Lecture: Causal Reasoning
Lecture script · about 15–20 minutes spoken · Week 10
Opening
Picture a friend who has worn the same striped socks to 3 exams and passed all 3. Before the next exam, the socks go on again. Or picture a headline that says people who use a fitness app are fitter. Each one takes a pattern and turns it into a cause.
That move shows up everywhere. A nursing student meets it in a headline that links a habit to better health. A business major meets it when someone asks whether an ad campaign caused a jump in sales. A city-planning major meets it in a warning that one budget cut will set off a chain of problems. In every case, the useful question is the same: what else could explain this pattern?
Here's where we are. Week 1 taught you to find an argument, and Week 2 to put it in standard form. Week 3 gave you strength and cogency for inductive arguments. Weeks 6, 7, and 8 showed how words, irrelevant reasons, and hidden assumptions lead an argument astray. Week 9 taught you to judge a sample and an analogy.
This week builds on Week 9. A causal claim usually compares two groups, and each group is a sample. We'll cover seven ideas: correlation and causation, a table that hides a third factor, two more rivals to a cause, a fallacy about order, the slippery slope, Mill's methods, and the controlled comparison.
1. A pattern is not yet a cause
Let's start on a rainy street. The houses with more umbrellas in the hallway also have wetter doormats. Nobody thinks umbrellas make doormats wet. Rain does both. You saw the rain, so you never made the mistake. In most claims you'll hear, the rain is hidden.
So here are two terms. A correlation is a pattern in which two things tend to go together, so that one shows up more often when the other does; a correlation by itself does not show that either one causes the other. A causal claim is a claim that one thing makes another happen, which says more than that the two tend to go together and so needs more than a pattern to support it.
Every correlation has three rivals to the causal reading. A confounding factor is a third factor that drives both of two things that go together, so that they move together even though neither causes the other. Reverse causation is the alternative in which the causal arrow runs the other way from the one claimed, so that the supposed effect is in fact the cause. And coincidence is a pattern between two things that arises by chance rather than from any causal link, most likely when the pattern rests on only a few cases.
Here's a small case. A roommate notices that the 2 times the campus coffee cart closed early, the vending machine broke that afternoon. The roommate decides the cart closing breaks the machine. A power outage could explain both. The arrow could run the other way. And 2 afternoons could match by chance.
Pause and try this. In the umbrella street, which of the three rivals explains the pattern?
Name the hidden thing before you go on.
Here's the answer. It's a confounding factor. Rain drives both the umbrellas and the wet doormats, so they go together even though neither causes the other.
Check the rivals first: a third thing, the reverse, or chance.
2. Holding one factor fixed
Now let's test a pattern with real counts. Picture a beach clinic that keeps a summer log. Each day it records whether ice-cream sales nearby were high or low, and whether the clinic saw many sunburn cases or few. The log is the course's hot-weather table. It's illustrative, built for teaching, and every number in it is pinned.
The table covers 100 summer days. 40 were hot, and 60 were mild. Of all 100 days, 50 had high ice-cream sales and 50 had low sales.
Start with the overall pattern. On high-sales days, 28 out of 50 had many sunburn cases. That's 56 percent. On low-sales days, 16 out of 50 did, which is 32 percent. So many sunburn cases go with high sales more often. That's a correlation.
Now hold temperature fixed. That means you compare only days that are alike in temperature, so temperature can't explain a difference.
Take the hot days first. There were 30 hot days with high sales, and 24 of them had many sunburn cases. That's 80 percent. There were 10 hot days with low sales, and 8 of them had many sunburn cases. That's also 80 percent.
Now the mild days. There were 20 mild days with high sales, and 4 of them had many sunburn cases. That's 20 percent. There were 40 mild days with low sales, and 8 of them had many sunburn cases. That's also 20 percent.
The gap disappears. Within hot days it's 80 and 80. Within mild days it's 20 and 20. So hot weather is the confounding factor behind both.
Why did the gap show up at all? Because the two groups of days weren't alike. Of the 50 high-sales days, 30 were hot, which is 60 percent. Of the 50 low-sales days, only 10 were hot, which is 20 percent. Hot days bring sunburn whatever the ice-cream sales.
Here's an honest limit. Holding one factor fixed rules out that one factor. A real study would check more than temperature.
Pause and try this. Someone says the table must contain a counting error, since the overall numbers seem to blame ice cream. Is that right?
Think about whether any single count was wrong.
Here's the answer. No, it isn't. Every count is accurate, and the flaw is in reading a cause from groups that differed in temperature.
Compare like with like; then see if the gap survives.
3. Flip the arrow, then count the cases
Picture an ad for a fitness app. It says its users are fitter than people who don't use it. The ad wants you to hear that the app makes you fit. Before you agree, turn the arrow around.
People who are already fit, or already training, are the ones who download a workout app. So the arrow could run from fitness to the app. That's reverse causation. The same shape shows up in a classroom. Students who sit in the front row may earn higher grades. But students who already care about their grades are the ones who choose the front row.
Coincidence is the third rival. Picture a city softball team that wins all 3 games a new mascot attends. A fan decides the mascot brings wins. But 3 games is a tiny sample, and a team can win 3 in a row with no help. That's Week 9's lesson again. Too small a sample can land on an unusual run by luck.
Pause and try this. In the front-row claim, which rival does the reverse question raise?
Say which way the arrow might run.
Here's the answer. It raises reverse causation. Caring about grades may lead students to the front row, rather than the seat leading to the grades.
Flip the arrow; then count the cases.
4. First is not the same as because
Back to the striped socks. Your friend wore them, then passed. The socks came first, and that order is the friend's whole case.
This mistake has a name. After this, therefore because of this (post hoc) is the fallacy of concluding that one event caused another only because it came first, with no comparison that rules out the other explanations.
