Most of the story takes place between two characters, a fifteen-year-old girl called Vera and a man named Framton Nuttel. They are contrasting characters in almost every possible respect. She is an adolescent girl, he is a man about middle age. She is a member of the family, he is a visitor and a stranger. Most conspicuously, she is described twice as being "self-possessed," whereas Framton Nuttle is on the verge of a nervous breakdown.
It may be that the visitor's neurotic appearance and behavior gives Vera the idea of making him think her aunt is insane. She tells him that Mrs. Sappleton's husband and her two brothers were killed by being sucked into a bog three years earlier while out hunting. According to Vera, her aunt still leaves the tall French window open for them because she expects them to return for tea. Then when Mrs. Sappleton appears and starts talking about the three men, Framton naturally believes she is insane.
When the three hunters actually appear and are heading towards the open window carrying guns, Framton assumes they must be ghosts--especially since Vera, who has been so self-possessed, puts on an expression of horror as she stares incredulously at the open window. Framton flees from the haunted house. The reader has been taken in by Vera's story up to the point where the three men enter through the open window and prove to be very human and very much alive.
Mr. Sappleton asks:
"Who was that who bolted out as we came up?"
Mrs. Sappleton replies:
"A most extraordinary man, a Mr. Nuttel . . . could only talk about his illnesses, and dashed off without a word of good-bye or apology when you arrived. One would think he had seen a ghost."
Saki uses contrasting characters to make each more vivid to the reader. Framton's name seems like an anagram. In other words, the letters seem scrambled, just as his nerves are scrambled. His nervous character makes Vera seem all the more calm, cool, and collected, while her "self-possession" makes Framton seem all the more neurotic and jittery. When Mrs. Sappleton appears and Framton takes her to be insane, that demonstrates to the reader that Vera's story has thus far had its intended effect. So when the three hunters appear in the gathering darkness stalking towards the open window, it is quite plausible that Framton will react as he does because Vera has totally convinced him.