# Three-way interaction: slope difference test if simple slope is insignificant

I am currently conducting a three-way interaction (linear OLS regression) with three continuous variables. My dependent variable is also continuous.

The three-way interaction term is significant (yes, I added all lower order terms).

To evaluate the three-way interaction more carefully I calculated simple slopes for each regression line (is the slope significantly different form zero?) and slope difference tests (is the difference between two slopes significant?).

One slope difference test is of particular importance to me. It is the slope difference test between:

• regression line 1) simple slope test is insignificant because the gradient is around 0

and

• regression line 2) simple slope test is significant because it has a strong negative gradient

The slope difference test is significant.

My question now is: Am I "allowed" to interpret this slope difference test although regression line 1) has an insignificant simple slope test? My guess is yes, because these tests answer two different questions. But I am not sure, hence my question.