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The phrase "a much larger effect" is correct and usable in written English.
It can be used when comparing the magnitude of an effect to another, indicating that it is significantly greater.
Example: "The new policy had a much larger effect on employee productivity than we initially anticipated."
Alternatives: "a significantly greater impact" or "a far more substantial effect".
Exact(59)
Varying the earnings effect over its estimated 95% CIs had a much larger effect on the incremental cost-effectiveness ratio ($45,746 to $27,921) than varying the missed work effect over its 95% CI ($38,136, $35,421).
Instead, cognitive ability, as measured by participants' Graduate Management Aptitude Test (GMAT) scores, had a much larger effect on outcomes.
They're going to have a much larger effect on the shape of the posterior distribution on its density.
Scratches on notched samples exhibited a much larger effect, reducing fatigue life by an order of magnitude.
"He showed you can have a much larger effect than by going to a self-appointed Christian conservative leader," Mr. Brinson said.
Since then, the view that incremental changes in a cause can suddenly produce a much larger effect has entered common currency.
However, the actual substance of the policy message — whether it was cooperative or uncooperative — had a much larger effect on Japanese perceptions.
For large population size, our overlapping-generations model predicts a much larger effect of population size than Henrich's discrete-generations model.
For example, penis size has a much larger effect on attractiveness for taller men, than it does for shorter men," Dr Mautz said.
The choice of the carbon precursor had a much larger effect on the IG/ID ratio of the synthesized CNT fibers than the other operating variables.
This study supports the idea that a river flood has a much larger effect in time and space than what is occurring within the channel.
More suggestions(16)
a much higher effect
a substantially larger effect
a much broader effect
a significantly larger effect
a far larger effect
a much earlier effect
a much bigger effect
a much wider effect
a much better effect
a much larger impact
a considerable larger effect
a much larger productivity
a much larger whole
a much larger problem
a much larger view
a much larger operation
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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