After reading Henry James's 1989 novel1a, The Turn of the Screw, and then comparing it to Jack Clayton's 1961 movie adaptation, The Innocents, I was convinced that Miss Giddens (Deborah Kerr) was of sane mind yet she was also witnessing the presence of spirits.
One reason that led me to believe the ghosts actually existed was that, when the governess spotted a man that was a complete stranger on the tower, the person looked like no other person she had ever seen. The person just stared back at the governess and then disappeared.
Another believable incident occurred when the governess spotted a person on the other side of the window in the dining room that looked like the same person she had seen on the tower at around the same time of hour and month. Once again the person just vanished into thin air.
Also, when the governess described the image of the person she had seen, Mrs. Grose (Megs Jenkins) said that she knew it was Quint (Peter Wyngarde), the former valet to the master and said that he was dead. It made the apparitions seem believable because the governess had never seen Quint but could describe what he looked like to Mrs. Grose.
Another convincing event happened when the governess could feel the presence of another unseen person, Miss Jessel (Clytie Jessop), while she and Flora (Pamela Franklin) were visiting the lake. The governess believed that the children simply ignored the presence of the apparitions but that they could actually see them.
A third encounter with the apparition happened inside of the house. The governess felt something astir in the house after everyone had gone to bed and found the apparition in the hallway on the staircase landing, and it was staring back at her.
I believe that both the book and the film did a good job at convincing me the audience member that the ghosts were in fact real and not a figment of Miss Giddens' imagination. The setups were effective to leave enough questions in the viewer or reader's mind so that the person had to make a decision of whether or not he or she believed in the ghosts. I enjoyed the suspension in both the book and the film and to say the least, I am a believer.