Read
Build the mental model
Move through the guided explanation first so the central distinction and purpose are clear before you evaluate your own work.
Inductive Logic
Causal Inference and Mill's Methods
Teaches the difference between correlation and causation, introduces Mill's methods for causal inference, and develops a rival-factor analysis routine students can apply to real causal claims.
Read the explanation sections first, then use the activities to test whether you can apply the idea under pressure.
Start Here
What this lesson is helping you do
Teaches the difference between correlation and causation, introduces Mill's methods for causal inference, and develops a rival-factor analysis routine students can apply to real causal claims. The practice in this lesson depends on understanding Causal Inference and Confounding Variable and applying tools such as Sample Quality and Relevant Similarity correctly.
How to approach it
Read the explanation sections first, then use the activities to test whether you can apply the idea under pressure.
What the practice is building
You will put the explanation to work through evaluation practice, quiz, diagnosis practice, analysis practice, rapid identification, and argument building activities, so the goal is not just to recognize the idea but to use it under your own control.
What success should let you do
Critique 4 causal arguments with explicit rival-factor analysis and proportionate conclusions.
Reading Path
Move through the lesson in this order
The page is designed to teach before it tests. Use this sequence to keep the reading, examples, and practice in the right relationship.
Study
Watch the move in context
Use the worked examples to see how the reasoning behaves when someone else performs it carefully.
Do
Practice with a standard
Only then move into the activities, using the pause-and-check prompts as a final checkpoint before you submit.
Guided Explanation
Read this before you try the activity
These sections give the learner a usable mental model first, so the practice feels like application rather than guesswork.
Core idea
Correlation is not causation
Two things can happen together without one causing the other. Ice-cream sales and drowning rates both rise in the summer, but ice cream does not cause drowning. Both are caused by a third factor — warm weather — that drives people to the beach and to the ice-cream stand. That third factor is a confounder, and recognizing confounders is the first step toward responsible causal reasoning.
Correlation is still useful as evidence. It is often the first clue that a causal relationship might exist. But it is only a clue. A responsible causal argument starts from correlation and then asks what else could explain the pattern before settling on a causal story.
What to look for
- Do not jump from 'X and Y go together' to 'X causes Y.'
- Ask what third factor could explain both.
- Ask whether Y might cause X instead.
Correlation is a starting point for causal reasoning, not its conclusion.
Practical method
The rival-factor routine
A simple routine for evaluating causal claims lists three rival explanations before accepting the proposed cause. The first rival is reverse causation: maybe Y causes X, not the other way around. The second is a common cause: maybe Z causes both X and Y. The third is coincidence: maybe there is no real pattern and the observed correlation is just noise in the data.
For each rival, ask what evidence would rule it out. If none of the rivals can be ruled out on the available evidence, the causal claim is not yet justified. If some can be ruled out, the claim becomes more plausible. This routine converts causal arguments from bold assertions into proportionate, evidence-based inferences.
What to look for
- Write down the proposed cause and effect.
- List reverse causation, common cause, and coincidence as rivals.
- Say what evidence would rule each rival out.
A causal claim earns its strength by surviving a rival-factor check.
Classical tools
Mill's methods
John Stuart Mill offered five classical methods for identifying causes, and two of them are central for beginners. The method of agreement notices that when multiple cases of an effect all share exactly one common antecedent, that antecedent is a candidate cause. The method of difference notices that when two cases are identical except for one factor, and the effect appears only where the factor is present, that factor is a candidate cause.
The method of difference is the intuition behind controlled experiments. Two groups are made as similar as possible, one gets the treatment, the other doesn't, and the outcome is compared. Randomized controlled trials are the clean modern form of this logic. When you cannot run an experiment, you reason observationally — looking for natural conditions that approximate agreement or difference.
What to look for
- For agreement: look for a shared factor across all cases of the effect.
- For difference: look for the one factor that distinguishes a case where the effect appears from an otherwise similar case where it does not.
