The use of indices formed from the ratio of 2 variables often generates spurious correlations with other variables that are mathematically coupled. In this context, we examined the correlations between percent flow-mediated dilation, baseline diameter, and shear rate. In a sample of 315 participants, with and without substantial vascular risk factors, the observed correlation coefficients between the variables were of a similar magnitude to those reported in the literature. We then applied a Monte Carlo procedure based on random permutations to remove any physical or physiological explanation for these correlations. We found that the median residual correlation coefficients were comparable with those observed in our original sample. When the confounding influence of artery size was adjusted for, the mean difference in percent flow-mediated dilation between high-risk and low-risk samples was halved. These findings indicate that the widely reported correlations between flow-mediated dilation, basal artery diameter, and shear rate have a substantial spurious component. This is because percent flow-mediated dilation and shear rate are mathematically coupled to artery size.