I need to sum some variables that are on different scales to make a new one. I'm wondering If it's correct to calculate the percentile scores first, and then to sum them up.
Imagine I have to measure general beauty and I have three variables: beauty of the hair, beauty of the face and beauty of the body. You could have a beautiful face and hair, but if you have an ugly body then you won't be considered beautiful (this is why I need to consider all the variables together and not just one by one separately). Also, you'll be perceived as beautiful if you are the most beautiful person among all the acquaintances of a specific group of people. Suppose they don't know anybody else except you and the other people in the group. Accordingly, no matter if someone more beautiful than you is in another group. This is why I'd like to use percentiles, instead of raw scores.
The three variables do not correlate. What if they do? Would things be different?