- Use controlled experiments or natural experiments whenever possible.
Mill's methods formalize how to isolate causes by comparing carefully chosen cases.
Failure patterns
When causal claims go wrong
Post hoc ergo propter hoc treats temporal order as causal proof. Cum hoc ergo propter hoc treats simple correlation as causal proof. Single-cause fixation assumes that a complex phenomenon has one dominant cause, ignoring that many effects are products of multiple interacting factors. Spurious correlation happens when a pattern is real in the data but has no causal meaning — sometimes because of chance, sometimes because of shared trends over time.
The repair in every case is the same: go back to the rival-factor routine. Name the rivals, ask what rules them out, and state the causal conclusion proportionately. Sometimes the only honest conclusion is 'there is a correlation, but we cannot yet tell why.' That is a perfectly good inductive result.
What to look for
- Watch for 'before and after' claims without controls.
- Watch for 'together, so caused' claims without rivals considered.
- Be willing to stop at 'correlated but causally unclear' if that's where the evidence is.
Disciplined causal reasoning often concludes 'it's too soon to say' — and that's a real finding.
Core Ideas
The main concepts to keep in view
Use these as anchors while you read the example and draft your response. If the concepts blur together, the practice usually blurs too.
Causal Inference
Reasoning that moves from evidence to a claim about what caused a given outcome.
Why it matters: Causal claims require stronger standards than simple association — they have to rule out rival explanations.
Confounding Variable
A third factor that influences both the supposed cause and the supposed effect, producing a correlation that does not reflect direct causation.
Why it matters: Confounders are the main reason correlation is not causation; naming them makes hidden rivals visible.
Reference
Open these only when you need the extra structure
How the lesson is meant to unfold
Concept Intro
The core idea is defined and separated from nearby confusions.
Rule Or Standard
This step supports the lesson by moving from explanation toward application.
Worked Example
A complete example demonstrates what correct reasoning looks like in context.
Guided Practice
You apply the idea with scaffolding still visible.
Independent Practice
You work more freely, with less support, to prove the idea is sticking.
Assessment Advice
Use these prompts to judge whether your reasoning meets the standard.
Mastery Check
The final target tells you what successful understanding should enable you to do.
Reasoning tools and formal patterns
Rules and standards
These are the criteria the unit uses to judge whether your reasoning is actually sound.
Sample Quality
A broader and more representative sample usually supports a stronger generalization, and projection should not exceed what the sample warrants.
Common failures
- The sample is too small for the claim's scope.
- The sample is biased by self-selection or convenience sampling.
- The target population is much broader than the evidence allows.
Relevant Similarity
An analogical argument is stronger when the similarities cited are relevant to the conclusion and when important disanalogies are accounted for.
Common failures
- The similarities are superficial and not connected to the feature being projected.
- Important differences between the source and target cases are ignored.
Correlation Is Not Yet Causation
A causal conclusion requires more than noticing that two things occur together; rival explanations must be considered and ruled out.
Common failures
- A causal claim is drawn directly from a correlation.
- Confounders, reverse causation, and coincidence are ignored.
- A single case is treated as proof of a general causal pattern.
Proportionate Conclusion
The language of the conclusion should match the strength of the support — probably, likely, some evidence for — rather than bare assertion.
Common failures
- Expressing defeasible conclusions with certainty language.
- Making a universal claim on the basis of a limited sample.
Patterns
Use these when you need to turn a messy passage into a cleaner logical structure before evaluating it.
Sample-to-Population Generalization
Input form
natural_language_argument
Output form
structured_generalization
Steps
- Identify the observed sample.
- Identify the target population.
- State the projected conclusion.
- Evaluate sample size and representativeness.
- State the conclusion with appropriate caution.
Watch for
- Projecting beyond the evidence.
- Ignoring sample bias.
- Using certainty language for a defeasible claim.
