That is all right. You and I do not have to play the definition game here. We both have strong understandings of what the other means by supernatural or super normal. It is best to limit the word games to take a serious look at these tough to analyze phenomena.
Putting trust in the numbers outputted is a tough one, because you also have to have some trust in the methods and corrections used to derive the values. To invent a category like Effect Size for Non Contact Therapeutic Touch, and to retain some kind of faith in the manipulated value down the line, takes a real creature of faith, not science, perhaps.
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In any case, here is the truth of it. The results are always borderline, never a smashing success that will convert throngs of skeptics once it is out. The results suggest more and better designed experiments might be a worthy enterprise for future researchers, they do not prove a thing, and only barely are strong enough to keep a discussion going.
Any alert follower is aware that these forces must be awfully weak, that is minute, in the human frame of experience. A person praying full time is not known to get results any different from the one praying only on his lunch break. That is a bet I would love to get a piece of. And I know there are plenty of deniers around who would bet on what they want to be true rather than what they suspect is true.
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I have not worked on any such studies, so I do not know the mechanics from the inside. What I suspect is one makes some awesome leaps of faith in assigning certain initial values in such a system. If a person wants to play word games in mathematics, statistics is the place to do it. The same techniques work exquisitely well when sampling products off an assembly line at random for testing. But these are not light bulbs but people and their consciousnesses in all their complexity. I would have great trouble putting faith in any statistical study of these matters. There are too many unknowns not represented in the equations. I would have to follow the study from beginning to end myself and participate in it it actively.
With any study of this complexity, fault could always be found.
The thing is, there is no study in all these links that converts anyone I can think of on the spot. If there are results that strong, I missed them. They all suggest more study might be in order or show positive results so small as to suggest that some other factor the experimenters have not considered may well be at work.
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Still--someone arguing for the results will say--the results are positive, and by the rules of the game agreed on large enough to be considered significant.
Fine, I say, for light bulbs.