# Why does changing how I code my dummy variable change significance?

I have data where my dependent variable is a binary choice (Option A or Option B). I have two predictors: time pressure (pressure or no pressure) and alpha score (continuous).

I am examining whether pressure and alpha score interact to affect choice.

When I code time pressure with a dummy variable where pressure = 1 and no pressure = 0, alpha score is a highly significant predictor: However, when I change how I arbitrarily coded this dummy variable and instead set it so pressure = 0 and no pressure = 1, this changes the significance of alpha score (not to mention some of my coefficients): And yet, the interaction and the dummy variable are not changing (only changing in sign).

What is causing these changes?

And, in light of this, what is the most appropriate way to write up/interpret these results?

Thank you so much for any help you can offer!

If it's important, the distribution of alpha score is not different across conditions, and I have 409 participants in the time pressure condition and 407 participants in the no time pressure condition.

## 1 Answer

It usually makes no sense to interpret main effects in the presence of an interaction involving that variable because the main effects each have the meaning of being the difference in mean (or log-odds in a logistic regression) of the response when the other variable is at its reference level (or at zero if it is numeric). When you change the coding, you change the reference level and therefore you change the estimates. So the models are actually the same, they are just parameterised differently. Since the models are the same, but the parameters have different meanings, their statistical significance must differ too.

Edit: In your example, the intercept is the log-odds of the response when both variables are at their reference level (or zero if they are coded as numeric). In your first model with no pressure coded as 0, this is 0.37. In the model with pressure coded as 0 it is 1.28, a difference of 0.91 so this the contribution of pressure to the log-odds of the response when the other variable is 0. Now note that this is exactly the main effect of no_pressure in model 1, confirming the above interpretation of the main effect in the presence of an interaction. This analysis can be readily extended to the other main effect and the interaction.