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If the data is between (0,1) because of some kind of vector normalization to get rid of background noise, is it still OK to do log transformation to improve normality? Or we have to do logit transformation? We are going to do discriminant analysis such as PCA or LDA, which have normality assumption as far as I know.

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    $\begingroup$ Normalization to scale data w/I (0,1) won’t get rid of background noise. $\endgroup$ Oct 31, 2014 at 2:30

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To determine if a given transformation improves normality, you should make some kind of test of normality, such as a Q-Q plot or Shapiro–Wilk test.

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It's not really of tremendous importance, but there are a number of functions that transform data from a 0, 1 range to a -Inf, Inf range for the purposes of cogency alone. Examples are complementary log-log transformations, Fisher z-transformations, logit, and probit transformations. Unmotivated by the nature of a specific scientific question, it doesn't really make sense to apply any of these transformations out-of-context.

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  • $\begingroup$ Thank you. For the normality assumption, does the distribution need to be from -inf to +inf? If the data is restricted within (0,1), is it still possible to pass the normality test? And if we could not found a good transformation, is logistic regression a better choice? $\endgroup$
    – shu
    Nov 2, 2014 at 0:14
  • $\begingroup$ No not at all! Consider the large sample approximation to the sample proportion. Proportions are distinctly bounded from 0 to 1 but these normal approximations subsume a negligibly small range beyond those values. $\endgroup$
    – AdamO
    Nov 2, 2014 at 15:42

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