# What does it mean when a variable is significant as a binary variable but not as an ordinal variable?

Let's say I am running Cox proportional regression model for a variable with 4 levels (strongly agree, agree, disagree, strongly disagree). When I code it as an ordinal variable with these 4 categories, it is an insignificant contributor. However, if I make this variable binary (agree vs disagree), it is significant. Is this still appropriate? When is it okay to convert an ordinal to a binary variable? How do I go about interpreting this result? Thank you!

• Please, can you elaborate on how this ordinal variable is coded (e.g., 0,1,2,3) and which software you use.
– Alex
Oct 5, 2022 at 0:30
• I am using SPSS, and it is coded as you describe (0, 1, 2, 3) with each number indicating a specific category. If it were binary it would just be 0 and 1 Oct 5, 2022 at 0:58
• I think the issue here is that if the variable is purely numeric, as you confirmed, and the model assumes that the "distances" between 0 and 1, 1 and 2, 2 and 3 are equal, and the coefficient reflects that one step. But in real life the "distances" can be unequal and the model less linear, so the linear model's bad fitting leads to statistical non-significance. If you omit this assumption that the variable is ordinal/ordered and use it just as a non-ordered categorical variable, you may try to get individual hazard ratio coefficients and see how these four categories relate to each other.
– Alex
Oct 5, 2022 at 11:59
• How to code this in R was described in this question. For SPSS, I unfortunately cannot advise :-(
– Alex
Oct 5, 2022 at 11:59
• A plot would go a long way to understand what's going on with your data. Oct 5, 2022 at 17:23