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The phrase "as arbitrary units" is correct and usable in written English.
It can be used when discussing measurements or values that are not standardized and are instead defined for a specific context or purpose.
Example: "The results were reported in terms of temperature changes measured as arbitrary units, making direct comparison difficult."
Alternatives: "in non-standard units" or "in relative units".
Exact(60)
Fluorescence expressed as arbitrary units.
Results are presented as arbitrary units of densitometric sum red.
Activity was expressed as arbitrary units per milligram protein.
MMP activity was quantified using a laser densitometer and expressed as arbitrary units (au).
The pain area was digitized and expressed as arbitrary units (Sigma scan Pro 4.01.003) [12]12].
Band intensities were normalized by β-actin expression and expressed as arbitrary units.
Data were expressed as arbitrary units.
All proteins were expressed as arbitrary units (AU).
The resultant value was expressed as arbitrary units.
The fluorescence intensities were expressed as arbitrary units.
Enzymatic activity is expressed as arbitrary units of relative value.
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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