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The phrase "a substantially higher rate" is correct and usable in written English.
It can be used when comparing rates, such as interest rates, prices, or statistics, indicating that one rate is significantly greater than another.
Example: "The new policy resulted in a substantially higher rate of customer satisfaction compared to the previous year."
Alternatives: "a significantly greater rate" or "a markedly higher rate".
Exact(30)
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.
Similar(30)
ESPN's heavily promoted live airing of Tiger Woods's first tee shot at the Masters Thursday at 1 42 p.m. Eastern generated a substantially higher rating for "Sports Center than it usually gets in that part of the afternoon.
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.
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.
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.
More suggestions(19)
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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