Hello Chiara,

There's no blanket answer for this; it depends on the variable(s) involved and the specific way in which the distribution departs from being normal. As a simple example, a transformation such as log(x) will not ameliorate a problem with negative skew.

You could always avoid the ordinary parametric version of the test and use bootstrap/resampling instead to determine whether the relevant effects were non-zero. Doing so allows you to avoid concerns about normality assumptions.

Good luck with your work.

Hi Chiara Fini

I suggest using the bestNormalize package, available CRAN. This package contains a suite of transformation-estimating functions that can be used to normalize virtually any data. The function of the same name attempts to find and execute the best of all potential normalizing transformations. In this package, they define “normalize” as in “to render data Gaussian”, rather than transform it to the 0-1 scale. Good luck!

Best transformation depends on the nature of the data. You can use this data transformation guide:

https://xdplot.blogspot.com/p/data-transformations-guidelines.html

One idea is to choose a different model that doesn't require normal residuals. For example, a generalized linear mixed model (glmm).

That being said... Transforming variables is often fruitful to get "better behaved" data, but adds some complications in interpretation, since the variable you're measuring is now some other thing. In some disciplines, certain transformations are common. For example, in water quality reasearch, it is common to use a log transformation, and readers can read results on e.g. "log nitrate concentration" without difficulty. Other transformations --- or using transformations in disciplines in which they are uncommon --- can lead to some convoluted results or confusion on the part of the reader.

One approach in transforming data that is often helpful is to convert the dependent variable to normal scores. That is, to use normal scores transformation. There are several closely-related varieties of this, and the calculation are relatively easy.

EDIT: I posted an example here, with the caveat that I wrote this: https://rcompanion.org/handbook/I_13.html

My R function described here (https://www.rdocumentation.org/packages/rcompanion/versions/2.3.26/topics/blom), calculates a few varieties: van der Waerden, Blom, Elfving, Rankit, Tukey.

For a quick demonstration of normal scores transformation, you can go to https://rdrr.io/snippets/ , and run the following code:

# # #

library(rcompanion)

Dependent = rlnorm(100,1,1)

hist(Dependent)

Elfving = blom(Dependent)

hist(Elfving)

# # #

You should get a log-normal histogram and a normal histogram.

Of course, forcing your dependent variable to be normally-distributed doesn't guarantee your residuals will turn out normal ---- or that the data is conditionally normal. It still depends on your model.

mahalanobis

Well knowing nothing else, I'd look at a Box-Cox transformation program. R has a super one. Best, David Booth

Thanks to all!

Please plot the pattern of data. What distribution is suitable for them (you can use software like EASYFIT). Now, search for transformation from the present distribution to Normal distribution.