# Logistic regression with independent variable values less than 1

I have one independent variable which has values less than 1, and want to see how the odds of having a disease change when the independent variable increase by 0.1. I ran a binary logistic regression to predict an outcome (disease vs healthy) and as expected it turned out odds ratio had a crazy high value and confidence intervals. Therefore I took the 10th root of odds ratio and CI and now odds are interpretable, however, I don't know if what I did makes sense at all from a mathematical standpoint...

• I don't see how being less than 1 is a big deal for a predictor (I won't willingly use outdated terminology "independent variable"). Perhaps all you need is a change of units of measurement. 10th root doesn't sound helpful and I don't know why or how that would make results interpretable. I suggest that you show data and/or output from your software. – Nick Cox Jun 21 '18 at 8:44
• In practice, the predictor is always less than 1, it's the norm. FYI I get statistically significant difference between the two groups and a fair effect size ( cliff's delta 0.7, where a two completely separated distributions have delta =1 and complete overlap is 0). Also, I saw an example online where they were using time in seconds and minutes as predictor. To interpret the odds of having a disease for one extra minute of excercise they exponentiated the odds to the 60th power. – frada Jun 21 '18 at 9:21
• Sorry, but I don't think that's made your question clearer. – Nick Cox Jun 21 '18 at 10:24
• If you have as implied just one predictor you should be able to show us (a sample of) your data and certainly software output. – Nick Cox Jun 21 '18 at 10:34
• I'll try my best: I have a set (n=32) of values for a predictor ranging from 0.342 to 0.827 arbitrary units. I have 2 groups (disease vs control) whose medians of said predictor are significantly different. I want to test its predictive ability so I run a binary logistic regression. Odds ratio come out extremely high (thousands). So I want to see how much a change of 0.1(instead of 1) in the predictor value increase/decrease the odds of disease. If I take the 10th root of the odds then I have real-world odds ratio i.e 5 (CI 2-15). The problem is I don't know if this is sound mathematically... – frada Jun 21 '18 at 10:37