# Does the result of “interaction” tell whether nor not the moderator variable worked?

I’m reading a research paper and the author prepared two print-advertisements of jam, one with an old lady (Ad1) the other one with an exotic lady (Ad2). Both print-advertisements (Testanzeige) have the same written information.

Hypothesis: With the increase of the need for variation (CSI), the Advertisement Attitude to the print Advertisement, in which the product was exotic presented, would increase too.

After a factor analysis the Advertisement Attitude was divided into two factors: amusement (Unterhaltungswert on the left column) and credibility (Glaubwuerdigkeit on the right column).

Based on this table, the author wrote:

The hypothesis, that the need for variation (CSI) has a moderation effect on the Advertisement Attitude Is rejected for the factor amusement Is supported for the factor credibility

So I assume I should watch $0.82$ and $0.121*$

What I cannot understand:

1.The original hypothesis is about the print advertisement which was exotic presented, but the table presents the total results, it that possible I can somehow tell from the results of the interaction that this is indeed for the the Ad2? (Absolute no information about that in the study)

2.The original hypothesis is about the impact of CSI on Ad Attitude, shouldn’t I watch the results from CSI $(-0.072, -0.064)$? I assume I should watch the results of the interaction because CSI is moderator?

3 How should I interprete the first row: Testanzeigen (Print AdvertisementS) $(,093* -,028)$ ? The scores from the objects' attitude to BOTH advertisements?

• The table is on page 17 of this document in case if you'd like to see the full text in German. – Penguin_Knight Jun 23 '14 at 18:59
• You're welcome. By the way, my vote is exotic lady = 1 and old lady = 0. I will be very amused to see a young lady wearing bikini while spreading jam on a toast (WHY is she doing that?); but on any day I'll actually eat the jam toast prepared by an old lady. – Penguin_Knight Jun 23 '14 at 19:10
• @Penguin_Knight So if I understand you correctly, the variable of Testanzeige should be either 1 or 0, right? How should the regression looks like? Y (Ad-Attitude) = b0+ b1*X1(Ad,the variable is either 1 or 0)+ b2*X2 (CSI)+b2*X1*X2 +error – yue86231 Jun 23 '14 at 19:23
• @Penguin_Knight That means, to my third question: ,093 is how the type of Ad impacts the Ad-Attitude, did I interprete it correctly? – yue86231 Jun 23 '14 at 19:35
• PS: Is Ad type a dummy variable in this context? – yue86231 Jun 23 '14 at 19:43

Let's just focus on credibility for now, they are the same model so no need to duplicate the effort.

The regression is:

$y = \beta_0 - 0.028 Ad- 0.064 CSI + 0.121 Ad\times CSI$

If Ad1 = 0 and Ad2 = 1, and if CSI low = 0 and CSI high = 1:

For Ad1, low CSI:

$y_{Ad1, Low} = \beta_0$

For Ad1, high CSI:

$y_{Ad1, High} = \beta_0 - 0.064$

For Ad2, low CSI:

$y_{Ad1, Low} = \beta_0 - 0.028$

For Ad2, high CSI:

$y_{Ad2, High} = \beta_0 - 0.028- 0.064 + 0.121$

Using this substitution method, you should be able to figure out the differences. Notice that the result can change if they use 1/2 coding instead of 0/1.

If Ad1 = 1 and Ad2 = 2, and if CSI low = 1 and CSI high = 2:

For Ad1, low CSI:

$y_{Ad1, Low} = \beta_0 - 0.028- 0.064 + 0.121$

For Ad1, high CSI:

$y_{Ad1, High} = \beta_0 - 0.028 - 2\times 0.064 + 2\times 0.121$

For Ad2, low CSI:

$y_{Ad1, Low} = \beta_0 - 2\times 0.028- 0.064 + 2\times 0.121$

For Ad2, high CSI:

$y_{Ad2, High} = \beta_0 - 2\times0.028- 2\times 0.064 + 4\times 0.121$

So, figuring out the coding is crucial. Most of the time we would model binary as 1/0, and you may either make the same assumption or contact the authors.

• Thanks Penguin_Knight very much for the explaination, now I understand the results with the interaction. But I cannot understand why CSI is the moderator, the type of Ad could also be the moderator, couldn't it? – yue86231 Jun 23 '14 at 20:02
• ^ Yes, you're correct. – Penguin_Knight Jun 23 '14 at 20:04
• So there is no rule which variable should be the moderator, actually they could all be seen as normal independent variables. The "moderator" is just a title we randomly give them. The interaction is the main point to watch, not who the moderator is. – yue86231 Jun 23 '14 at 20:08
• ^ Yes and no. In epidemiology (my own field), interaction is used to test effect modification, and not moderation. When we talk about moderation, it's more aligned with "mediation/moderation analysis", which is a special type of regression that does require the users to specify which one is the moderator. If the authors just used interaction term and call it a "moderation test," I'd consider that a misnomer or loss in translation. – Penguin_Knight Jun 23 '14 at 20:13
• And what you said is largely correct. CSI could have modified the effect of Ads, and Ads could have modified the effect of CSI on the factor score. When there is a significant interaction, interpret the main effect AND the interaction because main effect alone is no longer universally applicable. – Penguin_Knight Jun 23 '14 at 20:18