Cherry picking: pointing to individual cases or data that seem to confirm a particular position, while ignoring a significant portion of related cases or data that may contradict that position
Perhaps even more importantly, they may be seeing unusual cases that are not representative of more “typical” cases in one way or another – a so-called selection bias.
Let us first examine the descriptions of what actually happened. A specific anecdote may be accurately observed and described, or not so accurately. If important details are altered or left out entirely, the anecdote may indeed be worthless. However, the exact same thing can be said about empirical studies.
If the data doesn't fit your pre-conceived conclusions, just change the subject!
Remember, there are NO empirical, double blind controlled studies on whether parachutes reduce the incidence of deaths or injuries after falling out of airplanes. Or that appendectomies are effective in preventing complications and deaths from appendicitis. And yet we all take those things for granted.