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The phrase "a substantially high rate" is correct and usable in written English.
It can be used when discussing a rate that is significantly elevated compared to a standard or average level.
Example: "The company reported a substantially high rate of customer satisfaction this quarter, exceeding all previous records."
Alternatives: "a significantly high rate" or "an exceptionally high rate".
Exact(5)
However, in the current study, injecting drug users reported a substantially high rate 80% of participants reported experiencing childhood trauma.
Our experiments strongly suggest that pre-copulatory sexual cannibalism occurs at a substantially high rate in natural populations of L. tarantula, and that this behaviour is an evolved female adaptation to a limited supply of high-quality prey.
The ACL has long been thought to have poor healing capacity, with a substantially high rate of failure (40% to 100%), even after surgical repair using suture.
If the sporadic GC42 distribution resulted from multiple independent losses, one should expect a negligibly low rate of GC42 gain but a substantially high rate of GC42 loss.
In most regions, approximately 60 70% of women reported use of at least one OTC medication during the course of their pregnancies, mostly for pain conditions, heartburn and upper airways disorders, indicating a substantially high rate of self-medication during pregnancy.
Similar(55)
Divergence in the nuclear genome is lower but still substantial, likely reflecting a substantially higher rate of mutation for the mtDNA [ 22].
Graduates with scientific training are employed at a substantially higher rate than the national average.
Interest will usually be charged at a substantially higher rate - typically around 25%to3030% EAR - and so will the fees.
In fact, research suggests that people with associate's degrees don't hold jobs, or earn more money, at a substantially higher rate than high-school graduates.
Segments within the retail industry have a substantially higher rate of work-related fatality due to workplace violence compared to the retail industry overall.
"It's no surprise I think to most Australians that children who are in immigration detention have a substantially higher rate of things like mental illness, failure to thrive – which is a medical term – and depression.
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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