Who can act? Critical assumptions at the foundations of statistical analysis

Peter J. Taylor

Original version July 2010


Thinking about a simple teaching example on the t-test for comparing the average (mean) for some measurement in a group versus the average in another led me to articulate a sequence of thoughts and questions about the foundations of statistical analysis. In particular, my inquiry explores contrasts between: the statistical emphasis on averages or types around which there is variation or noise; variation as a mixture of types; the dynamics (or heterogeneous mix of dynamics) that generated the data analyzed; and participatory restructuring of these dynamics in the future. Two key issues are: Who is assumed to be able to take action—who are the "agents"—and who are the subjects that follow directions given by others? What can it mean to explain differences among averages? Questions are noted to be addressed in a future supplement.