moderation analysis

Question 1

moderation vs mediation

Answer 1

Moderation: “When does the relationship change”

Mediation: “Why does the relationship exist”

Question 2

moderation

Answer 2

Moderation occurs when the strength or statistical direction (positive vs. negative association) of the relationship between two variables depends on the level of a third variable (the moderator). In other words, the moderator variable affects when or for whom the relationship between the independent and dependent variables is strongest.

The Big Question: Does the relationship between X and Y change depending on the value of Z?

Question 3

moderation formula model

Answer 3

Y = B0+ B1X+ B2(Z) +B3(X*Z) + E

Question 4

moderation model key terms

Answer 4

𝛽1 : Main effect of X
𝛽2: Main effect Z
𝛽3: Interaction effect (moderation)

Question 5

breaking down the model

Answer 5

X = age

main effect: B1 - effect of X when is_qualitative = 0 (qualitative researchers)

is_qualitative main effect: B2 - effect of research type when X = 0

interaction effect: B3 - how much the age effect changes for qualitative researchers

Question 6

understanding the interaction plot / what to look for

Answer 6

parallel lines –> no moderation (interaction effect = 0)

non-parallel lines –> moderation present

different slopes –> the effect of age differs by research type

Question 7

separate analyses

Answer 7

Instead of one model with interaction, we can run two separate models:

For Quantitative Researchers Only:
𝑆𝑇𝑆=𝛽𝑞𝑢𝑎𝑛𝑡0+𝛽𝑞𝑢𝑎𝑛𝑡1×Age+𝜀

For Qualitative Researchers Only:
𝑆𝑇𝑆=𝛽𝑞𝑢𝑎𝑙0+𝛽𝑞𝑢𝑎𝑙1×Age+𝜀

Question 8

why this matters (approaches)

Answer 8

both approaches give the same answer:

1. One model with interaction: Tests if slopes differ significantly
2. Two separate models: Shows the actual slope values
3. The difference: Tells us the size and direction of moderation
4. Statistical test: Interaction model provides p-value for the difference

Question 9

the statistical problem

Answer 9

When you filter the data you are estimating separate slopes without formally testing whether those slopes differ statistically.

Question 10

what does the statistical problem mean

Answer 10

That means you lose:
1. The interaction term test, which is the formal test of moderation (e.g., age * gender).
2. Statistical power, because each subgroup model uses fewer observations.
3. Shared variance, because between-group variance is removed from estimation.

This can inflate standard errors and obscure small but meaningful interactions

Question 11

visual model of moderation (drawn)

Answer 11

Age (X) –> STS (Y)
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Research Type (M)

The effect of age (X) on STS (Y) depends on research type