# Split v. Interaction Significance

I have a question about splitting the sample versus interacting a variable. My understanding is that if you split the sample and then conduct an analysis you are essentially interacting each independent variable.

I have split my sample based on a a dummy variable. My results are the following:

              Model 1 (Split Var=0)      Model 2 (Split Var=1)
X1         0.614*                    -0.073
(0.304)                   (0.487)
Constant  -2.896*                    -3.589*
(0.820)                   (1.019)


However, when, I estimate a model with an interaction term the results are the following:

    x1               0.614*
(0.304)
Split Var       -0.714
(1.273)
X1* Split Var   -0.682
(0.574)
Constant        -2.896*
(0.820)


I am surprised by two things. 1) the interaction variable is insignificant. If in the split sample the x1 variable is significant, shouldn't the interaction variable be significant? 2) the coefficient for the main effect (x1) is identical to the coefficient in model 1 for variable x1.

How would you interpret the results? Is this not a conditional relationship? Does the effect of x1 not vary by the split var?

• How have you coded your variables? In response to your second surprising finding, if you've used dummy coding then that may explain why the coefficients are the same in both models. For your second surprising finding, I don't have any links to hand but there are likely several questions on here addressing just that point. You may also want to read around the "interaction fallacy". Jul 20, 2016 at 8:03

## 1 Answer

The coefficient for $x1$ in both models is the same because of the way you coded the dummy variables. It is the slope for $x1$ in the first group. The coefficient for the constant is identical too. The the coefficient for $split$ is the difference in intercepts and the coefficient for the interaction is the extra slope in the second group. Try adding the relevant ones together and you can reconcile what you got.