Questions: Mediation Analysis and Indirect Effects in Causal Pathways

Question 1

A study finds that exercise (X) predicts lower depression (Y), that exercise predicts reduced inflammation (M), and that reduced inflammation predicts lower depression. A researcher claims inflammation mediates the exercise-depression link. What is the minimum additional analysis required to establish mediation?

• A. Confirming that all three correlations are statistically significant
• B. Showing that the direct effect of exercise on depression becomes non-significant when inflammation is controlled
• C. Estimating and testing whether the indirect effect (a × b, the product of the X→M and M→Y paths) differs significantly from zero
• D. Establishing that exercise was measured before depression in the study design

Answer: (C)

Showing that three pairwise correlations exist does not establish mediation — it only shows that the variables are related. Mediation requires specifically testing the *indirect effect*, the product of the a path (X→M) and the b path (M→Y controlling for X). This product captures whether the influence of X on Y actually flows *through* M. Modern practice uses bootstrapping to test whether the indirect effect's confidence interval excludes zero. The direct effect becoming non-significant (full mediation) is a possible outcome, but partial mediation is also valid — the indirect effect test is the core requirement either way.

Question 2

A researcher uses observational data to show that number of books at home (M) fully mediates the relationship between parental education (X) and children's reading scores (Y). She concludes she has identified the causal mechanism. Which limitation applies most critically?

• A. The analysis requires experimental data — observational mediation requires at least 1,000 participants
• B. She should have used the Sobel test rather than bootstrapping for more accurate inference
• C. Observational mediation cannot rule out unmeasured confounders — a third variable causing both M and Y would produce the same statistical pattern without genuine mediation
• D. Mediation analysis only applies when the mediator is a continuous variable

Answer: (C)

This is the fundamental limitation of observational mediation. A confounder — say, parental reading habits — could cause both more books in the home (M) and higher reading scores (Y) independently, producing a significant indirect effect even if books do not causally transmit the effect of parental education. The mediation model is statistically consistent with a causal mechanism but cannot distinguish it from confounding without experimental control. Experimental designs (manipulating both X and M in a 2×2 factorial) or at least longitudinal designs establishing temporal order are needed for stronger causal claims.

Question 3

Finding that X is correlated with M and M is correlated with Y is sufficient to establish that M mediates the X-Y relationship.

• T. True
• F. False

Answer: False

Three pairwise correlations are a necessary but not sufficient condition for mediation. The specific requirement is that the *indirect effect* (a × b) is significant — that the influence of X on Y specifically flows through M. For example, all three correlations could exist if M is simply a common correlate of both X and Y with no mediating role. Testing mediation requires the product of the a and b paths and bootstrapped confidence intervals to determine whether that product is reliably nonzero.

Question 4

In mediation analysis, the indirect effect is computed as the product of the a path (X→M) and the b path (M→Y while controlling for X).

• T. True
• F. False

Answer: True

The a path quantifies how much M changes per unit of X. The b path quantifies how much Y changes per unit of M, holding X constant (to isolate M's contribution net of any direct effect of X on Y). The product a × b represents the portion of X's total effect on Y that passes through M — the indirect effect. Baron and Kenny's original steps described mediation in terms of regression coefficients, and this product is now tested directly using bootstrapping rather than the Sobel test, which assumes a normal sampling distribution that often does not hold for products of coefficients.

Question 5

Why is experimental manipulation of both X and M stronger evidence of mediation than finding the same statistical pattern in observational data? What would an ideal experimental test of mediation look like?

Model answer: In observational data, any pattern consistent with X→M→Y could equally reflect confounding — unmeasured variables that affect both M and Y — making it impossible to conclude that M causally transmits X's effect. An ideal experimental test uses a 2×2 factorial design: X is randomly assigned (e.g., stress vs. no stress), and M is also manipulated independently (e.g., rumination induced vs. blocked). If the effect of X on Y is eliminated when M is blocked, and reintroduced when M is activated, this provides direct evidence that M is the causal mechanism — confounders are controlled by randomization and the mediating role is tested directly rather than inferred from correlations.

Experimental mediation designs (attributed to Spencer, Zanna, and Fong) provide what observational mediation cannot: causal identification. The logic is similar to surgical dissection — by manipulating the proposed mechanism directly, you can confirm or disconfirm that it is genuinely necessary for the X→Y effect. When full experiments are not possible, longitudinal designs at least establish temporal order (X before M, M before Y), which is a necessary if not sufficient condition for the causal chain.