The symmetry angle: a novel, robust method of quantifying asymmetry

Quantification of asymmetry is a common objective in both research and clinical settings. The most common method for quantification of asymmetry of discrete variables is calculation of the symmetry index. Essentially a measure of the percent difference between sides, the symmetry index requires the choice of a reference value. This is a limitation as the choice of value is not always clear, and can lead to inconsistent results and artificially inflated values. Therefore, the purposes of the current study were to examine the limitations of the symmetry index in depth, define a new method of quantifying symmetry that is robust to those limitations (the symmetry angle), and compute the correlations between the two measures. The results showed that, when using the symmetry index, the interpretation of asymmetry can be highly affected by the choice of reference value. The symmetry angle does not require the choice of a reference value. Therefore, it is not prone to the same limitations. While symmetry angle values tend to be smaller than symmetry index values, the measures are very highly correlated. This suggests that the symmetry angle is a good substitute for the symmetry index. Future studies of asymmetry may benefit from the use of the symmetry angle, as it is equally effective for identifying intra-limb differences as the symmetry index, but is not prone to problems due to normalization and provides a standard scale (+/-100%) to interpret results.