Lost in state space? Methodological considerations in Complex Dynamic Theory approaches to second language development research

Since we can only make the observations our method allows us, we will have to adjust our method of investigation to the phenomena and questions we are interested in within the context and timescale of our focus. If we want to test hypotheses about the grand sweep effects of factors affecting language use at one moment in time, traditional group studies using statistics based on the Gaussian distribution are the most appropriate method. But if we are interested in investigating the changing relations in complex adaptive or dynamical systems, we should use nonlinear analyses of longitudinal data in which the denseness of the observations is adjusted to the expected rate of development. The resulting time series can then be analyzed using techniques that allow nonlinearity of the relations and that value variability as containing meaningful information. However, while there is general consensus about the requirements for traditional research in terms of the choice of parametric or nonparametric statistics, desirable power, effect sizes, and other conventions, the requirements and conventions for complexity research are not set. With the increasing popularity of complex dynamic approaches to second language development, and with more and more researchers applying complexity methodology, there is an urgent need for quality norms for this type of research. In this contribution I will make a modest proposal to some quality criteria in complexity research.