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I'm trying to calculate a scaled odds ratio and convert them into percentages for an analysis I am doing.

I have just one independent variable in the model, SAT score. Dependent variable is college acceptance. The SAT score is in 1-point increments, so odds ratio calculated was for 1-point change.

However, I want to make this into something more interpretable in real life. The odds ratio for 1-point change in SAT score was 1.08.

How do I calculate the odds ratio for 10-point or 25-point increase in SAT score? My understanding is just raising OR to the power of the point increase, i.e. 1.08^10 and 1.08^25.

Can I convert the odds ratio into percent change in college acceptance for a 10 or 25-point increase in SAT score?

Thank you.

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How do I calculate the odds ratio for 10-point or 25-point increase in SAT score?

From your question, I assume you have the following logistic model: $$ \mathrm{logit}(\texttt{Acceptance})=\beta_0 + \beta_1\texttt{SAT_score} $$

The odds ratio for one unit increase in $\texttt{SAT_score}$ is $\exp(\beta_1)$, where $\beta_1$ is the coefficient for $\texttt{SAT_score}$ on the log-odds scale. The odds ratio for $u$ units increase in $\texttt{SAT_score}$ is $\exp(\beta_1\cdot u)$. So for $u=10$ or $u=25$, you have $\operatorname{OR}_{10}=\exp(10\beta_1)$ and $\operatorname{OR}_{25}=\exp(25\beta_1)$.

Can I convert the odds ratio into percent change in college acceptance for a 10 or 25-point increase in SAT score?

Not in general, no. Remember that the logistic regression fits a logistic curve on the probability scale which looks like this:

LogReg

You see that the probability increases by different amounts for a 1-unit increase, depending on where you start. In other words: The slope of the curve is different at all points. What you could say is something like this: "When the SAT score increases from 500 to 510, the probability of acceptance increases from 7% to 8.56%". In order to calculate this, simply predict the two probabilities for the different SAT scores based on the model. If you want to quantify the uncertainty of the difference of two predicted probabilities, see the answers to this post.

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