Analogical Argument Schema
Input form
pair_of_cases
Output form
structured_analogy
Steps
- Identify the source case and its known features.
- Identify the target case.
- List the similarities claimed.
- Ask whether those similarities are relevant to the projected feature.
- List important differences that might block the projection.
- State the conclusion proportionately.
Watch for
- Citing similarities that have nothing to do with the projected feature.
- Omitting disanalogies that matter.
Causal Comparison Table
Input form
causal_claim
Output form
rival_factor_analysis
Steps
- State the observed correlation.
- List the proposed cause.
- List at least one rival factor or confounder.
- Compare the evidence for each possibility.
- State the conclusion proportionately.
Watch for
- Ignoring rival factors.
- Treating one pattern as conclusive proof of causation.
Worked Through
Examples that model the standard before you try it
Do not skim these. A worked example earns its place when you can point to the exact move it is modeling and the mistake it is trying to prevent.
Worked Example
Sleep and Performance — a walked analysis
Causal claims require stronger support than a simple observed correlation. Naming rivals and ruling-out evidence turns a bold claim into a defensible one.
Claim
Students who sleep more perform better, so sleep causes the improvement.
Rival Factors
- stress level — low-stress students may both sleep more and perform better
- course load — students with lighter loads have more time to sleep AND more time to study
- prior habits — conscientious students may both sleep on time and prepare earlier
Ruling Out Moves
- Measure stress and course load directly and see if the sleep-performance link survives controlling for them.
- Run a randomized intervention: assign one group a sleep-improvement protocol and compare performance changes.
Proportionate Conclusion
There is a correlation between sleep and performance, but causal strength is modest until confounders are controlled. An experimental study would provide much stronger evidence.
Worked Example
Mill's method of difference in a trial
This is why randomized experiments are causally strong: they embody Mill's method of difference.
Setup
A randomized trial assigns otherwise-similar patients to two groups. Group A gets drug X, group B gets a placebo. Group A recovers at twice the rate of group B.
Analysis
The two groups were made as similar as possible, so the main difference is the drug. Under Mill's method of difference, the drug is a candidate cause of recovery. Because assignment was random, confounders are distributed evenly, reverse causation is blocked by timing, and coincidence is made unlikely by the size of the effect.
Pause and Check
Questions to use before you move into practice
Self-check questions
- What evidence actually supports the causal conclusion?
- What rival factors have not been ruled out?
- Is the conclusion a cause-claim, or just a strong correlation?
Practice
Now apply the idea yourself
Move into practice only after you can name the standard you are using and the structure you are trying to preserve or evaluate.
Evaluation Practice
InductiveRun the Rival-Factor Routine
For each case, name the proposed cause, list at least two rivals (reverse causation, common cause, or coincidence), say what evidence would rule each rival out, and state a proportionate conclusion.
Four causal-claim cases
Some cases have defensible causal stories, some do not. Walk through the routine carefully before judging.
Case 1 — Sleep and grades
Students in a large university course who reported sleeping at least seven hours per night had higher average exam scores than students who reported less sleep. The study concludes that sleeping more causes better exam performance.
What confounders might drive both sleep and grades?
Case 2 — Ice cream and crime
Cities with higher ice-cream sales also have higher rates of violent crime in any given week. Therefore, ice cream somehow contributes to violent crime.
Is there a third factor that drives both?
Case 3 — New curriculum
A school district introduced a new math curriculum in September. By June, the average state test score had risen by four points compared to the previous year. The district attributed the improvement to the new curriculum.
What else might have changed between the two school years?
Case 4 — Vaccine and rash
In a controlled trial, children who received the new vaccine developed a mild rash at twice the rate of the placebo group within 24 hours of injection. The trial investigators concluded that the vaccine causes the rash.
What role does the control group play in blocking the usual rivals?
Use one of the cases above, identify the evidence base, and judge how strong the conclusion is once you account for rival factors.
