Well, if someone told me that an angel visited them, that would be anecdotal. if an angel visited ME, that would be strong evidence. if a guy came to my door saying he was an angel, I'd ask for strong evidence (fly in the air or something to that extent) before I took his word for it. (A sceen from Dogma comes to min when the voice of God appears in the woman's bedroom). I wouldnt accept "the guy down the street says I'm an angel" as strong evidence.
Strong evidence is something that can be duplicated through scientific experiments. Viewing an apple fall to the ground would be strong evidence that the earth has gravity. Being at a high enough altitude to see the curvature of the earth is strong evidence that the earth is round.
On a similar note: visitation from a leprachaun would change my beliefs on leprachauns. I dont believe in them now, but if one appeared to me and brought me to his pot-o-gold at the end of his rainbow, then i'll believe in him. Of course if I was taking hallucinogens at the time, i'd probably not trust my sensory devices.