More individuals or more groups? Incorporating sampling effort, statistical power, and model accuracy when designing experiments
摘要
When testing differences between populations, ecologists often face a tradeoff between collecting repeated measures from the same unit or independent replications across units. In studies of social insects, for instance, one can sample many individuals within a colony or fewer individuals from more colonies. This choice affects not only statistical power but also the accuracy of variance estimates, which may in turn inflate type-I error. The cost of sampling an additional independent replicate often differs from that of a repeated measure, requiring an efficient experimental design. We use a simulated case study based on social insect research to explore how sampling strategies impact type-I and type-II errors in linear mixed-effects models. In crossed designs—where each colony experiences all levels of a fixed effect—sampling strategy had minimal impact. In contrast, nested designs—where different colonies experience different treatments—were highly sensitive to sampling allocation, with poor variance estimates leading to elevated type-I error rates. Increasing independent replications generally improved accuracy but is more costly, as confirmed by our literature survey showing social insect studies sampled nearly three times more repeated measures than independent replicates. To address this, we developed two optimization protocols that incorporate both sampling cost and balanced accuracy. By integrating power analysis with realistic effort constraints, we provide a practical roadmap for designing efficient, multiscale experiments. While our study was focused on social insects, our results can generalize to other systems requiring a balance between repeated measures and independent replications.