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Ghost in a Statistics formula?

The weirdest lawsuit ever!

Once upon a time in Delhi, a writer sojourned for a weekend at a Five Star hotel, “on a date with magic”.

Those were his exact words to his wife, who didn’t seem too impressed at the strange discourse!

“Date with magic, huh? I didn’t know that hotels admit clowns” was her retort.

But little did he know that a few weeks later, he would be suing the very hotel for “intentionally inflicting damage upon his mental health”.

“Please describe, in your own words, the events that have led you to sue the defendant”

Mr. Banerjee looked terrified. He had never been in a courtroom before, and now, just like that, he was fighting a court battle, against a 5-star hotel he had recently stayed in, over an incident that had since caused him to “sleep at night as much as your court delivers justice”.

“I had booked a weekend stay at Hotel Marigold. I have been suffering from writer’s block and thought that a prolonged stay in the lavish confines of a hotel was just what I needed to get the creative juices flowing. I picked this hotel because it is a work of art, has rooms with the best view of the city, and also happens to be a stone’s throw from my house. It was midnight. Around 3 am. I was sitting in the study in my hotel room, working on my next novel. I had kept the lighting dim, to supplement my feeling of seclusion. Suddenly, I sensed some movement in the oval-shaped mirror in the study, but when I looked up the mirror, there was nothing. So, I went back to my novel. Then, after another 5 minutes, something strange happened….”

His voice choked.

“Please take a deep breath, Mr. Banerjee, and tell us about the spooky event that happened next”, said the lawyer of the defendant, Mr. Iyer.

“Excuse me, sir, are you mocking me here?”, retorted Mr. Banerjee.

“No, sir. Not at all. I am merely asking you to continue”, said Mr. Iyer, in a calm, matter-of-fact tone.

“It-it started with the study lamp. It started flickering, which I thought might have been voltage fluctuation, still strange given the Hotel tariff-”

“Mr. Banerjee, what was the spooky event that happened next?”, Mr. Iyer quickly cut in, as if to quickly distract any attention from Marigold Hotel’s stiff room prices.

“Yes, mister, I am telling you precisely that, given you let me finish. It started with the study lamp. Then, the next minute, I heard the sound of a door opening, and it turned out to be the restroom door, which was now ajar. I was starting to feel a little scared. I decided to take a look. But, just as I got up, a magazine fell on the study from the wooden rack. I stopped in my tracks. It was one eerie incident too many now. My face was sweating now, my hands starting to tremble. It took me forever to turn around. But I did, and as I ever so slowly picked up the journal that had fallen, a small fragment of paper fell from in between the pages of the journal. And…there it was, written on the fragment in bold, blood-red ink -

His voice broke again, and this time he even started sobbing, eventually settling down after being given a glass of water.

“As it happens, Mr. Banerjee cleverly put that fragment of paper in his shirt pocket, and as a result, we now have our first evidence, which we would like to present in the court”, said Mr. Banerjee’s lawyer, as he passed the fragment of paper from his file to the judge.

The fragment of paper immediately generated interest and was switching hands very quickly. In no time, almost the entire court had had a look at it.

“Hmm, may we know what is so spooky about the letter p being less than 0.05?” asked the judge.

“My lord, this is an equation related to Hypothesis testing in statistics. Mr. Bannerjee has a firm belief that ghosts don’t exist. At least, he did…”

The lawyer cast a quick sideways look at his client with an expression of sympathy but went back to his speech after he caught the judge looking at him.

“Anyway. Let’s assume that his hypothesis is true. But, as we know, truth isn’t just black or white. It’s a spectrum…”

The lawyer again took a brief pause to take a gulp of water. The judge was now losing patience.

“Let’s assume for a minute that our Mr. Iyer is the CEO of a nuts and bolts company and not this mediocre advocate-”

“Objection, judge” barked Mr. Iyer in protest.

“Granted. No personal remarks, Mr. Rai.”

“Sorry, judge. Anyway, back to my point. If Mr. Iyer is told that the shipment received by him has bolts of diameter 5 cm, but the sample that he takes out of the bag measures 4.9cm, he may reason that it’s close enough to 5cm, and hence, the information conveyed to him is correct.”

“If however, the sample measures 4cm, he may reason that it deviates too much from the expected value, and deem the information incorrect.”

“Now, Mr. Iyer, being an optimist, was 95% confident that any deviation in the bolt size would be within a small, acceptable range. By that logic, if the bag indeed contained bolts of diameter 5 cm, the chances of getting the odd sample which deviated as much as 1 cm were less than 5%.”

