Unless you believe that all anecdotal evidence is accurate, how do you decide which to believe and which to discard?
~~ Paul
Well, as I understand it in a jurisprudence setting (that's what I get for dating lawyers

), eyewitness testimony is only part of the package.
I saw him rob the bank;
she saw him rob the bank;
they saw him rob the bank, his fingerprints were there, his DNA was there, his alibi doesn't check out, the people who say they saw him are cross-examined, and through the adversarial justice system, things get settled one way or the other. The eyewitness testimony is questioned and examined and given the most skeptical treatment possible very extensively. One side is arguing against it passionately and presenting all evidence to discredit it. So that's the huge difference between eyewitness testimony in a court system and in a situation where someone's supposedly seen something "paranormal."
Then there's the issue of medical case studies based on a single person. The problem here is that we
do see a lot of weird medical claims (strange allergies, some bizarre substance being the cure for everything, vaccines causing autism, psychic surgery, we don't need to go through the whole list), and their claimed success is always based on dramatic improvement in individual cases. But there's a world of difference between these anecdotes and actual case studies. A good example is when one patient may have a reaction to a particular medication that's never been recorded before. This would be reported (probably by this person's doctor), and written up in a peer-reviewed journal. The author might have a hypothesis as to why this reaction happened, but it must be based on information already available. If it's a legitimate case study, others will come in to support it, the mechanism can be studied, and conclusions can be drawn. This is exactly what happened with the issue of certain fruits that absolutely should not be eaten with some very common drugs (Tegretol, the statins, and Seroquel being the main offenders.) Unfortunately, this information hasn't made its way down to the general public very well yet.
But evidence based on something that comes from a single individual doesn't work this way when applied to situations where paranormal claims are involved. So I don't think that the issue is
just the way that the claim that's being made; a lot of it has to do with the
type of claim that's being made. I would probably be just as suspicious of a study supposedly proving aliens that was promoted as double-blind and run by distinguished researchers.