Once when I was younger my father told my brother, sister, and myself that there was a ghost story that happened in the family apartment in Chinatown. Apparently it had something to do with a friend who was visiting the family from out of town. The story took place in the 1950's or later, and whatever the friend experienced scared her enough that she left in the night and never returned.
For a long time, my father denied ever having mentioned that there was a ghost story. Only recently, and seeing that my siblings and I were grown, did he finally admit ever telling the story and give us the full story:
During the 1950's my grandparents still owned a large Chinese restaurant on Mott Street. Since it opened until very late, they often came home after closing around four in the morning. My father and his siblings often helped out working there, and would often come home late as well.
It just so happened that a friend of my aunt's was staying over that week. Since my aunt was busy working at the restaurant, her friend relaxed in the family apartment, which had a piano in the living room.
One evening, the guest was alone in the apartment and decided to play several songs on the piano. She knew that there was nobody in the apartment and played without disturbance.
At a certain point, the guest stopped playing and when she did, she heard the sound of someone clapping their hands in the same room with her. The guest knew that she was supposed to be alone in the apartment. She was so scared by this that she left before anyone from my family returned from work.
Through all the time that I had spent (with people and alone) in that apartment, I'd never experienced anything strange at all. One possible explanation may be the thin walls that the old buildings in Lower Manhattan have (the building was built in 1886), and the fact that someone in the building's stairwell could hear a lot of what's going on inside the apartment.
Could the guest have mistaken the sound of someone clapping in the stairwell with someone in the room? Or were the clapping hands so umistakably near that there was no mistaking that the invisible person was in the same room? Either way, my family jokes that my aunt's friend's piano playing must have been pretty good...