Simpson's paradox in trend analysis: An example from El Leoncito airglow data

Abstract

We use our mesopause region temperature data from El Leoncito (31.8°S, 69.3°W) to illustrate how the increased length of the dataset alone does not simplify trend analysis. This is because the adequate interpretation of trend results does not only depend on the statistical characteristics of the data time-series. A longer dataset may make unexpected features stand out, which require an explanation before definite conclusions on long-term trends can be drawn. While the rotational temperatures derived at El Leoncito from the OH(6-2) airglow band appear rather homogeneous at first sight, the O2 temperatures measured with the same instrument and optical filter exhibit features strongly reminiscent of Simpson´s classical statistical paradox, in that straight-forward trends derived from parts show signs opposite to those of the complete data set. The resolution of this paradox requires more efforts to diagnose and remove the impact of instrumental artifacts besides taking any other geophysical variation that does not directly contribute to long-term change into account. Intercomparison with other instruments is certainly useful, but may warrant the elimination of new uncertainties discovered in the act.