Guidelines for balancing the number of trials and the number of subjects to ensure the statistical power to detect variability - Implication for gait studies.

Variability is one of the most crucial outcomes in human movement studies: variance and standard deviation of various parameters have been reported in numerous studies. However, in many of these studies, the numbers of trials and subjects have been intuitively determined and not justified with statistical considerations. Here, we investigated the impact of the numbers of trials and subjects on statistical power, based on the assumption that results per trial follow a normal distribution, using mathematical analysis and numerical simulation. An inverse-like relationship was observed between the number of trials and subjects required to ensure the statistical power for detecting differences in variance between subject groups or conditions. For instance, assuming a 1.2-times difference in population variance between pre-and post-training sessions as an alternative hypothesis, our simulation demonstrated that combinations of the number of subjects and trials, such as measuring 100 trials from each of 12 subjects under each condition, or measuring 20 trials from each of 60 subjects, can guarantee an 80 % of statistical power. Planning research based on such mathematical considerations will enable meaningful statistical interpretations in studies focusing on movement variability, such as gait studies.