Actually.. that is the precise definition of anecdotal. You may be thinking of "hearsay", which is a legal term for unreliable evidence relying on second hand reporting.
In medical research, anecdotal evidence is "I gave my patient X drug, and it cured Y disease", or "I gave these three patients X drug, and it cured them". It is considered interesting, in terms of stimulating research, but totally invalid in terms of demonstrating or refuting benefit.
In order to actually demonstrate the benefit of a particular intervention, one would need to say something like: "We gave 10 patients with this disease drug X, and another 10 patients with the same disease drug Y, and a third group of 10 patients a sugar pill. 9 out of ten patients in the first group were cured, but only 2 of ten in the second two groups were better". (I won't go into the details of double blinding, etc..).
SO, what we really need is some sort of study that says "We looked at 5 Caribbean islands frequented by divers with similar populations of visitors and locals, and found out that on Bonaire there were 51.8 thefts per 1000 person-weeks, while on Roatan the number was 9.5. However, there were 1.2 cases of armed robbery per 1000 person-weeks on Bonaire, as compared to 3.1 on Roatan".
THEN you could make an intelligent decision on where you want to dive, depending on (a) how much gold bullion you routinely leave in your dive bag, and (b) whether or not you hold advanced martial arts training and have a kevlar wet suit...