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The phrase "a much higher influence" is correct and usable in written English.
It can be used when discussing the degree of impact or effect that something has compared to another.
Example: "The new policy has a much higher influence on employee productivity than the previous one."
Alternatives: "a significantly greater impact" or "a far stronger effect".
Exact(1)
With the expected shift towards steerable antennas with medium or high gain, the antenna pattern has a much higher influence on the effective channel between the transmitter and receiver.
Similar(59)
Circulation dynamics within the lagoon would also be altered, and there would potentially be a much higher oceanic influence (e.g. nutrients, temperature, plankton, etc).
To see the influence at a much higher permittivity value, we replot the PBG diagram for silicon.
On the other hand, the surface roughness of wood is influenced to a much higher degree by environmental factors such as temperature, humidity etc. than a metallic structural material like aluminum.
This might provide an alternate explanation for why viruses are capable of evolving to a much higher mutation rate [ 48] under the influence of the responding rate of immune systems [ 49].
Introduction of prostate-specific antigen (PSA) testing in some countries has exacerbated this problem, leading to a much higher reported incidence rate, but having little influence on mortality rates (Evans and Møller, 2003).
Although this farm had a much higher proportion (7/15) of positive flocks than predicted (2.5/15), it did not have undue influence on the models.
Quite surprisingly, the former showed a negligible influence of thermal changes on nitrification rates, while the latter showed a much higher dependence.
HRP has a much higher turnover rate then GOx, so the distance hydrogen peroxide must diffuse has a crucial influence on the rate of reaction.
"Restaurants have a much higher failure rate".
There was a much higher default rate.
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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