Start with the recap, study the fully worked examples, then use the practice problems to
check your understanding of Correlation vs Causation.
This page combines explanation, solved examples, and follow-up practice so you can move
from recognition to confident problem-solving in Statistics.
Concept Recap
Correlation shows that two variables move together in some pattern; causation means one variable actually makes the other change. Observing a correlation does not prove causation because a hidden third variable (confounder) may be driving both.
Ice cream sales and drowning deaths both increase in summer. Are ice creams deadly? No! A third factor (hot weather) causes both. This is why 'correlation = causation' - just because things happen together doesn't mean one causes the other.
Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea:Correlation vs Causation asks whether the same cases connect two variables or groups in a pattern that can be described carefully.
Common stuck point:Students often know a procedure related to correlation vs causation but skip the recognition step: Am I studying a relationship between variables, and have I separated association from causation? That leads to a calculation or graph that looks reasonable but answers a different question.
Sense of Study hint:Ask: Am I studying a relationship between variables, and have I separated association from causation?
Common Mistakes to Watch For
Before you work through the examples, skim the mistake guide so you know which shortcuts and
sign errors to avoid.
A study finds that towns with more ice-cream shops tend to have higher crime rates. Does this mean ice-cream shops cause crime? Explain.
Example 3
medium
A newspaper headline reads: 'Students who sleep more get higher grades — sleeping longer causes better academic performance!' Critically evaluate this claim.
Practice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easy
Ice cream sales and drowning deaths both rise in summer. Does buying ice cream cause drowning?Ice cream sales vs. drowning deaths — correlated but not causal
Example 2
easy
Cities with more police also have more crime. Do police cause crime?
Example 3
easy
Children with bigger feet read better. Does foot size cause reading skill?
Example 4
easy
In a randomized controlled trial, a drug group recovers more than a placebo group. Is a causal claim justified here?
Example 5
easy
People who use sunscreen get more skin cancer in a beach town survey. What hidden variable best explains this?Sunscreen use vs. skin cancer rate — sun exposure is the hidden confounder
Example 6
easy
Roosters crow before sunrise every day. Does crowing cause the sun to rise?
Example 7
easy
Students who skip breakfast score lower on tests. Name one plausible confounder.
Example 8
easy
Two variables are correlated. What is the minimum study design needed to support a causal claim?
Example 9
medium
Towns with more churches have more bars. Does building a church cause a bar to open? Identify the confounder.Churches vs. bars per town — population size drives both
Example 10
medium
A study finds people who exercise are healthier. A skeptic says healthy people are simply more able to exercise. What flaw does the skeptic raise?
Example 11
medium
Sales of a product rose after an ad campaign, but a competitor also went out of business that month. Can the ad alone be credited with the increase?
Example 12
medium
Nations with more chocolate consumption win more Nobel prizes. Is chocolate a cause? Give a likely confounder.Chocolate consumption vs. Nobel prizes — national wealth confounds both
Example 13
medium
A new tutoring program enrolls volunteers, who later outperform non-volunteers. Why can't we conclude the program caused the gain?
Example 14
medium
Higher umbrella sales coincide with more car accidents. Identify the confounder and state whether umbrellas cause accidents.Umbrella sales vs. car accidents — rain drives both
Example 15
medium
A headline says 'People who sleep 8 hours earn more.' List the three causal possibilities to consider before believing sleep raises income.
Example 16
medium
In an observational study, smokers have more lung cancer. What single feature would most strengthen a causal interpretation here?
Example 17
medium
Students who own more books score higher on reading tests. Name one plausible confounder and state whether owning books is proven to cause higher scores.
Example 18
challenge
Studies show coffee drinkers have higher heart-disease rates, but coffee drinkers also smoke more. After adjusting for smoking, the coffee effect vanishes. What does this reveal about the original correlation?
Example 19
challenge
A city raised its minimum wage and unemployment rose the same year a recession hit the whole country. Design the comparison that would best isolate the wage policy's effect.
Example 20
challenge
Two variables X and Y are strongly correlated. Propose a concrete test using a new intervention that could distinguish 'X causes Y' from 'a confounder causes both.'
Example 21
easy
A study shows people who eat breakfast have higher GPAs. Does breakfast cause higher GPA?
Example 22
easy
In a randomized trial, half the participants get the drug at random. Why does randomization help support a causal claim?
Example 23
easy
Countries with more cell phones per person have higher life expectancy. Is owning a cell phone causing longer life?Cell phones per person vs. life expectancy — not causal
Example 24
easy
A controlled lab experiment shows pressing a button turns on a light. Is this causal?
Example 25
easy
People who get more sleep have higher productivity. Could productivity be causing the sleep instead?
Example 26
medium
Towns with more libraries have lower crime rates. Suggest a likely confounder.
Example 27
medium
In a randomized double-blind trial, drug X reduces blood pressure more than placebo. Can the study support a causal claim that drug X lowers blood pressure?
Example 28
medium
More students who tutor others also score well on a test. Identify two possible explanations besides "tutoring causes high scores."
Example 29
medium
Cities with more pizza restaurants have more car accidents. Probable explanation?Pizza restaurants vs. car accidents — population size drives both
Example 30
medium
A nutrition blogger says "60% of disease-free people drank green tea, so green tea prevents disease." What is the main flaw?
Example 31
medium
In a study, students assigned at random to a new study app scored higher on math tests than those assigned to the old app. Can the school claim the new app improves scores?
Example 32
medium
As shoe size grows, reading ability grows in elementary kids. Is shoe size causing reading? Name the lurking variable.Shoe size vs. reading ability — age is the lurking variable
Example 33
medium
Smoking and lung cancer are correlated. Why do scientists accept this as causal?
Example 34
hard
A scatter plot of teacher salary vs. student test scores in a country shows a strong positive correlation. Is paying teachers more guaranteed to raise scores?Teacher salary vs. student test scores — correlation is not causation
Example 35
hard
A study finds antidepressant users have higher suicide rates than non-users (observational). A naive reading: antidepressants cause suicide. What is the more plausible explanation?
Example 36
hard
A randomized trial finds the drug works in adults but only includes adults. Can we conclude it works in children?
Example 37
hard
Children in a town with a new park playground have lower obesity rates. A study compares before vs. after. What additional comparison would strengthen a causal claim?
Example 38
hard
News headline: "Drinking 8 glasses of water daily linked to lower stress." The study was observational with no control. Name two reasonable critiques.
Example 39
challenge
A study finds r=0.92 between US cheese consumption per capita and the number of people who died by becoming tangled in their bedsheets. What does this imply?
Example 40
medium
Data shows that countries with higher chocolate consumption per capita have more Nobel Prize winners. A blogger writes: 'Eating chocolate makes you smarter!' Give two reasons why this conclusion is flawed.
Example 41
hard
A pharmaceutical company observes that patients who take their new supplement have lower rates of heart disease compared to those who don't. The company wants to claim the supplement prevents heart disease. What type of study would provide the strongest evidence, and what conditions must it satisfy?