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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?

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  • $\begingroup$ How are the variables measured? What are the scales? $\endgroup$
    – Tim
    Dec 4, 2014 at 9:42
  • $\begingroup$ I have three different cases: first case, all variables are continuous (on different scales); second case, they are all ordinal (on different scales); third case, one is continuous and the other two are ordinal (on different scales). Way of measuring is reliable, I'm not worried about that in this case. $\endgroup$ Dec 4, 2014 at 9:47

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There are some problematic assumptions you seem to be making: - you rarely know population parameters, but those are not necessary to standardize. You can standardize based on your sample. - why would you calculate percentiles and what makes you think you can just sum them? If you are just interested in rank that may be appropriate but you don't give us enough to go on there. - why do you want to some separate measures? You must be trying to get at an underlying construct or create an index of some sort. Creating a single scale from different scales is a problem that an entire field of statistics addresses (psychometrics). I would recommend taking a look at some basic text book references on the topic.

I don't mean to sound harsh but you should probably provide some more details so we can provide more guidance.

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    $\begingroup$ Thanks Robin and excuse me if I'm a nub on the topic. I'm interested in percentiles, since what matters in my study are ranks and not absolute values. I'm thinking of summing variables since when they standalone they have no real meaning, but when you consider them all together they have it. It's like if you try to predict how often will you brush your teeths and you consider the availability of toothbrush and toothpaste separately.As for the population parameters I saw they were necessary from here.What the alternative? $\endgroup$ Dec 3, 2014 at 14:29
  • $\begingroup$ can you provide details on the question you are analyzing and the variables of interest? The example you give - why would you add up toothpaste and toothbrush availability? Only if you think they somehow measure the same thing, in which case you can test that with a reliability coefficient or look at their correlation. $\endgroup$ Dec 3, 2014 at 17:36
  • $\begingroup$ Following your comment and answer I updated my question with the very best hope to be more specific. $\endgroup$ Dec 4, 2014 at 9:39

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