The Intensity Inequality Index for Physical Activity: A New Metric for Integrative Analysis of Movement

Wearable sensors recording acceleration provide a powerful tool for analysis of physical activity (PA). Continuous, high-rate data acquisition over extended periods gives highly resolved measurement of movement intensity. While increased complexity of PA analytics allows for deeper insight, it brings a challenge to statistical testing, where commonly used approaches require a single defining metric for PA per participant.

We adapt an econometric measure to obtain a statistical test metric for movement intensity-the intensity inequality index, I≠. This is a "Gini coefficient for movement" that quantifies the inequality in distribution of time spent across a range of activity intensity values. The I≠ metric is calculated using a graphical method on plots of cumulative time versus cumulative intensity level. Hypothesis testing of I≠ is performed on 24-hour activity traces of 58 children, aged 7-11 years, to assess statistical differences in PA between typically developing children and those suspected of having developmental coordination disorder.

The I≠ test metric provided high statistical confidence with low sample numbers: P < .05 for n ≥ 30. When differentiating between groups, I≠ halved the sample size required for a statistical power of 80% at α = .05, in comparison to the alternative metrics of intensity gradient or log ratio of minutes at low and moderate to high intensity.

The inequality index provides a metric that is based on the accumulated time-counts across an activity intensity distribution. This integrative description of the distribution makes it a powerful statistical metric for PA.