Correlation and Causation Walk Into a Tea Stall

It’s a Tuesday morning in the wet season. The kettle hisses. The fan turns slowly, though nobody needs it today. Viji has his 60-day notebook open, and for once the number in the margin is big.

He has been recording two columns since the rains began: ginger tea sold, and biscuit packets sold.

r = 0.72

He knows what to do with that number now. He learned it from Correlation herself, months ago, on a hot afternoon when his cousin’s theory about temperature collapsed at 0.18. A correlation of 0.72 is not 0.18. 0.72 is strong.

His cousin has already worked out what it means: “Brother, ginger tea pulls biscuits. Cut ₹5 off ginger tea. People buy the tea, then they want something to dip. You’ll sell biscuits all week.”

Viji has done the arithmetic. Biscuits carry his best margin. If ginger tea really pulls biscuits along behind it, the discount pays for itself twice over.

He has the discount board written and leaning against the counter, ready.

The awning drips.

Correlation steps in under it — calm, clear-eyed, holding only a glass of tea, exactly as she was the last two times. She looks at the board, then at the notebook, and says, “0.72. That is mine, and it is real. I measured it correctly.”

Viji says, “So the cousin is right.”

She says, “I did not say that. I said the number is real.” She sits down. “I only ever report that two columns move together. I have never in my life reported why.”

A man walks in under the awning behind her — solid, unhurried, dark green shirt, water running off his shoulders. He is carrying a heavy lever with a red handle, the kind bolted to a wall beside a machine. He sets it upright on the counter with a thud.

He says, “I am Causation. I have no interest in your notebook.”

Viji says, “It’s 60 days of data.”

“It is 60 days of watching. I do not watch.” He puts a hand on the red handle. “I pull. I change one thing on purpose, and I see what moves. That is the only way anybody has ever found me.”

In the corner, near the bench where the regulars sit, a third person shifts slightly. Viji has not noticed him. He has been there since before the post began.

Correlation speaks first

Correlation turns the notebook so both of them can see it.

She says, “Here is exactly what I found, and I want to be precise, because people put words in my mouth. On days when ginger tea sales were high, biscuit sales were usually high. On days when ginger tea was low, biscuits were usually low. They rise and fall together, 0.72 worth.”

Viji says, “And that’s the same as saying one pulls the other.”

“No. It is consistent with one pulling the other. It is equally consistent with three other stories, and my number cannot tell them apart.”

She counts them on her fingers.

“One. Ginger tea causes biscuits, which is your cousin’s story.

Two. Biscuits cause ginger tea. Somebody buys a packet, the biscuit is dry, they want something hot. The arrow runs the other way and my number looks exactly the same. That is reverse causality.

Three. Something else causes both. Neither column touches the other. A third thing lifts them both on the same days, and I see them dancing in step and report 0.72. That is a confounder.

Four. Chance. With 60 days and two columns, not likely here. But if you had gone hunting through 40 columns for something that moved with biscuits, you would have found one, and it would have meant nothing.”

She sips her tea.

“Here is my claim to dignity, and it matters, because people repeat correlation is not causation like a magic word and then throw me away. If all you want is to predict — to look at this morning’s ginger tea and guess how many biscuit packets to put on the shelf — I am enough. 0.72 is genuinely useful for that. I become dangerous only at the moment you stop predicting and start intervening. Your discount board is an intervention.”

Causation speaks

Causation taps the red handle.

He says, “Her four stories all fit the same notebook. No amount of staring at that notebook separates them, because the notebook records a world that was already running. To separate them, somebody has to reach in.”

He says, “So reach in. Take 10 days. Not 10 days you choose — 10 days drawn at random, the way she taught you to stir the pot. On those 10 days, put ₹5 off ginger tea. On the others, do nothing. Then compare.”

Viji says, “And if the cousin is right?”

“Then biscuits rise on the discount days and not on the others, and I will shake your hand. If the cousin is wrong, ginger tea will rise, because you made it cheaper, and biscuits will sit exactly where they always sat.”

Viji ran it over the next fortnight.

Ginger tea on discount days rose from 38 cups to 53 — a jump of 39%. The discount worked; people do respond to ₹5.

Biscuits went from 44 packets to 45.

Viji stared at the two rows for a while. His biscuit sales wobble by about 7 packets from day to day. 1 packet is not a result. 1 packet is nothing at all.

He says, slowly, “I moved ginger tea a long way. Biscuits didn’t feel it.”

Causation says, “Then ginger tea does not pull biscuits. Whatever she saw, it was not my arrow.”

The man in the corner

The person on the corner bench stands up, and Viji realises he has been there all morning.

He is broad, grey, and damp, in a heavy grey coat. He does not introduce himself. He simply points up, through the awning, at the sky.

Correlation says, “Ah. There you are.”

Viji says, “Who is he?”

She says, “He is the cold. He is the reason for my 0.72, and he has been sitting in your stall since the rains started.”

She takes the notebook and splits the 60 days into two piles by the reading on his wall thermometer: 26 cold days, 34 warm ones.

