seeing isn't believing, double blindness is

One tactic of persuasion often put forth in favor of the supernatural is a (deeply sincere) report of someone's own past experiences; appropriately, this category of evidence is called anecdotal. A confession of an occurrence--an anecdote--may seem quite convincing to the witness. After all, it's not a tangle of philosophical premises or an admonition to "just trust", but an observation of reality. "Seeing is believing."

However, scientific studies of complicated phenomena that are tied to human experience, such as medicine, use different standards. First, if at all possible, the observer or subject shouldn't be notified that he or she is expected to report a positive result. That is, the observers should be placed without their knowledge in one of two groups. One group is the "experimental" group, which is expected to give a real report. The second group is the "control" group, which is not really undergoing the same test but is nevertheless under that impression (in some cases with a placebo). This way, the effect of observer bias is "controlled for": the observations of everyone in the control group are only based on bias. Their incorrect assumption is that they are giving a real report. The observers or subjects don't have awareness of what they are "expected" to say, so they're "blind". This method is "single-blind".

Yet bias could still be creeping into the study. What if the conductors/interviewers of the study, due to their own awareness of which group each observer is in, influence what the observers say, no matter how subtly? The conductors of the study have their own stake or bias, after all. They want a cleanly definitive set of observations that match the reality of what is under study. Those in the control group should report negative results and those in the experimental group should report positive results. A better way is to also "blind" the conductors of the study such that nobody involved knows who is in which group until the analysis afterward. During the study, that information is stored separately. Since both sides aren't aware of whether a particular observation really supports what is under study, the method is "double-blind".

Data that supports the existence of the supernatural is either measurable or not. If the data isn't measurable, then it must consist of human observations. But if the data is human observations, then the data collection should be double-blind in order to eliminate bias as much as possible. If the data collection can't be double-blind, then it should be single-blind. If the data collection can't be single-blind, then its level of relative credibility is indeed low. The inherent inability to systematically eliminate bias from observations of the supernatural is partly why some people are skeptical.