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The phrase 'by analysis' is correct and usable in written English.
It can be used when you are making a comparison of something or when you are offering an analysis of something. For example, "By analysis, the most efficient solution to this problem is to use a combination of both methods."
Exact(58)
Paralysis by analysis.
Golf has taken 'paralysis by analysis' to a whole new level".
Perhaps he is afraid of jinxing himself with paralysis by analysis.
"If you get paralysis by analysis you can come unstuck because rugby is a human game.
Hem tends toward paralysis by analysis; Haw dithers but eventually gets at things.
But what worries Foss Hansen more is what he calls "paralysis by analysis".
The scale of the mountain to climb is underlined by analysis from the Pew Research Center.
The shutdown is fueled more by anger than by analysis.
Like Marcel in Proust's masterpiece, she says, she feels that her life "needs redeeming by analysis and reflection".
Similar(2)
I don't know why they opted for [this] drive-by analysis".
Now, honestly, is this worth anything other than a quick drive-by-analysis?
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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