“On a cold day, people want ginger tea. On a cold day, people also stand about longer and buy biscuits. He lifts both columns with two separate hands, and neither hand touches the other.”

She computes inside each pile.

“Cold days only: r = 0.09. Warm days only: r = 0.11. The relationship inside each kind of day is almost nothing. My 0.72 came entirely from the gap between the two piles — cold days are high on both columns, warm days are low on both. Put the piles together and the two clouds line up into what looks like one beautiful straight line.”

Viji looks at the discount board leaning against his counter.

He says, “So if I’d run the discount, ginger tea would have gone up, biscuits wouldn’t, I’d have lost ₹5 a cup, and I’d have blamed the customers.”

Causation says, “And next winter, biscuits would have risen anyway, and you would have credited the discount.”

The same chat, in a chart

That picture is the same conversation, drawn. The first panel is what Viji saw: one cloud, one line, 0.72. The second panel is the same 60 dots with the thermometer switched on — two separate clouds, each of them flat. Nothing changed except that the cold is now visible. The little diagram underneath is the whole post: two arrows down, and the arrow the cousin believed in crossed out.

One last warning before they leave

Correlation finishes her tea and sets the glass down.

She says, “Two traps, and the second one catches the people who think they have already learned this lesson.”

“One. You can only account for the ones you wrote down. Viji was lucky — he had a thermometer on the wall, so the cold was a column he could split by. If he had never recorded temperature, the cold would still have been doing all the work, and no statistic in the world would have revealed it from those two columns alone. This is why I cannot be fixed by cleverness. Controlling for what you happened to measure is not the same as controlling for what matters.”

Causation says, “Two. Do not go the other way and throw every column you own into the model as a control. Some columns must not be controlled for. If a thing sits on the arrow — if the cold makes people linger, and lingering makes them buy biscuits — then lingering is a mediator, and controlling for it deletes the very effect you were trying to measure. There is a worse one still: controlling for something that both of your variables cause opens up a relationship that was never there. That one has a name, collider bias, and it is how careful people with clean data produce confident nonsense.”

Viji writes both down. Control for causes. Never for consequences.

The bill

They left the way people leave a tea stall in the rain, which is slowly. Causation shouldered his lever and went out into it without a word. Correlation finished her tea, said “see you when the ground dries”, and followed him. The grey man in the corner did not leave at all. He stayed until the season did.

Viji took the discount board out from where it leaned against the counter and turned it round. On the blank side he wrote the thing worth knowing: on cold days, fry more biscuits.

That is not a discount. It is a stock decision, and a stock decision only needs prediction, which is exactly what Correlation is good for. He could see the cold coming on the morning of, and 0.72 told him what to expect from it.

The cousin, inevitably: “So the ginger tea plan is off?”

Viji typed back, “Ginger tea sells more ginger tea. That’s all it does. The weather sells the biscuits.”

He turned to a fresh page in the notebook and wrote the sentence he wanted to keep:

Two columns moving together is a question, not an answer. To predict, watch. To act, pull a lever.

For the math-curious

What the correlation is actually reporting. Pearson’s r measures the strength of a straight-line relationship between two observed columns. Nothing in its formula distinguishes X → Y, Y → X, Z → X and Z → Y, or coincidence: $$ r_{xy} = \frac{\sum (x_i-\bar{x})(y_i-\bar{y})}{\sqrt{\sum (x_i-\bar{x})^2 \sum (y_i-\bar{y})^2}} $$ It is symmetric in x and y — swap the columns and the number does not move. A quantity that cannot tell which column you put first cannot tell you which way an arrow points.

Observing vs intervening. Causal work distinguishes the conditional distribution P(Y | X = x), which is what a notebook of past days reports, from the interventional distribution P(Y | do(X = x)), which is what happens when somebody reaches in and sets X. Confounding is precisely the case where these two differ. Viji’s discount fortnight estimated the second one; his 60-day notebook could only ever estimate the first.

Why randomising works. Assigning the discount to 10 randomly chosen days breaks every arrow that runs into the treatment. The cold cannot influence which days get the discount, because a coin decided it. Any remaining difference in biscuit sales must run from the discount. This is the entire logic of a randomised controlled trial, in a tea stall.

When you cannot randomise. Most real questions in management and economics do not allow a lever, so the field substitutes designs that imitate one: difference-in-differences, instrumental variables, regression discontinuity, propensity score matching, and fixed effects panels. Each buys causal interpretation with an assumption you must argue for, not test.

Which variables to control for. Draw the assumed structure as a DAG (directed acyclic graph) first, then read the adjustment set off it. Control for confounders (common causes). Do not control for mediators (variables on the causal path) if you want the total effect. Do not control for colliders (common effects) — conditioning on one induces a spurious association between its causes.

A useful sanity list. Before claiming causation from observational data, Bradford Hill’s considerations still earn their keep: strength, consistency across studies, temporality (the cause must precede the effect), a dose-response gradient, and a plausible mechanism. None of them is proof. Together they are an argument.

Correlation tells you the world has a pattern. Only a lever tells you what happens when you push on it.