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The phrase "theory against" is correct and can be used in written English.
It is typically used to indicate a contrast or conflict between two opposing theories or ideas. Here is an example sentence: "The debate between creationism and evolution is a classic example of theory against theory, with each side presenting compelling evidence to support their beliefs."
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Test your theory against the data, and see how it stacks up.
The problems of computation, and of testing theory against experiment, then become enormous.
Thanks to the new schedule, the Rangers have to test the theory against the Islanders only six times this season.
Testing the theory against academic results, they found the most significant design factor appeared to be how well the school allowed pupils to flow through it.
Before resigning ourselves to a similar spell of disillusioned sleeplessness, it might be instructive to test this theory against a particular case of philanthropy.
Firm-specific shocks do matter.Mr Gabaix tests this new "granular" theory against data for the largest 100 American firms between 1951 and 2008.
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Mr. Modigliani, who persisted in testing theories against experience, doubted this.
It's the standard: anti-Western, anti-Israeli, conspiracy theories against Islam".
Who is pushing the biggest conspiracy theories against Clinton during this campaign?
Most empirical exercises confront theory with numbers they test theories against the data; sometimes they even reject them.
On July 1, the Democrats got wind that the government planned to broadcast conspiracy theories against the opposition.
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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