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The composite (superposed epoch) analysis technique has been frequentlyemployed to examine a hypothesized link between solar activity and the Earth'satmosphere, often through an investigation of Forbush decrease (Fd) events(sudden high-magnitude decreases in the flux cosmic rays impinging on theupper-atmosphere lasting up to several days). This technique is useful forisolating low-amplitude signals within data where background variability wouldotherwise obscure detection. The application of composite analyses toinvestigate the possible impacts of Fd events involves a statisticalexamination of time-dependent atmospheric responses to Fds often from aerosoland/or cloud datasets. Despite the publication of numerous results within thisfield, clear conclusions have yet to be drawn and much ambiguity anddisagreement still remain. In this paper, we argue that the conflictingfindings of composite studies within this field relate to methodologicaldifferences in the manner in which the composites have been constructed andanalyzed. Working from an example, we show how a composite may be objectivelyconstructed to maximize signal detection, robustly identify statisticalsignificance, and quantify the lower-limit uncertainty related to hypothesistesting. Additionally, we also demonstrate how a seemingly significant falsepositive may be obtained from non-significant data by minor alterations tomethodological approaches.

Composite analysis with Monte Carlo methods: an example with cosmic rays and clouds