Anecdotal evidence is the use of personal experience as proof of an argument.
For example, my friend believes psychics are real because they have predicted her future correctly twice. Because she has experience with a psychic being correct, she refuses to believe studies that disprove their ability to see the future.
In this example, my friend refuses to believe that the psychic could have made a lucky guess, predicted something vague, or made an assertion that my friend forced to come true. For example, if the psychic predicted that she would meet her husband in New York City, then as long as my friend never left the city, the physic would be guaranteed to be correct. She values her personal experience above all other rationales. If we study the psychic’s predictions, we may find that she has a one in a thousand success rate. If my friend was her first and one-thousandth and first customer, then my friend would be confident her psychic is gifted while 1,999 other people would vehemently disagree.