Questions: Moderation and Interaction Effects in Conditional Relationships

Question 1

A clinical researcher finds that a stress intervention reduces cortisol by 15 points in older adults but increases cortisol by 3 points in younger adults. She reports 'a significant main effect of the intervention.' What is misleading about this summary?

• A. Nothing — the main effect correctly describes the average benefit of the intervention
• B. She should have reported mediation rather than a main effect
• C. The positive main effect obscures a disordinal interaction: the intervention helps one group but harms another, making the average misleading
• D. A crossover interaction means there is no moderation, only measurement error

Answer: (C)

A disordinal (crossover) interaction means the effect of the independent variable reverses direction across levels of the moderator. The positive average (main effect) is technically correct but practically misleading — it averages a helpful effect and a harmful effect together, concealing that the treatment is not uniformly beneficial. Reporting only the main effect hides the boundary condition that determines whether the intervention helps or hurts. This is the key reason moderation analysis matters: effects are not always constant across groups or conditions.

Question 2

In a regression model that includes both a main effect of X and an interaction term X × Z, how should the coefficient on X alone be interpreted?

• A. As the average effect of X on Y across all values of Z
• B. As the effect of X on Y when Z equals zero
• C. As the total effect of X on Y, controlling for Z
• D. As the interaction effect of X and Z combined

Answer: (B)

In a model with an interaction term, the coefficient on X is the conditional effect of X on Y when Z = 0 — not the average across all Z values. This is a critical technical point: if Z = 0 is not a meaningful value (e.g., Z is age in years, where 0 is not in the data), then the 'main effect' coefficient is not interpretable as a summary of the typical effect. This is why simple slopes analysis — estimating the effect of X at meaningful values of Z (e.g., Z = mean, ±1 SD) — is the standard follow-up to a significant interaction.

Question 3

A significant main effect of X on Y should exist before a significant interaction between X and Z can be found.

• T. True
• F. False

Answer: False

Interactions can occur without main effects. A crossover interaction, for example, can produce a positive effect in one group and a negative effect of equal magnitude in another, yielding a main effect of zero even though the interaction is strong. The presence or absence of a main effect is logically independent of the presence or absence of an interaction. This is explicitly listed as a common misconception in moderation analysis.

Question 4

Detecting a significant interaction in a regression model provides evidence that Z causally moderates the effect of X on Y.

• T. True
• F. False

Answer: False

A significant interaction coefficient shows that the association between X and Y differs across levels of Z — a pattern consistent with moderation. But association patterns, including interaction patterns, do not establish causation from observational data. The interaction could reflect a common cause, selection bias, confounding, or other non-causal mechanisms. Causal moderation claims require experimental manipulation of Z (or X) or strong causal identification assumptions.

Question 5

Why do moderation studies typically require much larger samples than studies designed to detect main effects, and what is the practical consequence of running an underpowered moderation test?

Model answer: Interaction effects are inherently smaller in magnitude than main effects (since the interaction only captures the differential — how much the effect changes across Z, not the effect itself), and detecting a smaller effect requires more statistical power. In simple cases, roughly four times the sample size is needed to achieve the same power for an interaction as for a main effect. An underpowered moderation test has high false-positive risk: noise in the data can produce a spurious crossing of the significance threshold, especially when multiple candidate moderators are tested. Underpowered interaction findings frequently fail to replicate, producing misleading 'for whom does this work?' conclusions that do not hold up.

The practical implication is that moderation hypotheses should be specified in advance (confirmatory rather than exploratory), tested with adequately powered samples, and reported with effect sizes alongside p-values. Post-hoc moderator fishing in underpowered datasets is one of the most common sources of irreproducible findings in psychology.