Fig. 3

a Plot of sample size calculations for low prevalence (10% and less) settings, demonstrating the effect on sample size of reducing prevalence towards 1%, and of increasing the statistical significance (α). In principle, this hypothetical surface could derive from any diagnostic. However, as more sensitive diagnostics are each applied, the surface shape will remain similar only now with a raised offset, as previously ‘missed’ infections are subsequently detected. Note that even at assumed 10% prevalence of Schistosoma-infected snails, sample sizes for any level of significance of α = 0.05 or more are already between 140 and 240 snails; this increases as prevalence reduces and as more precision and statistical significance are applied, to levels that are laregly impractical (1500–2700 snails). Formula used is: \( n={\left({Z}_{\frac{a}{2}}\right)}^2\rho \left(1-\rho \right)/{d}^2 \), where: n = sample size, p = estimated prevalence, d = precision of the estimate (with the assumption that d = 0.5*p given low prevalence setting), Zα/2 = the Z-statistic associated with the statistical significance α/2 (Z-statistic adjusted for each of α = 0.05 to α = 0.01) [94]. b Plot of prevalence of schistosomiasis across 100 schools (mean prevalence of 1.5%), ranked in ascending order according to the well-known pattern of overdispersion or focalisation. It may be proportionately easier to find infected snails in water contact sites surrounding those schools in red, while it will be harder around those schools in green. A flexible sample size criteria seems sensible where more geographical attention is given to those habitats in the vicinity of schools in red rather than around schools in green