Quiz
InductiveScenario Check: Causal Inference and Mill's Methods
Each question presents a scenario or challenge. Answer in two to four sentences. Focus on showing that you can use what you learned, not just recall it.
Scenario questions
Work through each scenario. Precise, specific answers are better than long vague ones.
Question 1 — Diagnose
A student makes the following mistake: "Treating correlation as if it were already proof of causation." Explain specifically what is wrong with this reasoning and what the student should have done instead.
Can the student identify the flaw and articulate the correction?
Question 2 — Apply
You encounter a new argument that you have never seen before. Walk through exactly how you would distinguish correlation from causation, starting from scratch. Be specific about each step and explain why the order matters.
Can the student transfer the skill of distinguish correlation from causation to a genuinely new case?
Question 3 — Distinguish
Someone confuses causal inference with confounder. Write a short explanation that would help them see the difference, and give one example where getting them confused leads to a concrete mistake.
Does the student understand the boundary between the two concepts?
Question 4 — Transfer
The worked example "Sleep and Performance — a walked analysis" showed one way to handle a specific case. Describe a situation where the same method would need to be adjusted, and explain what you would change and why.
Can the student adapt the demonstrated method to a variation?
Use one of the cases above, identify the evidence base, and judge how strong the conclusion is once you account for rival factors.
Evaluation Practice
InductiveStrength Ranking: Causal Inference and Mill's Methods
Rank these inductive arguments from strongest to weakest. Explain what makes one stronger than another.
Practice scenarios
Work through each scenario carefully. Apply the concepts from this lesson.
Argument 1
In a survey of 10,000 patients across 15 hospitals, the new treatment showed a 40% improvement over the control group.
Argument 2
My three friends who tried the supplement said they felt better, so the supplement probably works.
Argument 3
In every chemistry experiment conducted over 200 years, mixing sodium and chlorine has produced table salt.
Use one of the cases above, identify the evidence base, and judge how strong the conclusion is once you account for rival factors.
Diagnosis Practice
InductiveSample Critique: Causal Inference and Mill's Methods
Evaluate the sampling method in each scenario. Identify potential biases and suggest improvements.
Practice scenarios
Work through each scenario carefully. Apply the concepts from this lesson.
Study A
To learn about national reading habits, researchers surveyed visitors at a book festival and found that 95% read more than 10 books per year.
Study B
A tech company surveyed its own users about smartphone satisfaction and concluded that 88% of Americans are satisfied with their phones.
Study C
Researchers randomly selected 5,000 households from every state and conducted in-person interviews about dietary habits.
Use one of the cases above, identify the evidence base, and judge how strong the conclusion is once you account for rival factors.
Analysis Practice
InductiveAnalogy Builder: Causal Inference and Mill's Methods
Assess the strength of each analogical argument. Identify relevant similarities and differences, then explain whether the analogy supports the conclusion.
Practice scenarios
Work through each scenario carefully. Apply the concepts from this lesson.
Analogy 1
The human brain is like a computer. Computers can be reprogrammed. Therefore, human habits can be reprogrammed.
Analogy 2
A company is like a ship. A ship needs a captain. Therefore, a company needs a strong CEO.
Analogy 3
Earth and Mars are both rocky planets with atmospheres. Earth supports life. Therefore, Mars might support life.
Use one of the cases above, identify the evidence base, and judge how strong the conclusion is once you account for rival factors.
Evaluation Practice
InductiveDeep Practice: Causal Inference and Mill's Methods
Evaluate the inductive strength of each argument. Consider sample size, representativeness, and alternative explanations.
Complex inductive arguments
Rate each argument's strength on a scale of 1-5 and justify your rating with specific criteria.
Argument 1
A pharmaceutical company tested its new pain reliever on 200 adults aged 18-65 and found 78% reported reduced pain. They conclude the drug is effective for all adults.
