1. Myths about the cosmic order are instinctive and reflect the geographic milieu, serve the economic and technical demands of the age and legitimate the the social order - community norms, mores, ethic and hierarchy. These instincts are experienced as compelling numinous images or symbols or enacted as rituals. They are either an emergent communal expression or left to shamans, chiefs or kings, or religious leaders to articulate and disseminate. In modern times, culturally significant artists may take the role of shamans. The myths change with historically significant changes in technology and trade.
TEST If this is true, disruptions in the mythic consciousness would cause psychological disturbances because the capacity for mythic instinct has ceased to be rooted in a social economy - powerful but pointless or counterproductive numinous symbols and rituals. This would imply that when there is any geographic or technical upheaval (positive or negative) that uproots people from their traditional (social and economic) ways and narratives, there will be increases in psychological malaise or social or cultural pathologies (e.g., fanaticism or collective cultural dispiritedness).
Also, if true, themes experienced in dreams of psychologically healthy people or explored in literature would symbolize key socio-cultural trends or turning points where adaptations were needed. Who has the interpretive key would, however, be a difficult question to answer. (Think of Ondaatje's English Patient as a story about the need for changes in the narrative around national (tribal) identities at a time of massive technical change, when production is becoming global, not local, and it makes sense. As you can tell, I consider the EP as a culturally significant work.)
2. Embedded in our myths is a vestigial primate-ness and an alpha-male motif.
TEST Ethological studies of hominid communication suggests hierarchy predominates in the "vocabulary" of our cousins (see Kenneally, The First Word). Robert Bellah, a sociologist of religion, explains the transformation of mythic consciousness over pre-history and history (Religion in Human Evolution). A study might focus on the parallels between hominid communication and human language, (e.g., consider the unquestioning subscription to the narrative of the "divine right of kings" and similar scripts, which is just not explainable by any individual's will to power, Ian Morris.) This might go some way to explaining modern gender imbalance (now eroding, thanks to mass clothing production, vacs and dishwashers, finally - quite a lag, though - right, Betty?)
3. Attempts at the scientific rendition of mythic terms should be abandoned (are you listening, Rupert Sheldrake?). However, the phenomena that such terms wrongly label may have yet some scientific explanation. For example, phenomena labelled "psychic" may indicate something very different from witchy receptivity to mysterious "energies". Lacking appropriate explanatory models, these phenomena are packaged in pseudo-scientific terms and are thus rapidly dismissed by the majority of self-respecting scientifically literate folks. I'm sure nevertheless there are many (if not all) people who experience correctly knowing or understanding something without being able to explain exactly how they do. Not all of these people would say they were "psychic". Imprecise forebodings and mysterious anticipations may be no more paranormal than bird navigation, snakes detecting earthquakes or the suddenly conscious conclusions drawn by our unconscious processes of assimilating vast amounts of past and present perceptual cues.
Once the epithet, "psychic" is dispensed with, scientifically inclined people should have little trouble finding evidence of people who have drawn correct conclusions on the basis of unconsciously gathering and assimilating information. (My suspicion would be that the instincts mentioned in 1 inflect this process and, when it goes awry, the person suffers from a psychological malaise. On the other hand, when the narrative sustaining the social order is no longer credible, a collective reaction formation (a.k.a. fanaticism) or a dispirited culture will be the result.)
4. In the same vein as 3, consider ghosts. Instead of thinking of a ghostly experience as evidence of displaced spirits, maybe time is multidimensional and can be layered. Vivid experiences that people mistakenly explain as ghosts may be hints of something occuring in a prior layer of time, a temporal echo. (Pure speculation, admittedly - spectral speculation.)
TEST "Ghost sightings" would be more likely when spatial arrangements have changed very little over the years/centuries; e.g., a "sighting" of a ghost (a temporal echo) on a stairway or coming through a door would be unlikely in a modern building because a modern and ancient building on the same property would not likely have had architectural features occupying the same space.
None of these tests would prove anything conclusively, of course. The two themes I have covered are human instinct and scientific reification. The latter covers all 4, the former, the first 3. I'm interested in having these themes pursued in more depth.