The proof by example fallacy involves attempting to derive general conclusions from one or a few examples.
In its simplest form, proof by example works like this:
X, which is in the group G, has the property A. Therefore, all things in the group G have the property A.
Or, to give an extreme example, consider this illogical argument:
A car with Ohio license plates almost ran over me me. Therefore, people from Ohio are terrible drivers.
Such specious arguments may be the bread and butter of internet comment sections (not to mention racists and xenophobes everywhere), but they have no place in logical discourse.