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I'm trying to normalize some of the variables (biological parameters) from my dataset (some are positively, some are negatively skewed). As I was more familiar with, I used log or square root transformation. However, even after performing these transformations, I hadn't succeeded in normalizing all of these variables. Now I have some questions:

  1. Is it correct to use a Box-Cox transformation for all the variables?
  2. How can I report the Box-Cox transformed data (I need this transformation for performing multiple linear regression and Cox regression)? For example, when using log transformation I used to report the increase in 1 SD for the transformed variable in the Cox analysis
  3. Hypothetically, is it correct to use in a linear regression analysis data that are transformed by different methods (log, square root, log of the reflected data)?

Thank you

Nick Cox
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Dimitrie
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    By 'normalize' do you mean "transform a variable to appear close to normal"? If so, why would you do that? – Glen_b Nov 10 '14 at 18:28
  • Transform a variable so that it has a normal distribution. So that I can use it (them) in different regression analyses. – Dimitrie Nov 10 '14 at 18:58
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    Not even marginal normality is required for regression, as is addressed in many, many threads here. There can be no objection to using different transformations (including none at all) in a project provided that those transformations lead to improved analyses. In regression the most important changes that transformation might make are to improve linearity. – Nick Cox Nov 10 '14 at 19:31
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    In statistics, variables are not "parameters", whatever the jargon in your branch of science. – Nick Cox Nov 10 '14 at 19:32
  • First of all, thank you for these ascertainments. Second, as I mentioned in my first post, my final objective is to use the transformed variables in a multiple linear and also in a Cox regression. I'm not a statistician, so my reasoning could be wrong. That's why I asked these questions here. – Dimitrie Nov 10 '14 at 20:00
  • Searching our site for [regression transform independent variable](http://stats.stackexchange.com/search?q=regression+transform+independent+variable) produces many good links. I chose the first of these as a duplicate, understanding that although it does not address all your questions, it and some of the remaining search hits will cover the bases. – whuber Nov 10 '14 at 21:06

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