Reading on (you may want to read my previous post before this one), I found another beautiful example of hypothesis testing in literature with a pretty clear p-value calculation. I am now reading P. G. Wodehouse’s “Right Ho, Jeeves”, first published in 1934 I believe.
Without further preamble I shall briefly sketch the situation in the plot prior to the hypothesis testing bit. Bertram “Bertie” Wooster has just had a long conversation with Madeline Bassett to “pave the way” for Augustus “Gussie” Fink-Nottle to propose to her. During Bertie’s interchange with Madeline he learns that she is actually in love with Gussie already. When he then leaves her just as Gussie appears on the scene and leaves the stage to him, Bertie is convinced that “[a]s regards these two, everything was beyond a question absolutely in order” and that as he “legged it back to the house, the happy ending must have begun to function.” This establishes the null hypothesis: Gussie has proposed to Madeline and that his proposal had been accepted. This is the theory with which Bertie faces the evidence as it later presents itself to him.
The story then takes us briefly away from this scene for Bertie to deal with a relationship gone temporarily sour between two other characters, before it eventually takes us to the next meeting between Bertie and Gussie. One last note: Jeeves is Bertie’s highly competent valet and the story is told by Bertie himself.
The task now confronting Bertram was to put matters right, and I was pacing the lawn, pondering to this end, when I suddenly heard a groan so lost-soulish that I thought it must have proceeded from Uncle Tom, escaped from captivity and come to groan in the garden.
Looking about me, however, I could discern no uncles. Puzzled, I was about to resume my meditations, when the sound came again. And peering into the shadows I observed a dim form seated on one of the rustic benches which so liberally dotted this pleasance and another dim form standing beside same. A second and more penetrating glance and I had assembled the facts.
These dim forms were, in the order named, Gussie Fink-Nottle and Jeeves. And what Gussie was doing, groaning all over the place like this, was more than I could understand.
We here have the data: Gussie groaning all over the place. And already a hint of a p-value. Bertie cannot understand this data in the light of his null hypothesis. But there is more to come on this calculation:
Because, I mean to say, there was no possibility of error. He wasn’t singing. As I approached, he gave an encore, and it was beyond question a groan. Moreover, I could now see him clearly, and his whole aspect was definitely sand-bagged.
Bertie is making sure of the data. He is checking for possible mistakes in the data set, but has to accept the correctness of the data.
“Good evening, sir,” said Jeeves. “Mr. Fink-Nottle is not feeling well.”
Nor was I. Gussie had begun to make a low, bubbling noise, and I could no longer disguise it from myself that something must have gone seriously wrong with the works. I mean, I know marriage is a pretty solemn business and the realization that he is in for it frequently churns a chap up a bit, but I had never come across a case of a newly-engaged man taking it on the chin so completely as this.
Bertie, finally, computes the p-value, the probability of the data under the null hypothesis: Among all newly-engaged men (for which the null hypothesis is true) he has never seen one “taking it on the chin so completely”. As he has never seen such a thing under the null, one would expect he gives this behavior a very low likelihood under the null. With Bertie’s statement that he is also not feeling well he indicates that he has already rejected (or is afraid he will have to reject) the null hypothesis. Indeed the alternative hypothesis that something has gone badly wrong in the supposed proposal soon emerges as the truth:
Gussie looked up. His eye was dull. He clutched the thatch.
“Goodbye, Bertie,” he said, rising.
I seemed to spot an error.
“You mean ‘Hullo,’ don’t you?”
“No, I don’t. I mean goodbye. I’m off.”
“To the kitchen garden. To drown myself.”
“Don’t be an ass.”
“I’m not an ass…. Am I an ass, Jeeves?”
“Possibly a little injudicious, sir.”
“Drowning myself, you mean?”
“You think, on the whole, not drown myself?”
“I should not advocate it, sir.”
“Very well, Jeeves. I accept your ruling. After all, it would be unpleasant for Mrs. Travers to find a swollen body floating in her pond.”
“And she has been very kind to me.”
“And you have been very kind to me, Jeeves.”
“Thank you, sir.”
“So have you, Bertie. Very kind. Everybody has been very kind to me. Very, very kind. Very kind indeed. I have no complaints to make. All right, I’ll go for a walk instead.”
I followed him with bulging eyes as he tottered off into the dark.
“Jeeves,” I said, and I am free to admit that in my emotion I bleated like a lamb drawing itself to the attention of the parent sheep, “what the dickens is all this?”
“Mr. Fink-Nottle is not quite himself, sir. He has passed through a trying experience.”
I endeavoured to put together a brief synopsis of previous events.
“I left him out here with Miss Bassett.”
“I had softened her up.”
“He knew exactly what he had to do. I had coached him thoroughly in lines and business.”
“Yes, sir. So Mr. Fink-Nottle informed me.”
“I regret to say, sir, that there was a slight hitch.”
“You mean, something went wrong?”
I could not fathom. The brain seemed to be tottering on its throne.
“But how could anything go wrong? She loves him, Jeeves.”
“She definitely told me so. All he had to do was propose.”
“Well, didn’t he?”
“Then what the dickens did he talk about?”
And the wonderful stuff goes on and on.