mean prevalence of infection in each study arm as the primary outcome. It was assumed that prevalence of infection in the reference arm has a mean of 20 with a coefficient of variation between clusters of 0.3, based on recent surveys in the study area, and that 80 power and 5 significance would be required. Therefore, with 48 clusters 4 arms of 12 clusters each the study would be able to detect a 28 lower prevalence prevalence ratio 0.78 between the Olyset Plus relative to the standard Olyset LLINs arms and between IRS with pirimiphos methyl relative to no IRS 24 clusters per arm for each of the two comparisons, with a sample of 80 children per cluster. Similarly, a 40 lower prevalence prevalence ratio 0.6 could be detected between any individual arm and another, for example Olyset Plus IRS vs Olyset Plus 12 clusters each. 