You can transform risk scores by using Box-cox transformation techniques.

Please refer to this article: 6.5.2. What do we do when data are non-normal (nist.gov)

A reference to how to do it in python: Transforming Non-Normal Distribution to Normal Distribution | Pythonic Excursions (aegis4048.github.io)

however, there are many other data transformation techniques.

It would help to explain how the score is constructed and to see a histogram, denosty plot and/or and ecdf plot of the data. Without understanding how the score is constructed it is impossible to ge any valuable advice if a transformation would make sense at all and what kind of transformation would be most appropriate.

PS: normal distribution allows negative values, so the fact that there are negative values ihas nothing to do with the question if the normal distribution model may be adequate/useful. Actually, the normal diostribution assumption is often not adequate when the values are strictly positive (becauce, as I said, the normal distribution allows negative values - and when such values are impossible, the normal distribution model should be in doubt).

Laxman Singh Bisht Thank you for the reply!

Since my database included negative numbers, I added the absolute of the most negative number, which is -4.5, to all the values. In that case, my values got 0 and positive. And then I did Box-cox transformation on them. After I checked the normality with Shapiro-Wilk Test, ERS variable got normally distributed.

However, I am not sure whether it is valid to play with the data like that since we want to publish an article with ERS data??

Jochen Wilhelm Thank you for the reply!

Actually, my Professor asked me to find a way to make the current data more normally distributed to do regression analysis in twin data. And, since there are negative values in the data, I believe it is not possible to transform the data. That's why I am looking for a way to apply a suitable transformation.