Is the use of the coefficient of variation a valid way to assess the swimming intra-cycle velocity fluctuation?

Objectives
Swimming intra-cycle velocity fluctuation has often been assessed using the coefficient of variation, which requires a mathematical assumption of a positive linear relationship between the velocity mean and standard deviation. As this assumption has never been tested, the current study aimed to investigate the within-participant relationship between the mean and standard deviation of the intra-cycle velocity.

Design
Cross-sectional study.

Methods
The intra-trial mean and standard deviation of one stroke cycle centre of mass velocity (vCMmean and vCMSD, respectively) were obtained from 80 front crawl trials (10 participants × eight swimming speeds) using whole-body three-dimensional motion analysis. The linear mixed-effect model and intra-class correlation analysis were used to test the linear relationship between vCMmean and vCMSD (n = 80) and the absolute agreement between vCMmean and vCMSD relative to those during the fastest trial (n = 70).

Results
Neither the linear regression model (95 % confidence interval range of the fixed effect of vCMmean: −0.003–0.031) nor the intra-class correlation coefficient (ICC = 0.07; p = 0.26) verified linear relationships between vCMmean and vCMSD, which violated the background assumption of coefficient of variation calculation.

Conclusions
When investigating the intra-cycle velocity fluctuation, the coefficient of variation should not be used alone. Researchers and practitioners should always interpret/report the obtained results together with the mean and standard deviation to avoid misleading conclusions and feedback because the coefficient of variation obtained from one cycle velocity data is likely biased by mean velocity.