The notion of concept drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time; as a consequence machine learning models may become inaccurate and need adjustment. Many online learning schemes include drift detection to actively detect and react to observed changes. Yet, reliable drift detection constitutes a challenging problem in particular in the context of high dimensional data, varying drift characteristics, and the absence of a parametric model such as a classification scheme which reflects the drift. In this paper we present a novel concept drift detection method, Dynamic Adapting Window Independence Drift Detection (DAWIDD), which aims for non-parametric drift detection of diverse drift characteristics. For this purpose, we establish a mathematical equivalence of the presence of drift to the dependency of specific random variables in an according drift process. This allows us to rely on independence tests rather than parametric models or the classification loss, resulting in a fairly robust scheme to universally detect different types of drift, as is also confirmed in experiments.