# One of the main effects not significant, but interaction term significant

A is significant

B is not significant

A x B is significant

Do I say that

(1) There exists a significant moderation effect. In other words, the effect of B on the dependent variable significantly depends on A?

or do I say that

(2) There exists a significant moderation effect. In other words, the effect of A on the dependent variable significantly depends on B?

• What’s wrong with saying that one variable has a significant p-value, another valuable has an insignificant p-value, and their interaction has a significant p-value?
– Dave
Sep 30, 2022 at 5:09
• Thanks @Dave, I am overthinking this.
– nerd
Sep 30, 2022 at 6:07
• If it solves OP's problem, could you reframe your comment as an answer, @Dave? IMO, the comment clears the possibility of any ambivalence re the query in hand. Sep 30, 2022 at 6:15

Say that your underlying model looks like this:

$$y = a + b + a \times b$$

Then the following describes the same relationship

• the effect of B on the dependent variable depends on A

$$y = a + b \times (1+a)$$

• the effect of A on the dependent variable depends on B

$$y = b + a \times (1+b)$$

Whether you use the one or the other depends on how you want to accentuate the relationship. Besides the statistical relationship between the variables there might be some underlying causal principle. Often that principle is taken as deciding on what is being called the moderator.

### Example

For instance: the relationship might be the about the growth of tomato plants.

• 'y' is the yield of tomatoes
• 'a' is the type of plant
• 'b' is the amount of fertilizer that the plants get

Say that one type of plant grows a lot of roots and is able to do very well in poor soil, then this plant might perform better in low fertilizer conditions, but it has no advantage in high fertilizer conditions where all types perform well.

For this situation you can have two interpretations:

• The one plant has an advantage. But, with adding fertilizer to the soil, this advantage of the plant is reduced. Something like that might be considered as modifying the effect of the plant type.

• From another perspective, one might consider the effect of fertilizer and see how it influences the yield. Adding fertilizer improves the yield. But, the type of the plant changes the degree by which fertilizer has an effect.

So whichever you use 'b modifies a' or 'a modifies b' depends on what angle of approach you take in explaining the relationship.