Here's the course's passage, word for word. "I wore my lucky socks to the exam and passed, so the socks helped me pass." Find the support. It's only that the socks came first. Run the rivals. Studying, sleep, and the exam's difficulty all came first too. And nothing compares exams taken with the socks against exams taken without them.
So the only support is that the socks came first, and the passage commits after this, therefore because of this. Notice what the verdict doesn't say. As Week 7 taught you, a fallacy is a flaw in the reasoning, not a false premise. The premise is true: the socks were worn, and the exam was passed.
The neighbor that isn't a fallacy is a causal claim backed by a comparison. A clinic that compares people who got a treatment with people alike in other ways has more than an order of events.
Pause and try this. Is the socks passage fallacious because its premise is false?
Separate the premise from the step.
Here's the answer. No. The premise is true, and the flaw is the step from "came first" to "caused it", which is a flaw in the reasoning.
First is not the same as because.
5. One link at a time
Now picture a council meeting. A city council member warns that one budget cut will set off a chain of problems. You can't dismiss that warning on sight, and you can't accept it on sight either. You check the chain.
A slippery slope is an argument that predicts one step will lead through a chain of further steps to a bad outcome. It is reasonable when each link in the chain is backed by evidence and a fallacy when the links are not. An unsupported slippery slope is the fallacy of predicting that one step will set off a chain of further steps ending in a bad outcome when the links in that chain are not backed by evidence.
Here's the course's passage. "If we let students bring coffee into the library, next they'll bring full meals, then grills, and soon the building will burn down." List the links. Coffee leads to meals, meals lead to grills, and grills lead to a fire. Nothing backs any of them. So the passage commits the unsupported slippery slope.
Now the contrast, which we discuss but never grade. A warning says cutting the late-night bus route leaves late-shift workers without a ride, so some drive instead and late-night traffic rises. Each step is backed by the city's own ridership counts. Every link is supported, so it's a reasonable slope.
That brings the course's fallacy set to 19 passages keyed, with 1 still to come in a later week.
Pause and try this. Both the coffee passage and the bus warning predict bad consequences. What separates them?
Look at what stands behind each link.
Here's the answer. The bus warning backs every link with ridership counts, and the coffee passage backs none, so only the coffee passage is a fallacy.
Test the slope one link at a time, not all at once.
6. Mill's methods
Picture a neighborhood potluck. That night, several guests get sick, and everyone wants to know which dish did it. The way you'd sort that out has a long history.
Mill's methods are the methods for finding causes set out in Mill's A System of Logic (1843): agreement, difference, residues, concomitant variation, and a joint method of agreement and difference. Mill's own chapter speaks of four methods while stating five, so this course works and grades only the first two.
The method of agreement is the method of finding a likely cause by looking for the one factor that every case of an effect shares while the cases differ in their other factors. At the potluck, the sick guests ate different main dishes, desserts, and drinks. But every one of them ate the potato salad. So agreement singles out the potato salad as the likely cause.
The method of difference is the method of finding a likely cause by comparing a case with the effect and a case without it that are alike in every factor but one, which singles out that one factor. Picture two plants of the same kind, in the same soil, watered on the same days. One sits on the kitchen windowsill and stays green. The other sits above a heating vent and wilts. The one factor that differs is the heat.
You can name the other three without working them. The method of residues subtracts what known causes already explain. The method of concomitant variation links two things that change in step, and the hot-weather table showed why that kind of pattern still needs the confounding check.
Pause and try this. The two plants differ in only one listed factor. Which of Mill's methods is that?
Ask whether you're comparing many cases or one pair.
Here's the answer. It's the method of difference. A case with the effect and a case without it are alike in every listed factor but one.
One caveat. Each method is only as good as your list of factors. A factor you never listed could be the real cause.
7. Let chance pick the groups
Picture a tutoring center that wants to know whether its evening review sessions raise exam grades. Students who chose to attend did better than students who didn't. But the students who chose to attend may have been the most motivated. That's a confounding factor.
A controlled comparison is a comparison that holds other factors fixed, or spreads them evenly by random assignment, so that a difference in outcome can be traced to the one factor that differs. Random assignment is deciding by chance which cases get a factor and which do not, so that other factors, including ones no one thought to measure, end up spread evenly between the groups.
So the center holds what it can fixed: one course, one exam, the same material. Then a lottery decides who attends the sessions now and who attends later. Motivation, and every other factor, should split about evenly between the groups.
This is the step past Mill's methods. Agreement and difference work only on the factors you thought to list. Random assignment handles the factors you never thought of. It also cures the front-row claim: assign seats by lottery.
Pause and try this. Would comparing far more students fix the tutoring center's problem, if students still chose for themselves?
Think about how the groups were formed.
Here's the answer. No, it wouldn't. Size can't fix groups that chose themselves, and assignment by chance can.
Let chance pick the groups; hidden factors then split evenly.
Closing
Let me pull it together. A correlation is a pattern, and a causal claim says one thing makes another happen. Every correlation has three rivals: a confounding factor, reverse causation, and coincidence. In the hot-weather table, 56 percent against 32 percent became 80 and 80 on hot days and 20 and 20 on mild days, so hot weather, not ice cream, is behind the sunburns. The fitness app and the front row show the arrow can run backward, and 3 wins can be chance. Post hoc infers a cause from order alone. A slippery slope is a causal chain, and it's a fallacy only when its links lack support. Mill's method of agreement finds what the cases share, and the method of difference finds what the pair doesn't. A controlled comparison holds factors fixed or lets chance pick the groups.
Next in this module come the slide deck, the Readings and Resources page, the lecture tutorial, the practice set, and the quiz. Then, in Week 11, Numbers in the News states causal and sampling claims in risks and base rates.
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