  The composite (superposed epoch) analysis technique has been frequently
employed to examine a hypothesized link between solar activity and the Earth's
atmosphere, often through an investigation of Forbush decrease (Fd) events
(sudden high-magnitude decreases in the flux cosmic rays impinging on the
upper-atmosphere lasting up to several days). This technique is useful for
isolating low-amplitude signals within data where background variability would
otherwise obscure detection. The application of composite analyses to
investigate the possible impacts of Fd events involves a statistical
examination of time-dependent atmospheric responses to Fds often from aerosol
and/or cloud datasets. Despite the publication of numerous results within this
field, clear conclusions have yet to be drawn and much ambiguity and
disagreement still remain. In this paper, we argue that the conflicting
findings of composite studies within this field relate to methodological
differences in the manner in which the composites have been constructed and
analyzed. Working from an example, we show how a composite may be objectively
constructed to maximize signal detection, robustly identify statistical
significance, and quantify the lower-limit uncertainty related to hypothesis
testing. Additionally, we also demonstrate how a seemingly significant false
positive may be obtained from non-significant data by minor alterations to
methodological approaches.
