A simple model to analyze the effectiveness of linear time normalization to reduce variability in human movement analysis

In this paper we propose a simple model to predict the effect of linear time normalization to reduce variability in human movement analysis. This model is based on analysis of the correlation between timing variables and total movement duration. We obtain a simple expression to predict the variation coefficient (CV) of the normalized variable as a function of the CV of the original one, the CV of the total movement duration and the correlation between both variables. Depending on the correlation coefficient, R, very different results can be obtained after normalization. If R is positive and high, the linear normalization process effectively decreases variability. However, an increase of variability of the normalized variable can be expected if R decreases. This model explains why linear normalization does not always reduce variability. The model is applied to an example of sit-to-stand movement in order to show its effectiveness and to illustrate the close relationship between the correlation coefficient and the suitability of linear time-scale normalization.