Variability is an essential characteristic of motor control and an important outcome in motor control research. Investigating variability has led to the development of theoretical frameworks such as speed-accuracy tradeoff (Shmuelof et al., 2012) and synergistic coordination (Scholz and Schöner, 1999), and concepts such as accuracy, precision, stability, and dexterity have been quantified for various applications such as sports and rehabilitation (Maki, 1997, Moon et al., 2016, Shinya et al., 2017). In most of these previous studies, variances and standard deviations were calculated as the most basic measures of variability in discrete event parameters.

In these previous studies, the numbers of trials and participants are highly dependent on practical considerations. For example, regarding gait variability, the use of a treadmill enables researchers to collect data from hundreds of steps, whereas it might not be feasible with ground walking. Additionally, the maximum number of steps that can be collected may be lower in older populations or those with certain pathologies, compared to a healthy, young control group. Despite such practical constraints, from a statistical perspective, the number of participants, or sample size, should be planned through power analysis to ensure adequate statistical power for detecting measures of variability.

The statistical power refers to the probability of correctly detecting a difference between groups or conditions as statistically significant given an expected effect size (Cohen, 1988). In t-tests or ANOVA, for instance, the denominator of the effect size formula includes the term for inter-subject variability, which includes not only individual differences in “true” values but also stochastic deviations due to sampling. Therefore, as the number of trials per subject increases, the effect size increases. This implies that there is a trade-off between the number of trials n per subject and the number of subjects N to ensure a certain level of statistical power for detecting a given difference in variance: a study that measures a small number of trials from many subjects and another study that measures a large number of trials from a small number of subjects can have the same level of statistical power. In this report, we attempted to suggest recommendations for the number of trials and participants to use for studying variability as an outcome, through mathematical considerations and numerical simulations.