I am working on some logistical regression models currently. I understand the interpretation of Odds Ratios, however a friend of mine has suggested standardising the continuous variable in my model. Which is fine, however, I am not sure how to interpret an odds ratio between a standardized continuous variable, and a categorical variable (dropout in this case).

Like what does that number, ratio, actually mean!?

Lets say I have a continuous variable (standardized) that represents a 'self-control' trait personality measure. Dropout is represented as 0 dropout, 1 complete. 'Self-control' significantly predicts dropout with an odds ratio of 1.5. So how would I interpret that? Higher self-control is predictive of completion rather than dropout. However, I want to understand, what, mathematically, that number, 1.5, means with a standardized scale?

Any help would be much appreciated.

Best,

A