Argument 2
Over 30 years of weather data from 50 stations show that average temperatures in the region have increased by 1.5 degrees Celsius. Scientists project this trend will continue.
Argument 3
A survey of 5,000 randomly selected voters across all states found 52% favor the policy. The margin of error is 1.4%. Political analysts predict the referendum will pass.
Argument 4
Every iPhone model released in the past 10 years has been more expensive than the last. Therefore, the next iPhone will be even more expensive.
Use one of the cases above, identify the evidence base, and judge how strong the conclusion is once you account for rival factors.
Evaluation Practice
InductiveReal-World Transfer: Causal Inference and Mill's Methods
Evaluate real-world inductive arguments from media, science, and daily life. Apply the criteria you have learned to assess their strength.
Induction in practice
Evaluate each real-world argument. Identify the type of induction and assess its strength.
News claim
A news article reports: 'Based on polling data from 1,200 likely voters in swing states, the candidate leads by 3 points with a margin of error of 2.8 points.' How strong is the inductive basis for predicting the election outcome?
Consumer reasoning
A product has 4.8 stars from 15,000 reviews on Amazon. A friend says: 'With that many positive reviews, the product must be excellent.' Evaluate this reasoning, considering potential biases in online reviews.
Scientific claim
A nutrition study followed 50,000 people for 20 years and found that those who ate fish twice weekly had 25% fewer heart attacks. The researchers conclude fish consumption reduces heart attack risk. What would strengthen or weaken this conclusion?
Use one of the cases above, identify the evidence base, and judge how strong the conclusion is once you account for rival factors.
Rapid Identification
InductiveTimed Drill: Causal Inference and Mill's Methods
Quickly classify each argument's inductive type (enumerative, analogical, statistical, causal) and rate its strength on a 1-5 scale. Speed and accuracy both matter.
Rapid inductive classification
Classify the inductive type and rate the strength (1-5) for each item. Target: under 45 seconds per item.
Item 1
The last 20 volcanic eruptions on this island occurred between March and June. The next eruption will likely occur between March and June.
Item 2
A clinical trial with 8,000 participants found the drug reduced symptoms by 35% compared to placebo, with p < 0.001.
Item 3
My neighbor's golden retriever is friendly. My cousin's golden retriever is friendly. Therefore, the golden retriever I meet at the park will probably be friendly.
Item 4
Every time the factory increased shifts, accident rates went up within two weeks. Adding a third shift will likely increase accidents.
Item 5
In a poll of 150 college students at one university, 73% supported the policy. Therefore, most college students nationwide support it.
Item 6
Countries that invested heavily in renewable energy in the 2010s now have lower energy costs. Investing in renewables lowers energy costs.
Use one of the cases above, identify the evidence base, and judge how strong the conclusion is once you account for rival factors.
Evaluation Practice
InductivePeer Review: Causal Inference and Mill's Methods
Below are sample student evaluations of inductive arguments. Assess each student's analysis: Did they correctly identify the argument type? Did they properly evaluate its strength? What did they miss?
Evaluate student analyses
Each student evaluated an inductive argument. Assess their work and identify what they got right and wrong.
Student A's analysis
Original argument: 'A survey of 200 Twitter users found 80% support the policy.' Student A wrote: 'This is a strong statistical argument because the sample size of 200 is large enough for reliable results.'
Student B's analysis
Original argument: 'The sun has risen every day for billions of years, so it will rise tomorrow.' Student B wrote: 'This is a weak inductive argument because past observations cannot guarantee future events. The sample is biased toward observed sunrises.'
Student C's analysis
Original argument: 'Rats given the chemical developed tumors. Therefore, the chemical likely causes cancer in humans.' Student C wrote: 'This is a strong analogical argument. Rats and humans share 85% of their genes, so results should transfer directly.'
Student D's analysis
Original argument: 'Five out of five mechanics I consulted said the transmission needs replacing.' Student D wrote: 'Strong inductive argument. Five independent experts agree, and mechanics have domain expertise. The only weakness is the small number of mechanics consulted.'
