Correlation, Causation, and the Post Hoc Fallacy

Q1. The post hoc ergo propter hoc fallacy involves:

1. Assuming that what is true for a group is true for every individual in that group
2. Inferring that because one event preceded another, the first event caused the second
3. Drawing a general conclusion from too few examples
4. Assuming that two things that look similar must have the same cause

Q2. The ice cream and drowning example illustrates which error in reasoning?

1. The post hoc fallacy — because ice cream sales rise before drowning rates
2. Confusing correlation with causation — both variables are caused by a third variable (hot weather), not by each other
3. A sampling error — the data was collected only in summer months
4. Reverse causation — drowning rates actually cause ice cream sales to rise

Q3. The passage states that ‘causation does imply correlation.’ This means:

1. If two variables are correlated, one must cause the other
2. If one variable causes another, they will tend to occur together (be correlated)
3. Causation is a stronger form of correlation
4. Only correlated variables can be causally related

Q4. A researcher finds that countries with more hospitals per capita have higher rates of disease. They conclude that hospitals cause disease. What is wrong with this reasoning?

1. The researcher has committed the post hoc fallacy by noting that hospitals were built before the diseases arose
2. The researcher has confused correlation with causation and may have the direction of causation reversed — countries with more disease may build more hospitals to respond to need
3. The researcher has used too small a sample of countries to reach any conclusion
4. The researcher has committed the fallacy of composition by assuming what is true of individual hospitals is true of the system

Q5. The example of income and health outcomes illustrates which point from the passage?

1. That health is more important than income for predicting life outcomes
2. That causation can run in multiple directions simultaneously — income may cause health, health may cause income, and both may share a common cause
3. That international comparisons of income and health are unreliable due to differences in data quality
4. That correlation between income and health proves that wealth improves medical care

Q6. A student argues: ‘Every student who scored above 95 percent in Class 10 attended private coaching. Therefore, private coaching causes high scores.’ The most significant weakness in this argument is:

1. The sample of students may be too small to draw any conclusion
2. Correlation between attending coaching and scoring highly does not establish causation — students who attend coaching may also have other characteristics (parental income, motivation, prior achievement) that cause both the coaching attendance and the high scores
3. The argument assumes all students who attend coaching will score above 95 percent
4. The argument fails to account for students who scored above 95 percent without coaching