Table 1.

Hypothetical Examples of XM interactions

Reasons	Hypothetical Examples
Theoretical Examples
Intervention changes mediator interest	Example: Program (X) affects tobacco use (Y) through changing interest in tobacco after offer (M)
	Control: M to Y relation is high
	Treatment: M to Y relation is reduced by program teaching participants to refuse tobacco offers
Intervention changes mediator meaning	Example: Program (X) improves participant’s diet (Y) through increasing health food knowledge (M)
	Control: M to Y relation is low
	Treatment: M to Y relation is increased by gaining knowledge about healthy diets
Intervention changes social context	Example: Program (X) changes the social context (M) to reduce fighting (Y)
	Control: M to Y relation is high
	Treatment: M to Y relation decreases after social competence passes a threshold
Methodological Examples
Longitudinal	Example: In a pre- and post-treatment study, there is change in M for the treatment, but M for the control group is stable
	Control: M to Y relation is low
	Treatment: M to Y relation is higher because of the increased variability in M
Nonlinear relations	Example: There is a nonlinear relation between M and Y, so the relation of M on Y depends on the value of M.
	Control: The M to Y relation is linear
	Treatment: Intervention changes the value of M, thus changing the linear relation between M and Y compared to the control group
Restriction of range	Example: The variability of M is non-constant across the observed values
	Control: The M to Y relation is the same as pre-intervention
	Treatment: Intervention changes M to a range of values where there is reduced (increased) variability, so the M to Y relation may artificially decrease (increase)
Measurement	Example: The intervention changes how participants in the study answer questionnaire items.
	Control: The M to Y relation represents typical response behavior
	Treatment: Intervention changes the way participants answer a questionnaire, endorsing items at a higher (lower) rate, so the M to Y relation may increase or decrease.

Note: The examples are for a binary X (treatment = 1 versus control = 0) not continuous X case, and are for different M to Y relations, not different X to Y relations.