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"a useful criterion" is correct and can be used in written English.
You can use this phrase when you are referring to a measure or standard that is used to judge or compare something. For example: When selecting a new candidate for the job, we used past experience as a useful criterion.
Exact(44)
It has been suggested that the 95% connection limit under statistical parsimony, which is commonly used in phylogeographic studies, is a useful criterion for indicating biological species boundaries [ 52].
This cutoff level is considered a useful criterion to establish gingivitis and is used as a basic principle in the standard practice of periodontal care.
But the commitment of the self to transcendent ideals has again become a useful criterion of value.
Mr. Botstein of Bard (No. 39 on the liberal arts list) agreed that alumni giving was not a useful criterion.
Though proper motions of the clusters are very small, those for individual stars provide a useful criterion for cluster membership.
In this section, we establish a useful criterion for the interior of a solid cone.
Similar(16)
This list can help you generate ideas about potential roles and organisations that could be a good fit, as well as providing a useful criteria to help you narrow down your list.
The central aim of this exposition is to find a useful criteria for the inductive limit state B→λtB canonically associated with ψ to be pure.
Similarity groups for A. hypogaea accessions were established, which is a useful criteria for selecting parental plants for crop improvement.
Since additive genetic correlations between predicted and measured melting rates were higher than 0.89, we concluded that NIRS is a useful criteria to select MR in breeding programs.
It is shown that the equality of stage discharge temperatures is a more useful criterion than the saving in power or improvement in COP because multi-staging has at best a marginal (<10%) effect on the latter.
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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