Steven M. Boker - Theories, Methods, and Data: A Dance and a Conversation

Three dimensions of Cattell's persons by variables by time data box are discussed in the context of three types of researchers each wanting to answer their own categorically different question. The example of the well-known speed-accuracy trade off is used to illustrate why these exemplify three different categories of statistical question. A conceptual model is presented for the speed-accuracy trade off example that could account for cross-sectional between persons effects, short term dynamics, and long term learning effects. Two fundamental differences between the time axis and the other two axes of the data box include ordering and time scaling. In addition, non-stationarity in human systems poses a pervasive problem along the time dimension of the data box. To illustrate this, the difference in non-stationarity between dancing and conversation is discussed in the context of the interaction between theory, methods, and data. An information theoretic argument is presented that the theory-methods-data interaction is better understood when viewed as a conversation than as a dance. Entropy changes in the development of a theory-methods-data conversation provide one metric for evaluating scientific progress.