Can science prove the existence of God? (If one does an analysis of data to sort out noise similar to the analyzing of data from radio telescopes then science can pronounce that there is a decent possibility of a God).What kind of data can increase the possibility of gods? What kind of data can decrease the possibility of gods?
It is the same as the checking whether cell towers cause health problems.
One lists and records the narratives from people. A lot of people and a lot of towers. And one does the same for people not close to cell towers.
Then one puts on filters to rate the veracity of each narrative. Are the answers consistent with each other (one asks questions that should give similar answers but are differently phrased)? Eliminate those with inconsistencies. Check for known illnesses BUT check it the symptoms got worse. Check for speed of progression of illnesses since (IMO) the illness can be speeded up compared to non-tower cases.
Do a credibility test on each participant. Do they have a tendency to exaggerate? Do they have bad memories? Do they tend to guess an answer if they are unsure? One filters to get reliable data.
Do something similar with regular people. Give them questions with known wrong answers and see how they respond. Check for mystic experiences and see how many can be related to imagination or hallucination. Check for common threads, especially across different religions.
Example. I asked someone what evidence assured them that God existed. They thought carefully and then gave the example of a man who changed his career and dedicated his life to casting out demons in tribal villages in South Africa. He did so successfully. Some may not have been demons but may have been psychological and worked anyhow. I got a demon out a man - just by a heated interchange so I do not scoff.
When one has a filtered list then one needs to explain how such events can be "manufactured" by the brain. I do not believe that under normal everyday circumstances that a spontaneous hallucination occurs. What science is looking for is "glitches" in the fabric of reality.
The problem is having the study done properly and scientifically in a way that does not presuppose an outcome. Far too many scientific studies do this. It is easy to see the ones that are just done to get the grant money where students take supposedly random polls with so much irrelevant data.
One can do a scientific analysis of various aspects of the supernatural and check for inconsistencies and contradictions. One God or multiple Gods? One God with helper Gods/spirits? Good versus evil - is it evolution or damaged personalities or can people respond impulsively to a demonic suggestion? Reincarnation - logical when compared to billions of souls existing in a do-nothing state?
And so on.