The best way to try and secure normality is by removing outliers and looking for missing data. I have a YouTube video on this that might be helpful.

https://www.youtube.com/watch?v=nm4a9bMOoEE&t=443s&ab_channel=Dr.S.RamaGokulaKrishnan

In case the data is not normally distributed even after removing the outliers, you could opt for non-parametric tests such as Kruskal-Wallis test. I have two papers where I have used this test that might be useful.

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What statistical analysis do you want to do, and why do you think that the percentages need to be normally distributed? Thanks for clarifying.

As Bruce said, you don't need a normal distribution to do a statistical analysis. Not every statistical analysis requires a normal distribution.

If you know the counts behind the proportions you might consider a binomial model. If the proportions are continuous (not based on counts), a model based on a beta-distribution or a quasi-binomial model might be appropriate.

If this is all too far from what you know or understand you may have a look at the logit-transformation.

You know the persentage dont need normality، and still you want to transform it!

It always amuses me that someone will tell you how to do something rather than warn you that in doing so you are doing something unnecessary and – if you omit outliers – something that falsifies your results!

Can I ask you why you feel that your data should be transformed? This might elicit some more directly useful answers.

Ronán Michael Conroy , then RG must be a very amusing place for you to be :)

If percentages are about 5%-30% (or 70%-95%) --> logit transformation

If percentages are about Poisson

If percentages are about 30%-70% --> no need for transformation

The trouble with the answers of Seyyed Amir Yasin Ahmadi and s. Rama Gokula Krishnan is that they are blind to two pieces of information that are critically important :

1. We don't know the data generation process. There are so many processes, univariate and multivariate, that can result in data expressed as percentages that I can't even begin to enumerate them. But without knowing what the process is we cannot begin to decide whether a transformation is needed and, if so, what it is.

2. We do not know the research question. There is no point in transforming a variable if this loses your ability to calculate a meaningful measure of effect size, for example. On the other hand, some measures of effect size are better expressed in log units.

Can I elevate this to the status of a general rule of data anallysis?

Do not ask "how do I do this" before you have answered the question of "Is this what I should do?"