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The phrase "lower degree of" is correct and usable in written English.
It is typically used to compare the level or amount of something with others, indicating that it is less than the others. Example: "The lower degree of rainfall in this region has caused severe drought and crop failures."
Exact(59)
We consequently accord it a "lower degree of protection than more traditional literary works". Id.
The Swedish tax system, by contrast, had a lower degree of progressiveness, but generated higher relative tax revenue.
Leghorns, selected for larger and higher egg numbers, have a lower degree of CFL compared with junglefowl (wild type).
Cold storage was also associated with a lower degree of granulocyte activation measured by the expression of CD11b (Fig. 1c).
The smaller the sensitivity entropy is, the lower degree of dispersion of uncertainty sources will be.
However, the N37T↑V variant protease displayed a lower degree of anti-correlation.
However, the realized volatility measures based on daily data exhibit lower degree of long-range dependence.
For the turbine design, lower degree of reaction is beneficial for turbine efficiency gains.
The lower double bond density led to a lower degree of polymer chain alignment.
Using of EDC resulted in lower degree of crosslinking, but better hydration properties.
Similar(1)
For female households, those arriving as teenagers exhibit a lower degree of specialization if intermarried.
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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