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The phrase "criteria were established" is grammatically correct and can be used in written English.
Example: In order to be considered for the job, a set of strict criteria were established by the hiring committee.
Exact(60)
All these criteria were established prior to data collection.
The PCM selection criteria were established.
These cutoff criteria were established to minimize computational requirements, as several of the genome assemblies were relatively fragmented.
Acceptable criteria were established with a case study of a 609.6 mm (24 in).
After criteria were established, database searches and hand searches of selected peer-reviewed journals were conducted.
A priori criteria were established to guide the revision of subscales.
Specific inclusion and exclusion criteria were established to identify articles about studies that qualified as RCTs.
To avoid possible biases, both experiments kept the small mass interval that includes both the and B0 signals blind until all selection criteria were established.
I undertook this task after much thought and prayer, and only after specific criteria were established defining the powers and goals of the commission.
General methodology was then applied on two examples: cities Belgrade and Ljubljana, and resulting criteria were established for both.
Additionally, system suitability criteria were established to assure that the assay consistently performs as it was intended.
More suggestions(16)
standards were established
criteria were tested
criteria were acknowledged
thresholds were established
criteria were prescribed
criteria were stated
qualifications were established
criteria were incorporated
criteria were organized
needs were established
guidelines were established
rules were established
criteria were formalized
approaches were established
benchmarks were established
criteria were maintained
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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