“This less than 5% chance, judge, is our culprit, p-value!”

“Mr. Banerjee, prior to this incident, have you ever taken a stroll in the dark, alone?”.

“Yes. Plenty of times. There is this park close to my house where I frequently go at night. It is always deserted and gives me just the right ambiance-”

“Thank you, sir. Now, to understand this concept better, let’s each of us put ourselves in the place of poor Mr. Banerjee, who, for all his life, believed that ghosts didn’t exist, a thought which gave him the courage to wander in the dark at night, and to stay, all by himself, in a ghastly hotel room-”

“Objection, judge. Any opinions on my client’s hotel are not relevant to this case” Mr. Iyer interjected.

“Objection granted” the judge ruled.

“Anyway, what I was trying to establish was, Mr. Banerjee, when he checked into Hotel Marigold, was at least 95% confident that he wouldn’t be awakened by ghosts at night. But we all have some creepy encounters, doors making sounds at night, unusual silence, or seeing a face pop up suddenly out of nowhere, which challenge this safe assumption. But, ultimately, after a momentary lull, we come back to reality, in which ghosts are but a myth.”

“But this comforting thought can only hold good up to a certain limit, also called Confidence Interval in statistics. 95% of the events we encounter would fall in this comfort range. As we near the threshold of this limit, our face begins to sweat, hands tremble, and then, next thing you know, you are too scared to check if the pair of hands coming out of your shirt are indeed yours’-”

“Mr. Rai, stop right there! Please don’t challenge my safe assumption that you are fit to be an attorney!!”

“Sorry, judge. I perhaps got a little carried away there. What I meant was that the placement of statistical statement p less than 0.05 or 5% on the phantom note could have been done to communicate to Mr. Banerjee that what he was thinking in that eerie moment was true: his hypothesis that ghosts don’t exist could be wrong. Is that spooky, Mr. Iyer?”

Mr. Iyer said-“Mr. Banerjee, what kind of novel were you working on?”

“It’s a horror-thriller.”

“There you go, judge. This is it. Our writer here had stayed in a hotel, and was up at night, pushing his eerie imagination as far as he could. Suddenly, due to immense electrical overload, there was a brief flicker of light, then the restroom door snapped open, which by the way happens quite a lot, but which, in tandem with the flickering lamp, and the time on the clock, had induced enough fear in the mind of someone who was already imagining those very situations for monetary gain-”

“Objection, judge”, fired Mr. Rai.

“Overruled”, said the judge, who seemed almost intrigued now.

Mr. Iyer continued:

“Thank you, judge. What I mean to say is, when this statistical artifact found itself in Mr. Banerjee’s hands, his perception of fear had already peaked, pushing his belief that this was a coincidence, to the brink. A strange note was just a gentle nudge to tip him over.”

“A bizarre note scribbled with a statistical formula found in a hotel room of all places. And, in the context of the situation, its statistical meaning-this may not be a coincidence, just happens to aid in convincing the writer that something is indeed very fishy. What are the chances of that happening?” fired a still optimistic Mr. Rai.

“Mr. Rai, are you trying to suggest that someone voluntarily placed it there, like a murder weapon? Do you really think anyone other than a mad scientist would even care what p less than 0.5 means? And why would some mad scientist attempt to scare an unknown writer into believing in ghosts, in a 5-star hotel? I must say, I was expecting to be spooked out, but your story is hilarious!”

At this point, the judge decided that enough was enough. This case was heading nowhere.

“Alright, gentlemen. I have heard your arguments. But I am still trying to figure out where does the hotel come into the picture? What happened to Mr. Banerjee was most inconvenient, but how can we attribute it to the hotel? Table lamps flicker all the time. Likewise, restroom doors open. As for the note, can you prove that a hotel staff member voluntarily placed that note there?”

Mr. Rai replied flatly, “No, sir.”

“Well, then we don’t have a case here! One fine writer chooses to stay in a hotel, stays up at night, only to get spooked by a piece of parchment lying in a journal. That, Mr. Rai, is your whole case! Common, let’s not waste the court’s valuable time! I rule the defendant, Marigold Hotel, not guilty in the case of “intentionally inflicting damage upon Mr. Banerjee’s mental health”.

“However, I have not failed to observe that it was indeed unprofessional and unbecoming of a 5-star hotel to leave a piece of garbage lying in a journal. I order Hotel Marigold to pay damages to the tune of 500 Indian Rupees to Mr. Banerjee for poor room upkeep. The court is adjourned!”

Nobody left the courtroom happy.

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