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The phrase "are arbitrarily categorized" is correct and usable in written English.
It can be used when discussing how items, concepts, or data are grouped without a specific or logical basis.
Example: "In this study, various species are arbitrarily categorized based on superficial traits rather than genetic relationships."
Alternatives: "are randomly classified" or "are subjectively grouped".
Dictionary
are arbitrarily categorized
adverb
In an arbitrary manner.
Exact(1)
Tajfel described "in-group bias", and showed, through a set of pioneering experiments, that humans tend to favor in-group members over out-group members in the distribution of rewards, even when these groups are arbitrarily categorized [ 14].
Similar(59)
Based on the 5-question MIDAS rating, participants were arbitrarily categorized into a 'low' disability group if they had a MIDAS rating of 0 10 and into a 'high' disability group if they had a MIDAS rating greater than 11 [36, 37] 37].
A1C results were arbitrarily categorized as optimal (<6.1%: the referent value), good (6.1 6.9%), moderate (7.0 7.9%), and poor (≥8.0%) glycemic control.
Outcome assessment was based on quantitative CRP concentrations measured at sequential time-points after surgery.> The degree of operative trauma was arbitrarily categorized into three types of surgery.
Cells were arbitrarily categorized into punctate LC3+ and LC3- groups (as guidance, LC3 punctation induced by amino-acid starvation was used as a positive control).
According to RLU/CO values, HPV-DNA positive cases were arbitrarily categorized into three groups having "low viral load" (RLU/CO from 1.0 to 50.0 RLU/CO), "intermediate viral load" (RLU/CO from 50.1 to 100.00 RLU/CO), and "high viral load" (RLU/CO > 100).
The M. genitalium concentration detected was expressed as number of geq [log10] per 1 mL of transport media and the M. genitalium load in each specimen was arbitrarily categorized as low (≤4 geq/mL [log10]), moderate (>4 - <6 geq/mL [log10]) or high (≥6 geq/mL [log10]).
They are arbitrarily selected and easily dismissed.
Riders are arbitrarily paired by John Chapman, promoter.
People who are arbitrarily using it need to be cautious.
Spectra are arbitrarily shifted.
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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