Use one of the cases above, identify the evidence base, and judge how strong the conclusion is once you account for rival factors.
Argument Building
InductiveConstruction Challenge: Causal Inference and Mill's Methods
Build strong inductive arguments from scratch. You are given a conclusion to support. Construct the best evidence, explain your sampling, and address potential weaknesses.
Build inductive arguments
For each conclusion, construct the strongest possible inductive support. Specify your evidence and methodology.
Task 1
Build an inductive argument supporting: 'Bilingual children develop stronger executive function skills.' Describe what study you would design, your sample, and why your evidence would be convincing.
Task 2
Construct an analogical argument that compares managing a sports team to managing a software development team. Make the analogy as strong as possible by identifying at least four relevant similarities.
Task 3
Build a causal inductive argument supporting: 'Reducing class sizes improves student performance.' Specify what data you would need and how you would rule out confounding variables.
Task 4
Create a strong statistical argument about voter turnout among young adults. Describe your sampling method, sample size, and why your approach avoids common biases.
Use one of the cases above, identify the evidence base, and judge how strong the conclusion is once you account for rival factors.
Diagnosis Practice
InductiveCounterexample Challenge: Causal Inference and Mill's Methods
For each inductive generalization, find or construct a counterexample that weakens the argument. Explain how your counterexample undermines the conclusion and what it reveals about the argument's limits.
Counterexamples to inductive generalizations
Each generalization seems reasonable. Find cases that challenge or refute it.
Generalization 1
Every tech startup that received Series A funding has gone on to achieve profitability. Therefore, receiving Series A funding leads to profitability.
Generalization 2
In every observed case, countries with higher education spending have higher GDP per capita. Therefore, increasing education spending will raise GDP per capita.
Generalization 3
All mammals observed so far give live birth. Therefore, all mammals give live birth.
Generalization 4
Every patient in the trial who received the drug recovered within a week. Therefore, the drug is an effective treatment.
Use one of the cases above, identify the evidence base, and judge how strong the conclusion is once you account for rival factors.
Analysis Practice
InductiveIntegration Exercise: Causal Inference and Mill's Methods
These exercises combine inductive reasoning with deductive logic, explanation assessment, or problem-solving. Apply multiple reasoning tools to reach well-supported conclusions.
Cross-topic inductive exercises
Each scenario requires inductive reasoning plus at least one other reasoning type.
Scenario 1
A study of 10,000 workers found that those who take regular breaks are 23% more productive. A company policy states: 'If a practice is shown to increase productivity by more than 15%, it shall be adopted.' Evaluate the inductive strength of the study, then apply the deductive rule to determine what the policy requires.
Scenario 2
Historical data shows that all five previous product launches in Q4 outperformed Q1 launches. Marketing proposes launching the next product in Q4. However, the market conditions have changed significantly due to new competitors. Evaluate the inductive argument and explain (abductively) why past patterns might not hold.
Scenario 3
A nutrition study found that people who eat breakfast perform better on cognitive tests. A school is considering a mandatory breakfast program. Evaluate the causal inference, identify confounders, and design a problem-solving approach to determine whether the program would work.
Use one of the cases above, identify the evidence base, and judge how strong the conclusion is once you account for rival factors.
Diagnosis Practice
InductiveMisconception Clinic: Causal Inference and Mill's Methods
Each item presents a common misconception about inductive reasoning or statistics. Identify the error, explain why it is wrong, and describe how the reasoning should actually work.
Common inductive misconceptions
Diagnose and correct each misconception about inductive reasoning.
Misconception 1
A student says: 'A larger sample size always makes an inductive argument stronger, regardless of how the sample was collected.'
Misconception 2
A student claims: 'Correlation proves causation as long as the correlation is strong enough. A 0.95 correlation coefficient means X definitely causes Y.'
