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The phrase "a much smaller effect" is correct and usable in written English.
It can be used when comparing the magnitude of effects in a context, indicating that one effect is significantly less than another.
Example: "The new policy had a much smaller effect on employee productivity than anticipated."
Alternatives: "a significantly lesser impact" or "a considerably reduced effect."
Exact(59)
By contrast, changes in stock-market wealth have a much smaller effect on spending.
The paper finds a large negative effect of spending cuts under such circumstances, a much smaller effect of tax hikes.
If it works, it should ensure that big orders have a much smaller effect on prices than they do on trading floors.
Even if we ignore the savings from worthy investments in roads and bridges, additional government spending has a much smaller effect on deficits than is commonly assumed.
For the top 1%, the discontinuities in the data have a much smaller effect, leading to a 10 percentage-point drop in total (most of which is accounted for by the difference between series (d) and series (f).
The two new trials sponsored by Roche for this purpose showed a much smaller effect of the drug, so small, that the committee voted 13-0 thet the studies did not confirm the initial benefit.
figures show that while raising taxes (on everybody) amounts to about two-thirds of the total deficit reduction in 2013, it has a much smaller effect on gross domestic product, the measurement for output.
An E.P.A. analysis of the proposed rules projects a much smaller effect, ranging from as few as 600 jobs lost to 1,300 jobs actually added in companies that make cleaner equipment.
Filters deposited without the spheres showed a much smaller effect.
With regard to the late warnings a much smaller effect was found.
However, this combination showed a much smaller effect on P. aeruginosa and S. flexneri.
More suggestions(17)
a substantially smaller effect
a much lower effect
a considerably smaller effect
a much lesser effect
a much faster effect
a much less effect
a much smaller exposure
a much earlier effect
a much smaller impact
a much wider effect
a much smaller effective
a much weaker effect
a much smaller part
a much smaller drop
a much smaller difference
a much smaller station
a much smaller role
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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