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"achieve normality" is correct and usable in written English.
You can use it to describe the process of restoring balance and stability in a situation that had become chaotic or unhealthy. For example, "After months of hard work, the country was finally able to achieve normality in terms of its economy and political situation."
Exact(60)
In a few instances, data were non-normally distributed and simple transforms did not achieve normality.
For variables that were not normally distributed, we used a log transformation to achieve normality.
As SPD, CC16, and CRP were non-normally distributed, we log-transformed these values to achieve normality.
Logarithm and Box Cox transformation were applied to achieve normality.
Root biomass data required logarithmic transformation to achieve normality.
Statistical analyses performed Nutrient intake data were adjusted to achieve normality by using a power transformation.
Linear regression was used to analyse length of stay (log-transformed to achieve normality) as an outcome.
All variables were log-transformed to achieve normality.
Element concentrations were log-transformed to achieve normality.
This ratio was square root transformed to achieve normality.
The duration of encounter was log transformed to achieve normality and homoscedasticity.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com