Misconception 3
A student writes: 'An inductive argument with true premises and a true conclusion is a strong argument.'
Misconception 4
A student argues: 'Since inductive arguments can never be certain, they are all equally unreliable. You might as well flip a coin.'
Misconception 5
A student says: 'A single counterexample completely destroys an inductive generalization, just as it destroys a deductive argument.'
Use one of the cases above, identify the evidence base, and judge how strong the conclusion is once you account for rival factors.
Argument Building
InductiveScaffolded Argument: Causal Inference and Mill's Methods
Build inductive arguments in stages. Each task provides some evidence and a partial analysis. Complete the analysis, identify gaps, and strengthen the argument step by step.
Step-by-step argument strengthening
Complete each partial analysis and improve the argument at each stage.
Scaffold 1
Claim: Mediterranean diets reduce heart disease risk. Stage 1: You have observational data from 5 countries. Describe what this evidence establishes. Stage 2: You add a randomized trial with 7,000 participants. How does this change the argument? Stage 3: A meta-analysis combines 15 studies. What does the full evidence base now support?
Scaffold 2
Claim: Later school start times improve teen academic performance. Stage 1: One school district changed start times and saw GPA increase by 0.2 points. Evaluate this evidence alone. Stage 2: Three more districts replicated the result. How does this change your assessment? Stage 3: A nationwide study with controls for socioeconomic factors confirms the pattern. What is the argument strength now?
Scaffold 3
Claim: Urban green spaces reduce crime rates. Stage 1: You have a correlation between park density and lower crime in 10 cities. What can and cannot be concluded? Stage 2: A natural experiment -- a city builds parks in high-crime areas and crime drops. How much stronger is the argument? Stage 3: Multiple cities replicate with randomized neighborhood selection. Evaluate the full argument.
Use one of the cases above, identify the evidence base, and judge how strong the conclusion is once you account for rival factors.
Evaluation Practice
InductiveSynthesis Review: Causal Inference and Mill's Methods
These exercises combine all aspects of inductive reasoning: sampling, generalization, analogy, causal reasoning, and statistical evaluation. Each task requires integrating multiple skills.
Comprehensive inductive review
Apply all your inductive reasoning skills together.
Comprehensive 1
A government report claims: 'Based on a longitudinal study of 25,000 households across 50 cities over 10 years, households that adopted solar panels reduced their energy costs by an average of 40% and increased their property values by 8%.' Evaluate: (a) the sampling methodology, (b) the causal claim about cost reduction, (c) the causal claim about property values, (d) whether an analogical argument from these households to commercial buildings would be strong.
Comprehensive 2
Design a study to test whether flexible work hours improve employee well-being. Specify: (a) your sampling method and why it avoids bias, (b) what you would measure, (c) how you would control for confounders, (d) what conclusion different results would support, and (e) the limits of your study's generalizability.
Use one of the cases above, identify the evidence base, and judge how strong the conclusion is once you account for rival factors.
Argument Mapper
Build an argument diagram by adding premises, sub-conclusions, and a conclusion. Link nodes to show which claims support which.
Add nodes above, or load a template to get started. Each node represents a proposition in your argument.
■ Premise■ Sub-conclusion■ Conclusion
Animated Explainers
Step-by-step visual walkthroughs of key concepts. Click to start.
Read the explanation carefully before jumping to activities!
Further Support
Open these only if you need extra help or context
Mistakes to avoid before submitting
- Ignoring alternative causes or confounders.
- Assuming that any change after an intervention is caused by the intervention.
Where students usually go wrong
Treating correlation as if it were already proof of causation.
Ignoring alternative causes or confounders.
Treating a single year-over-year change as proof that one intervention caused the change.
Historical context for this way of reasoning
John Stuart Mill
Mill's methods of causal reasoning remain useful because they force us to compare patterns across cases rather than jump straight from correlation to cause. The method of difference, in particular, is the logical skeleton of the modern randomized controlled trial.