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The phrase "a substantially higher participation" is correct and usable in written English.
It can be used when discussing levels of involvement or engagement that are significantly greater than a baseline or previous measurement.
Example: "The new marketing strategy resulted in a substantially higher participation rate among our target audience compared to last year."
Alternatives: "a significantly greater involvement" or "a markedly increased participation".
Exact(1)
Likewise in SCREEN, women show a substantially higher participation compared with men (Haidinger et al, 2009).
Similar(58)
Second, although substantially high participation rates among both eligible case and control subjects minimized potential selection bias, the use of cancer-free patients as controls, whose dietary habits may have differed from the general population due to health consciousness or disease concerns, might have lead to selection bias.
Or a substantially higher fine for littering.
There is a 10% threshold to enter parliament, which is a substantially higher bar compared with other countries.
Interest will usually be charged at a substantially higher rate - typically around 25%to3030% EAR - and so will the fees.
In keeping with the original agreement, the Port Authority would move its headquarters there, but pay a substantially higher rent.
Natives experience a substantially higher employment status persistence than immigrants.
The uninsured have a substantially higher probability of dying (about 42% higher, compared to the insured).
This is a substantially higher than our estimation of 280 patients.
The overall results showed that their proposed method attained a substantially higher degree of efficacy.
In all horizons, AC, compared to WDC, has a substantially higher specific surface.
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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