Influence of noise and effect characteristics on statistical power in the analyses of one-dimensional biomechanical trajectories

Statistical power analysis is fundamental for valid inference and sample size determination, but its application to one-dimensional data introduces additional complexity. In contrast to zero-dimensional data, statistical power for one-dimensional data does not have a unique definition. The statistical power analysis for two-sample hypothesis tests when the data is one-dimensional is further complicated due to the data characteristics, such as smoothness and differences between group mean trajectories, referred to as the effect trajectory. This study investigates how noise smoothness and effect trajectory jointly influence statistical power in the analysis of one-dimensional data, using two different definitions of statistical power: omnibus power and sensitivity. Analysis of six biomechanical datasets confirmed that diverse characteristics of the effect trajectory exist in practice and influence omnibus power trends. Using simulation experiments with different characteristics of the effect trajectories under varying smoothness levels, we assessed the statistical power for both statistical parametric mapping and its nonparametric version. The results show that when non-zero effects cover large portions of the domain, increasing smoothness decreases omnibus power, whereas for effects on smaller portions, smoother data enhances omnibus power. In contrast, sensitivity consistently increases with smoothness, independent of the effect's characteristics. These findings highlight that the relationship between smoothness and statistical power is not universal, but instead, depends on the definition of power and the underlying effect structure.