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The phrase "criterion for determining" is correct and commonly used in written English.
It is typically used to introduce a standard or guideline that is used to make decisions or come to a conclusion. Example: The main criterion for determining the success of our project will be the overall satisfaction of our clients.
Exact(60)
To complicate the matter further, Britain is insisting on a different criterion for determining the budget.
Spicule morphology has been the primary criterion for determining hexactinellid systematic groupings.
In 1986, Israel's chief rabbinate — two Orthodox rabbis elected by peers — endorsed it as a criterion for determining death.
Is there any clear, objective criterion for determining which conversations are only appropriate to have in person?
Obviously "fairness" would have been defined differently if The Times's criterion for determining fairness was based on provocation or lack thereof.
Some have argued that ballots should not be manually counted because there is no objective criterion for determining the effects of human error.
An ideal language was thus seen as the necessary criterion for determining the meaning, or meaninglessness, of statements about the world.
FHOYLE has suggested (Mon. Not. Roy. Astro. Soc., 107, 4 ; 1948) a criterion for determining the degree of condensation of interstellar material into stars.
Also derived is a dimensionless criterion for determining whether the pellets are partially covered by liquid.
Uniform vibration amplitude of the output surface is an important criterion for determining quality.
The criterion for determining whether there is substantial similarity is whether an ordinary lay observer would detect a substantial similarity between the works.
More suggestions(15)
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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