Interpreting Interactions when Main Effects are Not Significant

by Karen Grace-Martin

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If you have significant a significant interaction effect and non-significant main effects, would you interpret the interaction effect?

It’s a question I get pretty often, and it’s a more straightforward answer than most.

There is really only one situation possible in which an interaction is significant, but the main effects are not: a cross-over interaction.

Unlike many terms in statistics, a cross-over interaction is exactly what it says: the means cross over each other in the different situations.  Here’s an example of a two-by-two ANOVA with a cross-over interaction:
crossover-interaction
The two grey dots indicate the main effect means for Factor A.  Their height is pretty much the same, so there would be no main effect for Factor A.

The two grey Xs indicate the main effect means for Factor B.  Sure, the B1 mean is slightly higher than the B2 mean, but not by much.  In most data sets, this difference would not be significant.

But there clearly is an interaction.  The difference in the B1 means is clearly different at A1 than it is at A2 (one difference is positive, the other negative).

So yes, you would would interpret this interaction and it is giving you meaningful information.

What does it mean?  You’d say there is no overall effect of either Factor A or Factor B, but there is a crossover interaction.  The effect of B on the dependent variable is opposite, depending on the value of Factor A.

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{ 8 comments… read them below or add one }

PC Lin September 4, 2016 at 8:59 pm

Dear Karen, I have two independent variables and one dependent variable. At first, both independent variables explain the dependent variable significantly. However, when we add in the moderator, one independent become insignificant. Should I remove the insignificant independent variable? It seems to me, when I run regression using the whole data (n=232), both independent variables predict the dependent variable. When I use part of the data (n1= 161; n2=71) to run regression separately, one of the independent variable became insignificant for both partial data. How to explain it? Thank you very much.

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Danish August 19, 2016 at 3:28 pm

Dear Karen, i have 3 dependent variables (attitude towards the Ad & Brand and purchase intentions) my independent variables is Endorser type( one typical endorser and 2 celebrity endorser), I ran two way manova to find out whether there is a significant Endorser type*Gender interaction, which was found to be not significant, but the TEST BETWEEN SUBJECT table is showing significant interaction effect for PI, please tell me how to present this result.

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Sara March 26, 2016 at 7:28 pm

Thanks for explaining this. Is the same explanation apply to regression and path analysis? Also, is there any article that discuss this and is it possible to share the citation with us?

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YJL October 8, 2015 at 10:45 am

Hello, i have a question regarding interaction term as well..
My main variables are Governance(higher the better) and FDI.
and dependent variable is Human Development Index
In my case, only FDi is significant and postive, but Governance is not significant.
The problem is interaction term. it is negatively correlated with HDI.
Does it mean i have to interpret that FDI alone has positive impact on HDI,
but when it is executed in countries with good governance, it has negative impact on HDI? For me, it doesn’t make sense…

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svetlana March 31, 2015 at 3:59 pm

Dear Karen,
Could you please explain to me the follow findings:
my dependent variable is the educational achievements of the native students.
my independent variables are – the proportion of the immigrants at the school and the average parental education of the immigrants students.
I built the interaction between these two variables – the interaction was significant and the positive but the main effects were non-significant . how can I explain the results.
thanks a lot.
Svetlana

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buru May 9, 2015 at 9:02 am

It means that the proportion of migrants is not associated with differences in the dependent variable. Similarly foe migrants’ parental education. However if in a school you have many migrants and and they have high parental education, than native students will be more educated.

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Jane February 3, 2015 at 4:28 am

As always, Karen, your explanation is clear and to-the-point!

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Karen February 6, 2015 at 5:10 pm

Thanks, Jane!

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Please note that Karen receives hundreds of comments at The Analysis Factor website each week. Since Karen is also busy teaching workshops, consulting with clients, and running a membership program, she seldom has time to respond to these comments anymore. If you have a question to which you need a timely response, please check out our low-cost monthly membership program, or sign-up for a quick question consultation.

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