Questions: Correlational Research Design

Question 1

A study finds r = −.80 between hours of TV watched per day and academic performance. A researcher concludes that watching TV causes students to perform worse. What is the fundamental problem with this conclusion?

• A. The correlation is negative, so it cannot indicate any causal relationship
• B. The sample size might be too small to trust the correlation
• C. The directionality and third-variable problems mean we cannot determine whether TV causes low performance, low performance causes more TV, or a third variable causes both
• D. A correlation of −.80 is too weak to support any conclusion

Answer: (C)

Even a strong correlation like r = −.80 cannot establish causation because of two problems: directionality (students performing poorly may turn to TV as an escape, reversing the causal arrow) and the third-variable problem (poverty or family instability might cause both more TV and worse academic performance). The strength of a correlation says nothing about the validity of a causal interpretation.

Question 2

Neighborhoods with more churches have lower crime rates. A city planner proposes building more churches to reduce crime. What is the most serious threat to this reasoning?

• A. The correlation might not replicate in different cities
• B. A third variable — such as community social cohesion or income — likely causes both more churches and lower crime, so the correlation tells us nothing about the effect of churches on crime
• C. Churches and crime are not measurable on the same scale
• D. The directionality problem — crime might be causing more church attendance

Answer: (B)

This is the third-variable problem (confounding): community stability, social trust, or income levels might cause both more religious institutions and lower crime, producing a correlation that has nothing to do with any causal effect of churches. The planner is treating the correlation as causal evidence when it may reflect a shared cause. This is the classic 'spurious correlation' pattern.

Question 3

A correlation of r = 0 proves there is no relationship between two variables.

• T. True
• F. False

Answer: False

A zero correlation proves there is no linear relationship — but a strong nonlinear (curvilinear) relationship can produce r ≈ 0. For example, the relationship between anxiety and performance is often described as an inverted U: performance increases with mild anxiety, then decreases with severe anxiety. This relationship would show r ≈ 0 even though the two variables are strongly associated. Always inspect scatterplots rather than relying solely on r.

Question 4

Correlational research is often the most appropriate design for studying the effects of childhood trauma, even though it cannot establish causation.

• T. True
• F. False

Answer: True

Researchers cannot ethically induce childhood trauma — random assignment is impossible. Correlational design allows researchers to measure naturally occurring variation in trauma exposure and examine its associations with outcomes. This is a genuine strength, not merely a compromise: studying variables that cannot be manipulated is one of the core reasons correlational designs exist. The limitation (no causal inference) must be stated explicitly, but the design itself is appropriate and often necessary.

Question 5

Explain why the symmetry of the correlation coefficient — the correlation between A and B equals the correlation between B and A — is a clue to a fundamental limitation of correlational research.

Model answer: Symmetry means the coefficient carries no information about causal direction. If r(A,B) = r(B,A), then the statistic itself cannot distinguish 'A causes B' from 'B causes A' from 'a third variable C causes both A and B.' The number summarizes the strength and direction of the relationship but is silent on causation. This is the directionality problem in mathematical form: no matter which variable you designate as predictor or outcome, the correlation is identical.

This is a useful way to remember the limitation: if the math can't tell the difference between 'A causes B' and 'B causes A,' the data can't either. Establishing causal direction requires additional evidence — temporal precedence (A must precede B), ruling out confounders, or experimental manipulation — none of which a correlation alone can provide.