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The phrase "dramatically by" is grammatically correct and can be used in written English
It is typically used to describe something that changes or happens in a dramatic or sudden manner, with the word "by" indicating the cause or means of that change. Example: The company's profits increased dramatically by implementing new marketing strategies.
Exact(60)
HPV vaccination rates vary dramatically by state.
The murder rate varies dramatically by group.
But this picture was contradicted dramatically by his ex-girlfriend.
All three lessons were reinforced dramatically by what happened next.
It was used most dramatically by the Russian generals M.B.
He then recited the poem dramatically, by heart.
A Cancer Research UK report shows that deaths are "set to fall dramatically" by 2030.
The political landscape was changed dramatically by last November's China-US emissions deal.
You might make this point pedagogically, and dramatically, by using a fill-in-the-blank method.
The black-white gap, he pointed out, differs dramatically by age.
8.09pm: And there she is! Julie stands dramatically by the graveside.
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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