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.
Showing a random 20 of 50 problems.
Example 1
medium
List three explanations for why two variables might be correlated without one causing the other.
Example 2
medium
Smoking and lung cancer are correlated. Why do scientists accept this as causal?
Example 3
medium
Nations with more chocolate consumption win more Nobel prizes. Is chocolate a cause? Give a likely confounder.Chocolate consumption vs. Nobel prizes โ national wealth confounds both
Example 4
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 โ correlation is not causation
Example 5
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 6
medium
Cities with more pizza restaurants have more car accidents. Probable explanation?Pizza restaurants vs. car accidents โ population size drives both
Example 7
easy
In a randomized trial, half the participants get the drug at random. Why does randomization help support a causal claim?
Example 8
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 9
easy
What does "correlation does not imply causation" mean?
Example 10
medium
A nutrition blogger says "60% of disease-free people drank green tea, so green tea prevents disease." What is the main flaw?
Example 11
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 12
easy
Roosters crow before sunrise every day. Does crowing cause the sun to rise?
Example 13
easy
A controlled lab experiment shows pressing a button turns on a light. Is this causal?
Example 14
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 15
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 16
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 17
hard
A randomized trial finds the drug works in adults but only includes adults. Can we conclude it works in children?
Example 18
easy
Students who skip breakfast score lower on tests. Name one plausible confounder.
Example 19
easy
A study shows people who eat breakfast have higher GPAs. Does breakfast cause higher GPA?
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.'