When Time Makes a Difference: Addressing Ergodicity and Complexity in Education
The detection of complexity in behavioral outcomes often requires an estimation of their variability over a prolonged time spectrum to assess processes of stability and transformation. Conventional scholarship typically relies on snapshots to analyze those outcomes, assuming that group means and their associated standard deviations, computed across individuals, are sufficient to characterize the educational outcomes that inform policy, and that time does not matter in this context. In its statistically abstract form, the assumption that you can rely on snapshots is referred to as the ergodicity assumption. This paper argues that ergodicity cannot be taken for granted in educational data. The first section discusses artificially generated time series trajectories to illustrate ergodicity (white noise) and three types of non-ergodicity: short-term correlations between observations, long-term correlations (pink noise) and infinite correlations (Brownian motion). A second section presents daily attendance data observed in two urban high schools over a seven year period to show that these data are non-ergodic and suggest complexity. These findings offer a counter-example to the efficacy of using time-independent measures (‘snapshots’) to measure educational outcomes.