I see much of the pseudo-science that is prevalent in the world as showing how many people do not have a good handle on what constitutes sufficient evidence. I’ve mentioned before that we seem to be hard wired to place a high value on anecdotal evidence, this would have been the only way to obtain such information for a large part of our history. There is no one type of evidence that will do for all situations, the evidence must fit the crime so to speak. For example, in the case of a medicine, appropriate evidence would be the existence of well designed double blind clinical trials. Such trials would have a large random population of subjects, would ideally include both placebo and non-intervention controls, would account for confounding factors such as age, race, and income etc and would finally make all of this available for inspection.
Evidence for such things as psychic phenomena would likewise need to include carefully controlled studies that showed reproducibility of the phenomenon. These studies would need to control for psychological biases on the parts of both the subjects and the researchers. It also needs to be clear what margin is indicative of a positive result, which requires an understanding of the likelihood of obtaining a false positive by chance.
To quote Carl Sagan “Extraordinary claims require extraordinary evidence” so it really depends on the claim how much and what kind of evidence is required. The claim that I’m a great dancer is unimportant so you may just believe me but if I were to say that I can travel into the future then you would want to have something more reliable than just my say so. Remember that we need to guard against our innate tendency to place great weight on stories, especially if they agree with how we think life’s narrative should go. So ask for proof, you may be surprised – Take my word for it?