For the sake of this example, let’s say that the OR is 1.08. I can argue that for each extra exposure on scale X, the respondents are 8% more likely to do Y. So far, so good.

The average score on the X scale is 7. I originally considered that somebody with an average score on the X scale (7) was 56% more likely to do Y (7 x 8%) than somebody with a 0 score on the X scale. However, I have been told that this is incorrect – that the correct calculation is 1.08 to the power of 7 (= 1.71), or in other words that they are 71% more likely to do Y if they have an average score on X compared to somebody who has a 0 score on X.

Cam anybody confirm (1) that this is correct and (2) provide a good reference for this?

Thanks!